Digital Fountain Codes System Model and Performance over AWGN and Rayleigh Fading Channels
|
|
- Pearl Pitts
- 6 years ago
- Views:
Transcription
1 Digital Fountain Codes System Model and Performance over AWGN and Rayleigh Fading Channels Weizheng Huang, Student Member, IEEE, Huanlin Li, and Jeffrey Dill, Member, IEEE The School of Electrical Engineering and Computer Science, Ohio University Athens, OH 45701, USA ABSTRACT Digital fountain codes were originally packet-level forward erasure codes, but researchers have found that they are good at correcting bit errors. Modern LDPC and turbo codes have been shown to approach the Shannon limit. However, they are fixed rate codes and cannot well satisfy the Internet services that may encounter variable loss rates or asynchronous data access. For both packet and bit levels, fountain codes share the same belief propagation decoding mechanism with LDPC and turbo codes. We propose a general fountain codes system model over noisy channels. Conventional LT codes work poorly on AWGN and Rayleigh fading channels but Raptor codes offers near capacity performance if their pre-codes are a WiMAX LDPC code or our left-regular LDPC code. The code performance can be approved if we select more reliable received symbols for decoding. Our simulation results support the model design. Keywords: fountain code, LDPC code, Tanner graph, belief propagation, soft decoding, degree distribution. 1. INTRODUCTION The digital fountain concept was first published in 1998 [2]. The basic idea behind this name is that different receivers can reconstruct same source data from any subset of collected symbols, without or almost without need of retransmission. Besides, data access and transmission are successfully initiated at random time, without the knowledge of channel state and potentially with no limitation of user population. LT (Luby Transform) codes, the first class of practical fountain codes, were initially designed for the Binary Erasure Channel (BEC). Although LT codes are famous for simplicity, good performance and optimality, they do not support fast encoding or decoding for large dimension. Raptor Codes, a later class of fountain codes, can achieve linear coding complexity and vanishing probability of error. Today digital fountain codes have been applied to multimedia communications, especially in the context of reliable multicast/broadcast and point-to-multipoint that often encounter asynchronous user access, random reception pause or interruption and variable or unknown loss rate. Some researchers have demonstrated LT and Raptor codes performance upon noisy channels [3] [9]. However, as far as we know, not much has been published about fountain code application on additive white Gaussian noise (AWGN) or fading channels. In this work we give a picture of fountain codes on noisy channels. We present binary Raptor codes whose pre-codes are WiMAX LDPC (low-density parity-check) codes or LDPC codes created by our new method that guarantee H matrices of girth at least 6. In Section II, we recall harddecoding LT codes. In Section III, we review Raptor codes. In Section IV, we introduce our general system model for fountain codes over noisy channels. In Section V, we present simulation results and analysis. We make conclusion in Section VI. 2. LT CODES LT codes [10], the first fountain codes, are proven to be practical on the BEC. The LT code generates a limitless stream of encoded symbols, which are independent and identically distributed (i.i.d.), on the fly or in advance. The LT decoder can recover the source data from arbitrarily collected encoded symbols with small decoding overhead. This coding method acclimatizes the Internet environment characterized by variable or unknown packet loss rates. The process of LT encoding [10] is that from a degree distribution randomly choose a number of input symbols as the neighbors of an encoded symbol and then the encoded symbol is output as the XOR of its neighbors. At the receiver, the neighboring information of each collected encoded symbol is utilized to construct a Tanner graph [11] and the hard-decoder propagates in this bipartite graph the value of every degree-1 encoded symbol, in each iteration, to its neighbors, until all source symbols are recovered [10] [12]. If there is no degree-1 encoded symbol before the end of recovery, the decoding fails and the user may guess the undetermined source symbols or collect more symbols to decode. Note that the decoder is assumed to have the knowledge of the degree and neighboring indices of each received symbol. The model of hard-decoding LT codes on BEC is as follows. The encoder needs a generator matrix G to create encoded symbols, where k is the code dimension and m is unlimited. The encoded symbols are produced on the fly and it is equivalent to establishing G by generating i.i.d. columns, as many as needed, whose Hamming weights are determined by the Robust Soliton distribution proposed by Luby [10] and whose weight positions are uniformly distributed. The encoded symbols are transmitted once requested, but some of them are erased. At the receiver, with the n received symbols, the decoder builds a generator matrix G () and G is actually made by deleting those columns of G corresponding to the erased symbols. Apparently, the n received symbols are a random and variable subset of the m transmitted symbols. It is the Robust Soliton distribution that guarantees that with small overhead all source symbols are covered by encoded symbols and there is at least one degree-1 encoded symbol in each decoding iteration. Although these hard-decoding LT codes are very capable of correcting erasures regardless of loss rate, their performance can be poor if the decisions on some received symbols are wrong because the error is propagated throughout the message-passing decoding like a rolling snowball causing disastrous degradation. A remedy is stated in [23] to improve LT codes on AWGNC (AWGN channels) by setting a threshold at the decoder to erase those received bits that are more likely unreliable, but this harddecoding method cannot achieve significant coding gain.
2 3. RAPTOR CODES Raptor codes are an extension of LT codes with linear encoding and decoding complexity, which were developed by Shokrollahi [13] and Maymounkov [14] independently. A Raptor code is a concatenated code with an outer pre-code, which is a fixed rate erasure code like LDPC codes, and an inner LT code. The precode can be multistage. The inner LT code is also called weakened LT code [25] and usually cannot recover all its input symbols, but the pre-code corrects all the other erasures. The degree of the LT output encoded symbol is chosen from a distribution proposed by Shokrollahi. Raptor codes have been adopted by The 3rd Generation Partnership Project (3GPP) [15] for reliable data delivery in mobile broadcast and multicast. Why are Raptor codes concatenated with the weakened LT code, not the conventional LT code? The reason lies in coding speed, or computation cost. Computation cost can be defined by the degree of the encoded symbol. For example, to calculate an encoded bit of degree i, i bitwise additions are required, so the cost is i. In [10], due to the Robust Soliton distribution and the minimum number of collected symbols suggested by Luby, for large dimension k the LT code is no longer efficient since in average an encoded symbol needs at least a number of bitwise operations on the order of ln, where 01. Raptor codes solve this problem by achieving linear encoding and decoding complexity. Shokrollahi proved that the Raptor coding cost is on the order of ln1 for each symbol, where 0. Raptor codes with soft decoding have been reported to offer good error-correcting performance on noisy channels [3] [6] [16] [17] and can obtain more coding gain and significant lower error floors than Luby LT codes. 4. SYSTEM MODEL Using the system designs in [4] and [16] for reference, we give a wired and/or wireless source-to-multi-destination system: fountain-encoded symbols are sent from a single transmitter to multiple synchronous or asynchronous receivers on a noisy channel. Acknowledgement feedback is permitted so that data transmission can be terminated if no user requests. All synchronizations are perfect. Handoffs and communication loss occur at arbitrary time. This system is shown in Figure 1. u Hard decision Pre-code encoder m v I Pre-code decoder LT encoder m v,i m I,v Mod. & Tx Figure 1. System Model This system is general for linear block codes, LT and Raptor codes on AWGN and/or fading channels. Consider a source file,, of length k symbols requested by multiple users. When a Raptor code is adopted, is pre-encoded into an s Channel gain AWGN Receiver pattern LT r b decoder t h g Channel Matched filter user f t = jt intermediate sequence,, of fixed length N. If only an LT code is applied, the pre-code encoder and decoder are not needed, that is, and the LT decoder outputs. Similarly, in the case of pre-code only (PCO), the LT encoder and decoder are removed and that is a model for linear block codes. The intermediate symbols are turned into a limitless stream,, by the LT code. The vector, a modulated form of, is sent to the multiple users. A requester accesses the data at an arbitrary time and collects encoded symbols without need of the start of the source file. In this model, the transmitted symbols are modified by channel gain and/or AWGN. The channel gain is a non-negative real vector,, and its elements are in ordinal manner the gains of the symbols of. The gain vector can be a constant or approximate any fading models. The Gaussian noise, with zero mean and two-sided power spectral density (PSD) 2, is also in form of vector:,,. We assume the channel gain and the noise are constants over the entire slot of the i-th transmitted symbol. At the receiver, the output of the matched filter is sampled at the end of the symbol duration. At this point, the Gaussian noise is still zero mean and its variance is 2. Before input to the decoder, these samples are selected by the receiver pattern,, with 0,1 that stands by erasure, communication loss or symbol acceptance, which depends on the particular channel model. The fountain decoder utilizes the classic belief propagation (BP) technique applying Tanner graphs, which is standardized in LDPC decoding [18] [20]. For simplicity all symbols in this system are bits and they are transmitted in form of BPSK (binary phase shift keying). The belief propagated in the decoding procedure is log-likelihood ratio (LLR) [21] of binary random variable {1} in GF(2), given by ln (1) Where ln is the natural logarithm and is the probability that X takes on the value x. Assume 0 1 and, according to the derivation in [19], the observed LLR from the channel for the received bit is given by 4 (2) Note that, for error-free transmission and reception, 1 ( 1) for 1 ( 0). Consider a Raptor code of rate at an arbitrary user f illustrated in Figure 2. The Tanner graph of the LT generator matrix is built on the fly. The received output bits are the check nodes (c-nodes),, of the LT Tanner graph. The pre-code C is a rate LDPC code of dimension k and its H matrix is known by the decoder in advance. The variable nodes (v-nodes),, and,, are the same intermediate bits in the two graphs. and exchange updated belief with each other in every decoding iteration.,, are c-nodes of the Tanner graph of the pre-code s H matrix. All edges are bidirectional message-passing ways between v-nodes and c-nodes. [16] gives a concise and complete description of Raptor decoding that starts at the LT decoder by passing LLRs from the v-nodes to their neighboring c-nodes and, at the end of each LT decoding iteration, forwards its updated LLR, to. Taking the newly incoming messages as observed LLRs for,,, the LDPC decoder propagates belief for one iteration and then makes hard decision on,,. If the decision does not match any valid codeword, forwards its LLR, to for next iteration. adds, to its incoming LLRs from c- nodes in the previous LT iteration. This propagation is kept repeated until a valid codeword is decided from,, or the assigned maximum number of iterations are exhausted.
3 LT decoder Received bits r 1 r 2 r 3 r n-1 r n LDPC decoder Intermediate bits Check nodes v 1 v 2 v N-1 v N 1 m I,v 1 m v,i 2 m I,v 2 m v,i N 1 m I, v N 1 m v, I N m I, v N m v, I Figure 2. Raptor Decoder Configuration Here we need to point out that, within this model, soft decoding (noisy channel) and hard decoding (BEC) are the same in nature. Take the LT decoder as an example. Since the v-nodes bear no LLRs at the beginning of decoding, they send zero messages to their neighbors so this first half iteration is trivial and at this moment all edges are still bidirectional zero-llrpassing. In the second half of the first iteration, only degree-1 encoded bits can send non-zero LLRs to the v-nodes. One can verify this by looking at the equation computing the message sent from an output bit to a v-node in the l-th iteration [16],, 2tanh tanh 2 tanh 2 (3), where tanh and tanh are hyperbolic tangent function and inverse hyperbolic tangent function, L is the observed LLR of and is the LLR sent to the received encoded bit from, all its neighboring v-nodes except. Therefore, in the first iteration some v-nodes receive new LLRs and in the second iteration they send updated LLRs to their neighbors but the other v-nodes still send zero. According to Eq. (3), an erased encoded bit is useless for the LT decoder because it always forces its outgoing messages to zero. The decoder repeats this recursive process. More and more edges achieve non-zero LLRpassing, so more and more v-nodes are granted LLRs and these messages are kept updated iteration after iteration. However, for the channel model of BEC only, it is much more convenient to propagate bit values than LLRs. The reason lies in error-free reception and according to Eq. (1) the only message propagated on the Tanner graph is 1 which is absolute certainty. It is easy to see that, on the same LT generator Tanner graph, the path of bit value propagation for hard decoding is the same as the route of non-zero LLR flow for soft decoding. 5. FOUNTAIN CODES PERFORMANCE We investigate binary soft-decoding LT and Raptor codes on the AWGNC and memoryless Rayleigh fading channel. Luby s LT codes suffer high complexity and large-deviation bit error performance, but Raptor codes achieve impressive coding gains if the pre-code is a rate ½ LDPC code standardized by WiMAX [22] or created by our own approach based on splitting-andfilling technique [26]. If we chose those more reliable received symbols to decode, the fountain codes yield more coding gains. We proposed two remedies for LT codes: (1) discard less reliable received bits, (2) low code rate. The first scheme sets a I 1 I 2 I N-1 I N c 1 c 2 c N-k threshold at the matched filter output to deny all output samples whose absolute values are smaller than the threshold. Recall that error-free sample values are ±1 for source bits 1 and 0. At low signal-to-noise ratio (SNR), the performance of the both methods is very poor. Although they can achieve some coding gains at high SNR, the performance is unstable and the second method bears very high complexity. As stated in Section IV, in the first decoding iteration only degree-1 encoded bits can send out useful belief. Due to the Robust Soliton distribution, the fraction of degree-1 encoded bits is very small so the probability that a v-node has more than one degree-1 neighbor is also very small. If a v-node has only one degree-1 neighbor and its observed LLR does not match the corresponding source bit, the v-node will propagate this error to other nodes. Raptor codes are a good solution for both coding gain and complexity. We design rate 0.1 Raptor codes with two kinds of rate ½ pre-codes of dimension The first kind is a WiMAX LDPC code that has a systematic and irregular H matrix. This code has been well created and proven to achieve good near capacity performance on AWGNC. The second kind is a nonsystematic LDPC code with a left-regular H matrix whose column Hamming weight is 4. This pseudorandom H matrix was constructed by our own splitting-and filling approach and it has girth of at least 6 and its stopping distance is 6. As the column degree of the matrix is even, its rank is 1152 by modulo-2 arithmetic and its corresponding generator matrix is of size The performance of these two LDPC codes on AWGNC is shown in Figure 3. Uncoded BPSK WiMAX code Left-regular code SNR ( ) Figure 3. LDPC Codes on AWGNC (30 decoding iterations) According to Shokrollahi s proposed degree polynomial [13], for the LT output bits we set the following degree distribution, Ω (4) Rate 0.1 Raptor codes on AWGNC with the above two kinds of pre-codes were simulated for 1152 source bits and the result of 100 trials is illustrated in Figure 4. The left side shows that, after 15 decoding iterations, the bit error rate (BER) curves of the two Raptor codes are close at low SNR. At BER of the Raptor code with our left-regular LDPC code has about 0.5 db more coding gain than this LDPC code itself. In order for more coding gain, we set threshold as 0.6 at decoder to erase less reliable incoming bits (the overall code rate is still 0.1). The results after 8 iterations are illustrated in the right of Figure 4 and after 15 iterations the BER s can be as low as at 0 db. In case of memoryless Rayleigh fading occurring on AWGNC, the two Raptor codes achieve very good and close bit error performances, as illustrated in Figure 5.
4 Uncoded BPSK WiMAX pre-code Left-regular pre-code Figure 4. Raptor Codes on AWGNC WiMAX pre-code Figure 5. Raptor Codes on Rayleigh Fading Channel 6. CONCLUSION AND FUTURE WORK We have briefly described LT codes and Raptor codes. We focus on soft-decoding Raptor codes over AWGN channel. Our simulation result shows that, based on our system model, the rate ½ WiMAX LDPC code and our own regular LDPC code are very good pre-codes for the Raptor code on AWGNC. A proper symbol acceptance threshold can help achieve better performance. Future work will include investigation of optimal degree distribution for soft-decoding LT codes, high rate Raptor codes, and investigation of fountain codes on other fading channels. Symbol acceptance threshold can be sensitive to code performance so threshold design could be interesting. REFERENCES [1] D. J. Costello and G. D. Forney, Channel Coding: The Road to Channel Capacity, Proc. IEEE 2007, vol. 95, pp [2] J. W. Byers, M. Luby, M. Mitzenmacher, and A. Rege, A digital fountain approach to reliable distribution of bulk data, in Proc. SIGCOMM Comput. Comm. Rev., Vol. 28, No. 4, 1998, pp [3] R. Palanki, and J. S. Yedidia, Rateless codes on noisy channels, IEEE Proc. Inf. Theory, June 27 - July 2, [4] T. Stockhammer, H. Jenkac, T. Mayer, and W. Xu, Soft decoding of LT-codes for wireless broadcast, in Proc. IST Mobile, Dresden, Germany, Erasure threshold: 0.6 Left-regular pre-code [5] R. Y. S. Tee, T. D. Nguyen, L. L. Yang, and L. Hanzo, Serially concatenated Luby Transform coding and bitinterleaved coded modulation using iterative decoding for the wireless internet, in IEEE VTC'06 Spring, 7-10 May 2006, Melbourne, Australia. [6] Y. Ma, D. Yuan, and H. Zhang, Fountain codes and applications to reliable wireless broadcast system, in IEEE Inform. Theory Workshop, Chengdu China, Oct. 2006, pp [7] T. D. Nguyen, L. L. Yang, and L. Hanzo, Systematic Luby Transform codes and their soft decoding, in IEEE SiPS'07, October 2007, Shanghai, China. [8] D. T. Nguyen and L. Hanzo, An optimal degree distribution design and a conditional random integer generator for the systematic luby transform coded wireless internet, in IEEE WCNC'08, 31 March - 3 April 2008, Las Vegas, Nevada, USA. [9] W. Yao, L. Chen, H. Li, and H. Xu, Research on fountain codes in deep space communication, Congress on Image and Signal Processing, Vol. 2, May 2008, pp [10] M. Luby, LT codes, in Proceedings of The 43 rd Annual IEEE Symposium on Fountations of Computer Science, pp , November 16-19, [11] R. Tanner, A recursive approach to low complexity codes, IEEE Trans. Information Theory, Vol. 27, pp , September [12] D. J. C. MacKay, Information Theory, Inference, and Learning Algorithms, Version 7.0, Cambridge University Press, United Kingdom, [13] A. Shokrollahi, Raptor codes,, IEEE Trans. Inf. Theory, Vol. 52, No. 6, pp , June [14] P. Maymounkov, Online codes, Technical Report TR , New York University, November [15] The official home page of 3GPP, [16] B. Sivasubramanian and H. Leib, Fixed-rate Raptor code performance over correlated Rayleigh fading channels, Canadian Conference on Electrical and Computer Engineering, April 2007, pp [17] W. Yao, L. Chen, H. Li, and H. Xu, Research on fountain codes in deep space communication, 2008 Congress on Image and Signal Processing, Vol. 2, May 2008, pp [18] A. Shokrollahi, LDPC codes: An introduction, Digital Fountain, Inc., April [19] W. E. Ryan, An introduction to LDPC codes, in CRC Handbook for Coding and Signal Processing for Recoding Systems (B. Vasic, ed.), CRC Press, [20] X.-Y. Hu, E. Eleftheriou, D.-M. Arnold, and A. Dholakia, Efficient implementations of the sum-product algorithm for decoding LDPC codes, Proc. IEEE Globecom Conf. 2001, pp E, Nov [21] J. Hagenauer, E. Offer, and L. Papke, Iterative decoding of binary block and convolutional codes, IEEE Trans. Inf. Theory, vol. 42, March 1996, pp [22] T. W. Gerken, Implementation of LDPC Codes Using The IEEE e Standard, Problem report, West Virginia University, Morgantown, WV, [23] H. Wang, Hardware Designs for LT Coding, MSc Thesis, Dept of Electrical Engineering, Delft University of Technology, 2004, pp [24] O. Etesami and A. Shokrollahi, Raptor codes on binary memoryless symmetric channels, IEEE Proc. Inf. Theory, vol. 52, May 2006, pp [25] D. J. C. MacKay, Fountain codes, IEE Proc. Communications, vol. 152, Dec. 2005, pp
5 [26] H. Li, W. Huang and J. Dill, Construction of irregular LDPC codes with low error floors, 2010 International Conf. Computing, Comm. and Control Tech. accepted.
Volume 2, Issue 9, September 2014 International Journal of Advance Research in Computer Science and Management Studies
Volume 2, Issue 9, September 2014 International Journal of Advance Research in Computer Science and Management Studies Research Article / Survey Paper / Case Study Available online at: www.ijarcsms.com
More informationThe throughput analysis of different IR-HARQ schemes based on fountain codes
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 008 proceedings. The throughput analysis of different IR-HARQ schemes
More informationStudy of Second-Order Memory Based LT Encoders
Study of Second-Order Memory Based LT Encoders Luyao Shang Department of Electrical Engineering & Computer Science University of Kansas Lawrence, KS 66045 lshang@ku.edu Faculty Advisor: Erik Perrins ABSTRACT
More informationRAPTOR CODES FOR HYBRID ERROR-ERASURE CHANNELS WITH MEMORY. Yu Cao and Steven D. Blostein
RAPTOR CODES FOR HYBRID ERROR-ERASURE CHANNELS WITH MEMORY Yu Cao and Steven D. Blostein Department of Electrical and Computer Engineering Queen s University, Kingston, Ontario, Canada, K7L 3N6 Email:
More informationPerformance Evaluation of Low Density Parity Check codes with Hard and Soft decision Decoding
Performance Evaluation of Low Density Parity Check codes with Hard and Soft decision Decoding Shalini Bahel, Jasdeep Singh Abstract The Low Density Parity Check (LDPC) codes have received a considerable
More informationDigital Television Lecture 5
Digital Television Lecture 5 Forward Error Correction (FEC) Åbo Akademi University Domkyrkotorget 5 Åbo 8.4. Error Correction in Transmissions Need for error correction in transmissions Loss of data during
More informationMULTILEVEL CODING (MLC) with multistage decoding
350 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 3, MARCH 2004 Power- and Bandwidth-Efficient Communications Using LDPC Codes Piraporn Limpaphayom, Student Member, IEEE, and Kim A. Winick, Senior
More informationLab/Project Error Control Coding using LDPC Codes and HARQ
Linköping University Campus Norrköping Department of Science and Technology Erik Bergfeldt TNE066 Telecommunications Lab/Project Error Control Coding using LDPC Codes and HARQ Error control coding is an
More informationCapacity-Achieving Rateless Polar Codes
Capacity-Achieving Rateless Polar Codes arxiv:1508.03112v1 [cs.it] 13 Aug 2015 Bin Li, David Tse, Kai Chen, and Hui Shen August 14, 2015 Abstract A rateless coding scheme transmits incrementally more and
More informationFOR THE PAST few years, there has been a great amount
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 4, APRIL 2005 549 Transactions Letters On Implementation of Min-Sum Algorithm and Its Modifications for Decoding Low-Density Parity-Check (LDPC) Codes
More informationn Based on the decision rule Po- Ning Chapter Po- Ning Chapter
n Soft decision decoding (can be analyzed via an equivalent binary-input additive white Gaussian noise channel) o The error rate of Ungerboeck codes (particularly at high SNR) is dominated by the two codewords
More informationFrom Fountain to BATS: Realization of Network Coding
From Fountain to BATS: Realization of Network Coding Shenghao Yang Jan 26, 2015 Shenzhen Shenghao Yang Jan 26, 2015 1 / 35 Outline 1 Outline 2 Single-Hop: Fountain Codes LT Codes Raptor codes: achieving
More informationSoft decoding of Raptor codes over AWGN channels using Probabilistic Graphical Models
Soft decoding of Raptor codes over AWG channels using Probabilistic Graphical Models Rian Singels, J.A. du Preez and R. Wolhuter Department of Electrical and Electronic Engineering University of Stellenbosch
More informationCode Design for Incremental Redundancy Hybrid ARQ
Code Design for Incremental Redundancy Hybrid ARQ by Hamid Saber A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Doctor
More informationReliable Wireless Video Streaming with Digital Fountain Codes
1 Reliable Wireless Video Streaming with Digital Fountain Codes Raouf Hamzaoui, Shakeel Ahmad, Marwan Al-Akaidi Faculty of Computing Sciences and Engineering, De Montfort University - UK Department of
More informationPerformance comparison of convolutional and block turbo codes
Performance comparison of convolutional and block turbo codes K. Ramasamy 1a), Mohammad Umar Siddiqi 2, Mohamad Yusoff Alias 1, and A. Arunagiri 1 1 Faculty of Engineering, Multimedia University, 63100,
More informationBasics of Error Correcting Codes
Basics of Error Correcting Codes Drawing from the book Information Theory, Inference, and Learning Algorithms Downloadable or purchasable: http://www.inference.phy.cam.ac.uk/mackay/itila/book.html CSE
More informationDecoding of LT-Like Codes in the Absence of Degree-One Code Symbols
Decoding of LT-Like Codes in the Absence of Degree-One Code Symbols Nadhir I. Abdulkhaleq and Orhan Gazi Luby transform (LT) codes were the first practical rateless erasure codes proposed in the literature.
More informationStudy of Turbo Coded OFDM over Fading Channel
International Journal of Engineering Research and Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 3, Issue 2 (August 2012), PP. 54-58 Study of Turbo Coded OFDM over Fading Channel
More informationPerformance Optimization of Hybrid Combination of LDPC and RS Codes Using Image Transmission System Over Fading Channels
European Journal of Scientific Research ISSN 1450-216X Vol.35 No.1 (2009), pp 34-42 EuroJournals Publishing, Inc. 2009 http://www.eurojournals.com/ejsr.htm Performance Optimization of Hybrid Combination
More informationPower Efficiency of LDPC Codes under Hard and Soft Decision QAM Modulated OFDM
Advance in Electronic and Electric Engineering. ISSN 2231-1297, Volume 4, Number 5 (2014), pp. 463-468 Research India Publications http://www.ripublication.com/aeee.htm Power Efficiency of LDPC Codes under
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014
Spectral Efficiency and Bit Error Rate Measure of Wireless OFDM System Using Raptor Codes with SUI-3 channel models 1 Kuldeep Singh, 2 Jitender Khurana 1 M-Tech Scholar, Shri Baba Mastnath Engineering
More informationImprovement Of Block Product Turbo Coding By Using A New Concept Of Soft Hamming Decoder
European Scientific Journal June 26 edition vol.2, No.8 ISSN: 857 788 (Print) e - ISSN 857-743 Improvement Of Block Product Turbo Coding By Using A New Concept Of Soft Hamming Decoder Alaa Ghaith, PhD
More informationLec 19 Error and Loss Control I: FEC
Multimedia Communication Lec 19 Error and Loss Control I: FEC Zhu Li Course Web: http://l.web.umkc.edu/lizhu/teaching/ Z. Li, Multimedia Communciation, Spring 2017 p.1 Outline ReCap Lecture 18 TCP Congestion
More informationDecoding of Block Turbo Codes
Decoding of Block Turbo Codes Mathematical Methods for Cryptography Dedicated to Celebrate Prof. Tor Helleseth s 70 th Birthday September 4-8, 2017 Kyeongcheol Yang Pohang University of Science and Technology
More informationIDMA Technology and Comparison survey of Interleavers
International Journal of Scientific and Research Publications, Volume 3, Issue 9, September 2013 1 IDMA Technology and Comparison survey of Interleavers Neelam Kumari 1, A.K.Singh 2 1 (Department of Electronics
More informationNotes 15: Concatenated Codes, Turbo Codes and Iterative Processing
16.548 Notes 15: Concatenated Codes, Turbo Codes and Iterative Processing Outline! Introduction " Pushing the Bounds on Channel Capacity " Theory of Iterative Decoding " Recursive Convolutional Coding
More informationLDPC Decoding: VLSI Architectures and Implementations
LDPC Decoding: VLSI Architectures and Implementations Module : LDPC Decoding Ned Varnica varnica@gmail.com Marvell Semiconductor Inc Overview Error Correction Codes (ECC) Intro to Low-density parity-check
More informationOutline. Communications Engineering 1
Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion Digital transmission through baseband channels Signal space representation Optimal
More informationDual-Mode Decoding of Product Codes with Application to Tape Storage
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2005 proceedings Dual-Mode Decoding of Product Codes with
More informationDistributed LT Codes
Distributed LT Codes Srinath Puducheri, Jörg Kliewer, and Thomas E. Fuja Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Email: {spuduche, jliewer, tfuja}@nd.edu
More informationIncremental Redundancy Via Check Splitting
Incremental Redundancy Via Check Splitting Moshe Good and Frank R. Kschischang Dept. of Electrical and Computer Engineering University of Toronto {good, frank}@comm.utoronto.ca Abstract A new method of
More informationIEEE C /02R1. IEEE Mobile Broadband Wireless Access <http://grouper.ieee.org/groups/802/mbwa>
23--29 IEEE C82.2-3/2R Project Title Date Submitted IEEE 82.2 Mobile Broadband Wireless Access Soft Iterative Decoding for Mobile Wireless Communications 23--29
More informationFountain Codes. Gauri Joshi, Joong Bum Rhim, John Sun, Da Wang. December 8, 2010
6.972 PRINCIPLES OF DIGITAL COMMUNICATION II Fountain Codes Gauri Joshi, Joong Bum Rhim, John Sun, Da Wang December 8, 2010 Contents 1 Digital Fountain Ideal 3 2 Preliminaries 4 2.1 Binary Erasure Channel...................................
More informationContents Chapter 1: Introduction... 2
Contents Chapter 1: Introduction... 2 1.1 Objectives... 2 1.2 Introduction... 2 Chapter 2: Principles of turbo coding... 4 2.1 The turbo encoder... 4 2.1.1 Recursive Systematic Convolutional Codes... 4
More informationShort-Blocklength Non-Binary LDPC Codes with Feedback-Dependent Incremental Transmissions
Short-Blocklength Non-Binary LDPC Codes with Feedback-Dependent Incremental Transmissions Kasra Vakilinia, Tsung-Yi Chen*, Sudarsan V. S. Ranganathan, Adam R. Williamson, Dariush Divsalar**, and Richard
More informationConstruction of Adaptive Short LDPC Codes for Distributed Transmit Beamforming
Construction of Adaptive Short LDPC Codes for Distributed Transmit Beamforming Ismail Shakeel Defence Science and Technology Group, Edinburgh, South Australia. email: Ismail.Shakeel@dst.defence.gov.au
More informationIterative Joint Source/Channel Decoding for JPEG2000
Iterative Joint Source/Channel Decoding for JPEG Lingling Pu, Zhenyu Wu, Ali Bilgin, Michael W. Marcellin, and Bane Vasic Dept. of Electrical and Computer Engineering The University of Arizona, Tucson,
More informationMultiple-Bases Belief-Propagation for Decoding of Short Block Codes
Multiple-Bases Belief-Propagation for Decoding of Short Block Codes Thorsten Hehn, Johannes B. Huber, Stefan Laendner, Olgica Milenkovic Institute for Information Transmission, University of Erlangen-Nuremberg,
More informationMultitree Decoding and Multitree-Aided LDPC Decoding
Multitree Decoding and Multitree-Aided LDPC Decoding Maja Ostojic and Hans-Andrea Loeliger Dept. of Information Technology and Electrical Engineering ETH Zurich, Switzerland Email: {ostojic,loeliger}@isi.ee.ethz.ch
More informationReceiver Design for Noncoherent Digital Network Coding
Receiver Design for Noncoherent Digital Network Coding Terry Ferrett 1 Matthew Valenti 1 Don Torrieri 2 1 West Virginia University 2 U.S. Army Research Laboratory November 3rd, 2010 1 / 25 Outline 1 Introduction
More informationVector-LDPC Codes for Mobile Broadband Communications
Vector-LDPC Codes for Mobile Broadband Communications Whitepaper November 23 Flarion Technologies, Inc. Bedminster One 35 Route 22/26 South Bedminster, NJ 792 Tel: + 98-947-7 Fax: + 98-947-25 www.flarion.com
More informationInternational Journal of Digital Application & Contemporary research Website: (Volume 1, Issue 7, February 2013)
Performance Analysis of OFDM under DWT, DCT based Image Processing Anshul Soni soni.anshulec14@gmail.com Ashok Chandra Tiwari Abstract In this paper, the performance of conventional discrete cosine transform
More informationHigh-Rate Non-Binary Product Codes
High-Rate Non-Binary Product Codes Farzad Ghayour, Fambirai Takawira and Hongjun Xu School of Electrical, Electronic and Computer Engineering University of KwaZulu-Natal, P. O. Box 4041, Durban, South
More informationA Survey of Advanced FEC Systems
A Survey of Advanced FEC Systems Eric Jacobsen Minister of Algorithms, Intel Labs Communication Technology Laboratory/ Radio Communications Laboratory July 29, 2004 With a lot of material from Bo Xia,
More informationSingle Error Correcting Codes (SECC) 6.02 Spring 2011 Lecture #9. Checking the parity. Using the Syndrome to Correct Errors
Single Error Correcting Codes (SECC) Basic idea: Use multiple parity bits, each covering a subset of the data bits. No two message bits belong to exactly the same subsets, so a single error will generate
More informationFOR applications requiring high spectral efficiency, there
1846 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 11, NOVEMBER 2004 High-Rate Recursive Convolutional Codes for Concatenated Channel Codes Fred Daneshgaran, Member, IEEE, Massimiliano Laddomada, Member,
More informationEE 435/535: Error Correcting Codes Project 1, Fall 2009: Extended Hamming Code. 1 Introduction. 2 Extended Hamming Code: Encoding. 1.
EE 435/535: Error Correcting Codes Project 1, Fall 2009: Extended Hamming Code Project #1 is due on Tuesday, October 6, 2009, in class. You may turn the project report in early. Late projects are accepted
More informationGoa, India, October Question: 4/15 SOURCE 1 : IBM. G.gen: Low-density parity-check codes for DSL transmission.
ITU - Telecommunication Standardization Sector STUDY GROUP 15 Temporary Document BI-095 Original: English Goa, India, 3 7 October 000 Question: 4/15 SOURCE 1 : IBM TITLE: G.gen: Low-density parity-check
More informationDEGRADED broadcast channels were first studied by
4296 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 54, NO 9, SEPTEMBER 2008 Optimal Transmission Strategy Explicit Capacity Region for Broadcast Z Channels Bike Xie, Student Member, IEEE, Miguel Griot,
More informationINCREMENTAL redundancy (IR) systems with receiver
1 Protograph-Based Raptor-Like LDPC Codes Tsung-Yi Chen, Member, IEEE, Kasra Vakilinia, Student Member, IEEE, Dariush Divsalar, Fellow, IEEE, and Richard D. Wesel, Senior Member, IEEE tsungyi.chen@northwestern.edu,
More informationUniversity of Southampton Research Repository eprints Soton
University of Southampton Research Repository eprints Soton Copyright and Moral Rights for this thesis are retained by the author and/or other copyright owners A copy can be downloaded for personal non-commercial
More informationA Random Network Coding-based ARQ Scheme and Performance Analysis for Wireless Broadcast
ISSN 746-7659, England, U Journal of Information and Computing Science Vol. 4, No., 9, pp. 4-3 A Random Networ Coding-based ARQ Scheme and Performance Analysis for Wireless Broadcast in Yang,, +, Gang
More informationProject. Title. Submitted Sources: {se.park,
Project Title Date Submitted Sources: Re: Abstract Purpose Notice Release Patent Policy IEEE 802.20 Working Group on Mobile Broadband Wireless Access LDPC Code
More informationFPGA Implementation Of An LDPC Decoder And Decoding. Algorithm Performance
FPGA Implementation Of An LDPC Decoder And Decoding Algorithm Performance BY LUIGI PEPE B.S., Politecnico di Torino, Turin, Italy, 2011 THESIS Submitted as partial fulfillment of the requirements for the
More informationBangalore, December Raptor Codes. Amin Shokrollahi
Raptor Codes Amin Shokrollahi Synopsis 1. Some data Transmission Problems and their (conventional) solutions 2. Fountain Codes 2.1. Definition 2.2. Some type of fountain codes 2.3. LT-Codes 2.4. Raptor
More informationMULTIPATH fading could severely degrade the performance
1986 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 12, DECEMBER 2005 Rate-One Space Time Block Codes With Full Diversity Liang Xian and Huaping Liu, Member, IEEE Abstract Orthogonal space time block
More informationLab 3.0. Pulse Shaping and Rayleigh Channel. Faculty of Information Engineering & Technology. The Communications Department
Faculty of Information Engineering & Technology The Communications Department Course: Advanced Communication Lab [COMM 1005] Lab 3.0 Pulse Shaping and Rayleigh Channel 1 TABLE OF CONTENTS 2 Summary...
More informationUsing LDPC coding and AMC to mitigate received power imbalance in carrier aggregation communication system
Using LDPC coding and AMC to mitigate received power imbalance in carrier aggregation communication system Yang-Han Lee 1a), Yih-Guang Jan 1, Hsin Huang 1,QiangChen 2, Qiaowei Yuan 3, and Kunio Sawaya
More informationError Patterns in Belief Propagation Decoding of Polar Codes and Their Mitigation Methods
Error Patterns in Belief Propagation Decoding of Polar Codes and Their Mitigation Methods Shuanghong Sun, Sung-Gun Cho, and Zhengya Zhang Department of Electrical Engineering and Computer Science University
More informationTornado Codes and Luby Transform Codes
Tornado Codes and Luby Transform Codes Ashish Khisti October 22, 2003 1 Introduction A natural solution for software companies that plan to efficiently disseminate new software over the Internet to millions
More informationLow-Density Parity-Check Codes for Volume Holographic Memory Systems
University of Massachusetts Amherst From the SelectedWorks of Hossein Pishro-Nik February 10, 2003 Low-Density Parity-Check Codes for Volume Holographic Memory Systems Hossein Pishro-Nik, University of
More informationPERFORMANCE EVALUATION OF WIMAX SYSTEM USING CONVOLUTIONAL PRODUCT CODE (CPC)
Progress In Electromagnetics Research C, Vol. 5, 125 133, 2008 PERFORMANCE EVALUATION OF WIMAX SYSTEM USING CONVOLUTIONAL PRODUCT CODE (CPC) A. Ebian, M. Shokair, and K. H. Awadalla Faculty of Electronic
More informationREVIEW OF COOPERATIVE SCHEMES BASED ON DISTRIBUTED CODING STRATEGY
INTERNATIONAL JOURNAL OF RESEARCH IN COMPUTER APPLICATIONS AND ROBOTICS ISSN 2320-7345 REVIEW OF COOPERATIVE SCHEMES BASED ON DISTRIBUTED CODING STRATEGY P. Suresh Kumar 1, A. Deepika 2 1 Assistant Professor,
More informationOn the performance of Turbo Codes over UWB channels at low SNR
On the performance of Turbo Codes over UWB channels at low SNR Ranjan Bose Department of Electrical Engineering, IIT Delhi, Hauz Khas, New Delhi, 110016, INDIA Abstract - In this paper we propose the use
More informationPhysical-Layer Network Coding Using GF(q) Forward Error Correction Codes
Physical-Layer Network Coding Using GF(q) Forward Error Correction Codes Weimin Liu, Rui Yang, and Philip Pietraski InterDigital Communications, LLC. King of Prussia, PA, and Melville, NY, USA Abstract
More informationSoft Channel Encoding; A Comparison of Algorithms for Soft Information Relaying
IWSSIP, -3 April, Vienna, Austria ISBN 978-3--38-4 Soft Channel Encoding; A Comparison of Algorithms for Soft Information Relaying Mehdi Mortazawi Molu Institute of Telecommunications Vienna University
More informationLDPC Codes for Rank Modulation in Flash Memories
LDPC Codes for Rank Modulation in Flash Memories Fan Zhang Electrical and Computer Eng. Dept. fanzhang@tamu.edu Henry D. Pfister Electrical and Computer Eng. Dept. hpfister@tamu.edu Anxiao (Andrew) Jiang
More informationDigital Transmission using SECC Spring 2010 Lecture #7. (n,k,d) Systematic Block Codes. How many parity bits to use?
Digital Transmission using SECC 6.02 Spring 2010 Lecture #7 How many parity bits? Dealing with burst errors Reed-Solomon codes message Compute Checksum # message chk Partition Apply SECC Transmit errors
More informationError Control Coding. Aaron Gulliver Dept. of Electrical and Computer Engineering University of Victoria
Error Control Coding Aaron Gulliver Dept. of Electrical and Computer Engineering University of Victoria Topics Introduction The Channel Coding Problem Linear Block Codes Cyclic Codes BCH and Reed-Solomon
More informationTurbo Codes for Pulse Position Modulation: Applying BCJR algorithm on PPM signals
Turbo Codes for Pulse Position Modulation: Applying BCJR algorithm on PPM signals Serj Haddad and Chadi Abou-Rjeily Lebanese American University PO. Box, 36, Byblos, Lebanon serj.haddad@lau.edu.lb, chadi.abourjeily@lau.edu.lb
More informationImproved concatenated (RS-CC) for OFDM systems
Improved concatenated (RS-CC) for OFDM systems Mustafa Dh. Hassib 1a), JS Mandeep 1b), Mardina Abdullah 1c), Mahamod Ismail 1d), Rosdiadee Nordin 1e), and MT Islam 2f) 1 Department of Electrical, Electronics,
More informationTHE idea behind constellation shaping is that signals with
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 3, MARCH 2004 341 Transactions Letters Constellation Shaping for Pragmatic Turbo-Coded Modulation With High Spectral Efficiency Dan Raphaeli, Senior Member,
More informationXJ-BP: Express Journey Belief Propagation Decoding for Polar Codes
XJ-BP: Express Journey Belief Propagation Decoding for Polar Codes Jingwei Xu, Tiben Che, Gwan Choi Department of Electrical and Computer Engineering Texas A&M University College Station, Texas 77840 Email:
More informationCoding Schemes for an Erasure Relay Channel
Coding Schemes for an Erasure Relay Channel Srinath Puducheri, Jörg Kliewer, and Thomas E. Fuja Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Email: {spuduche,
More informationConstellation Shaping for LDPC-Coded APSK
Constellation Shaping for LDPC-Coded APSK Matthew C. Valenti Lane Department of Computer Science and Electrical Engineering West Virginia University U.S.A. Mar. 14, 2013 ( Lane Department LDPCof Codes
More informationSerial Concatenation of LDPC Codes and Differentially Encoded Modulations. M. Franceschini, G. Ferrari, R. Raheli and A. Curtoni
International Symposium on Information Theory and its Applications, ISITA2004 Parma, Italy, October 10 13, 2004 Serial Concatenation of LDPC Codes and Differentially Encoded Modulations M. Franceschini,
More informationAN IMPROVED NEURAL NETWORK-BASED DECODER SCHEME FOR SYSTEMATIC CONVOLUTIONAL CODE. A Thesis by. Andrew J. Zerngast
AN IMPROVED NEURAL NETWORK-BASED DECODER SCHEME FOR SYSTEMATIC CONVOLUTIONAL CODE A Thesis by Andrew J. Zerngast Bachelor of Science, Wichita State University, 2008 Submitted to the Department of Electrical
More informationPerformance of Combined Error Correction and Error Detection for very Short Block Length Codes
Performance of Combined Error Correction and Error Detection for very Short Block Length Codes Matthias Breuninger and Joachim Speidel Institute of Telecommunications, University of Stuttgart Pfaffenwaldring
More informationReduced-Complexity VLSI Architectures for Binary and Nonbinary LDPC Codes
Reduced-Complexity VLSI Architectures for Binary and Nonbinary LDPC Codes A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Sangmin Kim IN PARTIAL FULFILLMENT
More informationLecture 3 Data Link Layer - Digital Data Communication Techniques
DATA AND COMPUTER COMMUNICATIONS Lecture 3 Data Link Layer - Digital Data Communication Techniques Mei Yang Based on Lecture slides by William Stallings 1 ASYNCHRONOUS AND SYNCHRONOUS TRANSMISSION timing
More informationStudy on AR4JA Code in Deep Space Fading Channel
01 7th International ICST Conference on Communications and Networking in China (CHINACOM) Study on AR4JA Code in Deep Space Fading Channel Hui Li 1, Jianan Gao,Mingchuan Yang 1 *, Member, IEEE, Gu Lv 1,
More informationCapacity-Approaching Bandwidth-Efficient Coded Modulation Schemes Based on Low-Density Parity-Check Codes
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 9, SEPTEMBER 2003 2141 Capacity-Approaching Bandwidth-Efficient Coded Modulation Schemes Based on Low-Density Parity-Check Codes Jilei Hou, Student
More informationNovel BICM HARQ Algorithm Based on Adaptive Modulations
Novel BICM HARQ Algorithm Based on Adaptive Modulations Item Type text; Proceedings Authors Kumar, Kuldeep; Perez-Ramirez, Javier Publisher International Foundation for Telemetering Journal International
More informationp J Data bits P1 P2 P3 P4 P5 P6 Parity bits C2 Fig. 3. p p p p p p C9 p p p P7 P8 P9 Code structure of RC-LDPC codes. the truncated parity blocks, hig
A Study on Hybrid-ARQ System with Blind Estimation of RC-LDPC Codes Mami Tsuji and Tetsuo Tsujioka Graduate School of Engineering, Osaka City University 3 3 138, Sugimoto, Sumiyoshi-ku, Osaka, 558 8585
More informationDepartment of Electronic Engineering FINAL YEAR PROJECT REPORT
Department of Electronic Engineering FINAL YEAR PROJECT REPORT BEngECE-2009/10-- Student Name: CHEUNG Yik Juen Student ID: Supervisor: Prof.
More informationECE 6640 Digital Communications
ECE 6640 Digital Communications Dr. Bradley J. Bazuin Assistant Professor Department of Electrical and Computer Engineering College of Engineering and Applied Sciences Chapter 8 8. Channel Coding: Part
More informationPerformance of Turbo codec OFDM in Rayleigh fading channel for Wireless communication
Performance of Turbo codec OFDM in Rayleigh fading channel for Wireless communication Arjuna Muduli, R K Mishra Electronic science Department, Berhampur University, Berhampur, Odisha, India Email: arjunamuduli@gmail.com
More informationChapter 1 Coding for Reliable Digital Transmission and Storage
Wireless Information Transmission System Lab. Chapter 1 Coding for Reliable Digital Transmission and Storage Institute of Communications Engineering National Sun Yat-sen University 1.1 Introduction A major
More informationAn Improved Rate Matching Method for DVB Systems Through Pilot Bit Insertion
Research Journal of Applied Sciences, Engineering and Technology 4(18): 3251-3256, 2012 ISSN: 2040-7467 Maxwell Scientific Organization, 2012 Submitted: December 28, 2011 Accepted: March 02, 2012 Published:
More informationISSN: Page 320
To Reduce Bit Error Rate in Turbo Coded OFDM with using different Modulation Techniques Shivangi #1, Manoj Sindhwani *2 #1 Department of Electronics & Communication, Research Scholar, Lovely Professional
More informationPunctured vs Rateless Codes for Hybrid ARQ
Punctured vs Rateless Codes for Hybrid ARQ Emina Soljanin Mathematical and Algorithmic Sciences Research, Bell Labs Collaborations with R. Liu, P. Spasojevic, N. Varnica and P. Whiting Tsinghua University
More informationPacket Permutation PAPR Reduction for OFDM Systems Based on Luby Transform Codes
Journal of Computer and Communications, 2018, 6, 219-228 http://www.scirp.org/journal/jcc ISSN Online: 2327-5227 ISSN Print: 2327-5219 Packet Permutation PAPR Reduction for OFDM Systems Based on Luby Transform
More informationQ-ary LDPC Decoders with Reduced Complexity
Q-ary LDPC Decoders with Reduced Complexity X. H. Shen & F. C. M. Lau Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong Email: shenxh@eie.polyu.edu.hk
More informationClosing the Gap to the Capacity of APSK: Constellation Shaping and Degree Distributions
Closing the Gap to the Capacity of APSK: Constellation Shaping and Degree Distributions Xingyu Xiang and Matthew C. Valenti Lane Department of Computer Science and Electrical Engineering West Virginia
More informationHigh-Efficiency Error Correction for Photon Counting
High-Efficiency Error Correction for Photon Counting Andrew S. Fletcher Pulse-position modulation (PPM) using a photon-counting receiver produces an extremely sensitive optical communications system, capable
More informationTurbo coding (CH 16)
Turbo coding (CH 16) Parallel concatenated codes Distance properties Not exceptionally high minimum distance But few codewords of low weight Trellis complexity Usually extremely high trellis complexity
More informationCombined Modulation and Error Correction Decoder Using Generalized Belief Propagation
Combined Modulation and Error Correction Decoder Using Generalized Belief Propagation Graduate Student: Mehrdad Khatami Advisor: Bane Vasić Department of Electrical and Computer Engineering University
More information2020 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 6, JUNE Application of Nonbinary LDPC Cycle Codes to MIMO Channels
2020 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 6, JUNE 2008 Application of Nonbinary LDPC Cycle Codes to MIMO Channels Ronghui Peng, Student Member, IEEE, and Rong-Rong Chen, Member, IEEE
More informationLDPC Communication Project
Communication Project Implementation and Analysis of codes over BEC Bar-Ilan university, school of engineering Chen Koker and Maytal Toledano Outline Definitions of Channel and Codes. Introduction to.
More information