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 of LDPC and RS Codes Using Image Transmission System Over Fading Channels A.H.M Almawgani School of Electrical and Electronic Engineering,Universiti Sains Malaysia Seri Ampangan, 14300 Nibong Tebal, Pulau Pinang, Malaysia E-mail: almawgani2003@hotmail.com M. F. M. Salleh School of Electrical and Electronic Engineering, Universiti Sains Malaysia Seri Ampangan, 14300 Nibong Tebal, Pulau Pinang, Malaysia E-mail: fadzlisalleh@eng.usm.my Abstract This paper analyzes the performances of Low-Density Parity-Check (LDPC), Reed- Solomon (RS) codes and finds the optimize code rates used for the hybrid combination of both channel coding schemes. These codes are used as the Forward Error Correction (FEC) scheme for image transmission system over several wireless channels. The hybrid FEC scheme consists of LDPC and RS codes. Simulation results show that the performance of image transmission system with LDPC codes is better than the system with RS codes over Rician fading channel. Meanwhile, the system with RS codes has better performance over Rayleigh fading channel. The system with hybrid FEC scheme outperforms the system with LDPC codes as well as the system with RS codes for both fading channels. The hybrid combination of LDPC (1/3) and RS(18,24) produces the best performance as well as reveals the optimized code rates selection for the overall code rate of ¼. Keywords: Image transmission system, LDPC codes, RS codes, Rayleigh fading channel, Rician fading channel. 1. Introduction The demand for mobile multimedia applications has increased tremendously in recent years. Thus, tremendous efforts have been done to develop efficient data transmission schemes [1]. The received data over mobile channel are very erroneous. Therefore, a Forward Error Correction (FEC) scheme is employed to protect the data prior to transmission [2]. One of the FEC schemes is Low-Density Parity-Check (LDPC) codes developed by Gallager [3] in 1963. However, since then, the codes were forgotten because they were impractical to implement. LDPC codes remain in theory until Mackay discovers that the codes are the most effective error correcting codes that allows data transmission rate close to the Shannon s theoretical limit [4]. Today, LDPC codes have been chosen as the error correcting codes in the new DVB-S2 standard for transmission of digital satellite television [5].
Performance Optimization of Hybrid Combination of LDPC and RS Codes Using Image Transmission System Over Fading Channels 35 Reed-Solomon (RS) codes are another popular FEC scheme discovered by Reed and Solomon in 1960 [6]. RS codes are very effective in correcting random symbol errors and random burst errors. They are applied in many systems such as storage devices, mobile communications, digital television/dvb and high-speed modems. LDPC codes using message passing decoding algorithms have achieved excellent performance over additive white Gaussian noise (AWGN) channel as presented in [7-8]. In both works the authors present the general theoretical methods for determining the capacity of LDPC codes in AWGN channel. The work in [9] presents a hybrid FEC scheme for video transmission. The scheme combines LDPC and RS codes and use them as FEC scheme to achieve robust video communication in the presence of erasures and errors. In that work, a dynamic rate selection FEC scheme is developed where the code rates of LDPC codes and RS codes are dynamically adjusted according to the channels biterror and erasure-error. The overall combination code rate used is fixed to 1/4. In this paper the performance of Low-Density Parity-Check (LDPC), Reed-Solomon (RS) codes and their hybrid schemes are analyzed by an image transmission systems simulated over fading channels. The optimized code rates selection of the hybrid combination frequency-selective Rayleigh fading is also obtained. Simulation results show the performance of image transmission system with LDPC codes is better than the system with RS codes over Rician fading channel. Meanwhile, the system with RS codes has better performance over Rayleigh fading channel. The system with hybrid FEC scheme outperforms the system with LDPC codes as well as the system with RS codes over both fading channels. The hybrid combination of LDPC (1/3) and RS(18,24) produces the best performance as well as reveals the optimized code rates selection for the overall code rate of ¼. The remainder of the paper is organized as follows. Part II gives a brief introduction of LDPC codes and the erasure error correct ability of RS codes. The system module is presented in Part III. Simulation results and analysis is given in Part IV, and Part V concludes the paper. 2. Basic Information In this section the basic concept of LDPC and RS codes for error correcting capability is presented. A. Low-Density Parity-Check (LDPC) Codes LDPC codes can be described using m n matrix, or using a graphical representation [3]. 0 1 0 1 1 0 0 1 = 1 1 1 0 0 1 0 0 H (1) 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 The matrix defined in equation (1) is a parity check matrix with dimension m n where m is 8 and n is 4, for a ( 8,4) code. Let w r be the number of 1 s in each row and let w c be the number of 1 s in each column. In order for the matrix to be a low-density, two conditions i.e. w c m and w r n must be satisfied [3]. Therefore the parity check matrix should be very large. LDPC codes can also be represented using a Tanner graph [3] as shown in Figure 1. Tanner graphs are bipartite graphs. That means that the nodes of the graph are separated into two distinctive sets and edges are only connecting nodes of two different types.
36 A.H.M Almawgani and M. F. M. Salleh Figure 1: Tanner graph representation f 0 f 1 f 2 f 3 c nodes C 0 C 1 C 2 C 3 C 4 C 5 C 6 v nodes C 7 The nodes are called the variable nodes ( v -nodes) and check nodes ( c -nodes). Figure 1 represents the codes for the matrix shown in equation 1. The graph consists of m c -nodes (the number of parity bits) and n v -nodes (the number of bits in a codeword). The c -nodes (indicated as f i ) are connected to v -nodes (indicated as c j ) if the element hij in H is a 1. LDPC codes are also linear block codes. Hence, they are defined by parity check matrix. However, LDPC codes are different from the traditional block codes since their parity check matrix is very sparse, i.e. the elements in the matrix consists mostly 0's and very small number of 1's. The number of 1's in row is called the row weight and the number of 1's in column is called the column weight. LDPC codes are classified into two classes; regular and irregular codes. Regular LDPC codes have equal weight for each row and equal column. As explained in [10], a well constructed irregular LDPC code is only 0.045dB away from the Shannon limit at of 10-6 over AWGN channel. In contrast, regular LDPC codes exhibits lower performance. However, the constructions of their paritycheck matrices are much easier than those of irregular codes. B. Reed-Solomon Codes Reed Solomon (RS) codes are the subset of BCH codes as well as linear block codes. A particular RS code is specified as RS ( n, k) with s-bit symbols [6]. This means that the encoder takes k s-bit data symbols each time and encodes them into a codeword of n s-bit symbols. There are n k parity symbols of s bits each. A RS decoder can correct up to t symbols that contain error in a codeword, where 2 t = n k [11]. Figure 2 shows a typical RS codeword. Figure 2: Typical RS codeword n DATA k PARITY 2t RS codes are particularly suitable to correct burst errors, where a series of bits in the codeword are received in errors. 3. Methodology The image transmission system with FEC scheme is shown in Figure 3. The source image is first deciphered into a row of long data prior to channel encoding process. The channel encoder consists of either LDPC or RS encoder. Then, the data are modulated using Binary Phase Shift Keying (BPSK) modulation scheme before being transmitted via wireless channel. In this work, the Racian and Rayleigh fading channels are considered for evaluation of the system. At the receiver, the reverse processes are used to reconstruct the received data.
Performance Optimization of Hybrid Combination of LDPC and RS Codes Using Image Transmission System Over Fading Channels 37 Figure 3: Image transmission system. Channel encoder BPSK Modulation AWGN + Fading Channel Channel decoder BPSK Demodulation In the hybrid FEC scheme the LDPC encoder is followed by RS encoder as shown in Figure 4. Then the encoded data are modulated with BPSK scheme prior transmission over the wireless channels. At the receiver, the reverse processes are used for reconstruction of the received data. LDPC codes combat the bit-errors and RS codes combat erasure errors over wireless channels. In this work, the overall FEC scheme code rate is fixed to ¼. Three combinations of code rates are used as shown below; Scheme 1: LDPC (1/2)+RS(10,20) Scheme 2: LDPC (1/3)+RS(18,24) Scheme 3: LDPC (3/4)+RS(10,30). Figure 4: Hybrid LDPC and RS system diagram LDPC encoder RS encoder BPSK Modulation AWGN + Fading Channel LDPC decoder RS decoder BPSK Demodulation 4. Results The mobile system used for simulation is assumed to have the source rate of 100 kbps and carrier frequency of 900 MHz. A mobile speed of 120 km/h is considered, resulting a maximum Doppler shift of 100 Hz. The Rayleigh and Rician fading channels are two typical channel models for real-world mobile communications. Rayleigh fading channel represents one (frequency-flat or single path) or more major reflected paths (frequency-selective or multiple path) from transmitter to receiver. The Rician fading channel has a direct line-of-sight path from transmitter to receiver. Rician fading occurs when one of the paths typically a line of sight signal, is much stronger than the others. The Rician K factor is defined as the ratio of signal power in dominant component over the scattered. In this simulation, a K factor of 2 is used. The simulation results are expressed in term of PSNR (Peak-Signal-Noise-Ratio), (Bit- Error-Rate) as well as the visual images of the reconstructed images, respectively. The PSNR is calculated using the following formula; Assume I( x, y) be the original M N image and I (x, y) be the reconstructed image ^
38 A.H.M Almawgani and M. F. M. Salleh 2 ( p) PNSR = 10log (2) MSE M N Where MSE = 1 ^ 2 [ I( x, y) I (x, y)] and p is the maximum value of a pixel. For example, M N x= 1 y= 1 the gray image is represented by 8bits per pixel and the peak pixel value p is 255. M and N represents the width and height of the image respectively. The performance results are obtained by comparing the grayscale image with the reconstructed image. The performance comparison is indicated by the calculated PSNR values. In this work, the image transmission system uses the 256 x 256 grayscale image Lena as the input source. First, the system with LDPC channel coding scheme is simulated followed by the system with RS codes. Finally the system with hybrid FEC scheme is simulated using the above mentioned experiment setup. Table 2 summarizes the simulation results obtained using different channel coding codes for various channel conditions as well as SNR values. The infinite value shows that the reconstructed image is identical to the input image. Hence, there is no data lost during transmission due to perfect protection of data from LDPC codes. Figure 5 shows the visual comparison between the reconstructed and input images for system with LDPC, RS and hybrid codes respectively. Table 2: The P via mobile channels versus various SNR with different codes PSNR(dB) Type of code LDPC (1/3) Hybrid RS(3/7) and LDPC (3/4) Type of Channel 2 6 10 14 18 22 frequency-flat ("single path") Rician fading 12 17 45 frequency-selective ("multiple path") Rician fading 10 17 20 35 frequency-flat ("single path") Rayleigh fading 11 14 23 43 55 frequency-selective ("multiple path") Rayleigh fading 10 12 17 26 54 frequency-flat ("single path") Rician fading 37 49 frequency-selective ("multiple path") Rician fading 11 17 30 38 frequency-flat ("single path") Rayleigh fading 10 10 18 29 39 47 frequency-selective ("multiple path") Rayleigh fading 10 10 10 10 13 13 frequency-flat ("single path") Rician fading 12 17 47 frequency-selective ("multiple path") Rician fading 10 17 31 38 frequency-flat ("single path") Rayleigh fading 11 14 25 45 frequency-selective ("multiple path") Rayleigh fading 9 10 20 28 57 Figure 5: Image reconstruction with frequency-selective ("multiple path") Rician fading channel at SNR=11 db (a) Original Lena image (b) RS (1/3), PSNR= 25 db (c) LDPC (1/3), PSNR= 31 db and (d) Hybrid between RS (3/7) and LDPC (3/4), PSNR=35.4 db. (a) (b) (c) (d) Figure 6 to 9 show the performance of image transmission system in term of versus various SNR with different channel codes i.e. LDPC, RS and hybrid codes. A code rate equal to 1/3 is
Performance Optimization of Hybrid Combination of LDPC and RS Codes Using Image Transmission System Over Fading Channels 39 used for RS, LDPC and their hybrid. In Figure 6 shows the performance of image transmission system with LDPC codes is the best in Rician channel because LDPC codes have been adapted successfully to the flat Rician fading channel [12]. However, the performance of RS is better than LDPC in Rayleigh channel as shown in Figure 8 and 9. The performance of the image transmission system with hybrid FEC scheme is much better than the system with single channel coding scheme of either LDPC or RS codes as shown Figure 7, 8 and 9. Figure 10 shows the performances of three hybrid combination of LDPC+RS schemes with different code rates while having the same overall channel rate of R=1/4. It can be seen clearly that the Scheme 2 with LDPC (1/3)+RS(18,24) outperforms the other combinations when simulated over the frequency-selective Rayleigh fading channel. This shows that in burst error channel, the RS codes are dominant protector for the transmitted data with code rate of 18/24 or 3/4. Figure 6: Performance of LDPC, RS and hybrid codes over frequency-flat ("single path") Rician fading Hybrid RS(3/7) and LDPC(3/4) LDPC(1/3) 2 3 4 5 6 7 8 9 10 11 12 Figure 7: Performance of LDPC, RS and hybrid codes over frequency-selective ("multiple path") Rician fading 10 0 Hybrid RS(3/7) and LDPC(3/4) LDPC(1/3) 10-5 2 4 6 8 10 12 14 16
40 A.H.M Almawgani and M. F. M. Salleh Figure 8: Performance of LDPC, RS and hybrid codes over frequency-flat ("single path") Rayleigh fading 10 0 Hybrid RS(3/7) and LDPC(3/4) LDPC(1/3) 2 4 6 8 10 12 14 16 18 20 Figure 9: Performance of LDPC, RS and hybrid codes over frequency-selective ("multiple path") Rayleigh fading 10 0 Hybrid RS(3/7) and LDPC(3/4) LDPC(1/3) 2 4 6 8 10 12 14 16 18 20 22
Performance Optimization of Hybrid Combination of LDPC and RS Codes Using Image Transmission System Over Fading Channels 41 Figure 10: Performance of hybrid codes over frequency-selective Rayleigh fading with different combinations of RS and LDPC codes 10 0 LDPC(1/2) + RS(10,20) LDPC(1/3) + RS(18,24) LDPC(3/4) + RS(10,30) 10-5 10-6 5 6 7 8 9 10 11 12 13 5. Conclusions The performance analysis of LDPC codes, RS codes, and their hybrid for FEC scheme of image transmission system has been performed. The Rayleigh and Rician fading channels are used in the simulation and the results are presented in term of PSNR, and the visual images of the reconstructed images. It has been observed that the Forward Error Correction (FEC) scheme with LDPC codes has superior performance in Rician fading channel and that with RS codes performs well in Rayleigh channel. The hybrid scheme always outperformed the other two systems for the same code rate for both Rician and Rayleigh fading channels. The hybrid combination of LDPC (1/3) and RS(18,24) reveals the optimized code rates selection for the overall code rate of 1/4. Acknowledgement This work is funded in part by the USM fellowship, MOSTI through Science Fund grant with Grant Number 6013353, and USM RU grant with Grant Number 814012.
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