Performance Analysis of BPSK and QPSK Using Error Correcting Code through A WGN

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1 201O International Conference on Networking and Information Technology Performance Analysis of BPSK and QPSK Using Error Correcting Code through A WGN Suzi Seroja Sarnin Norasimah Kadri Aiza Mahyuni Mozi suzis045@salam.uitm.edu.my norasimah@salam.uitm.edu.my, aiza _ mahyuni@salam.uitm.edu.my Norfishah Ab Wahab, Faculty of Electrical Engineer fishah@salam.uitm.edu.my Nani Fadzlina Nairn Faculty of Electrical Engineer nanifadzlina@salam.uitm.edu.my Abstract- This paper highlight the performance analysis of BPSK and QPSK using error correcting code. To calculate the bit error rate, different types of error correcting code were used through an Additive White Gaussian Noise (A WGN) channel. Bose- Chaudhuri-Hocquenghem (BCH), Cyclic code and hamming code were used as the encoder/decoder technique. Basically, the performance was determined in term of bit rate error (BER) and signal energy to noise power density ratio (EblNo). Both BPSK and QPSK were also being compared in the symbol error capability known as t in which expected that the performance is graded in response to the increasing of value of t. All simulations were done using MA TLAB ru007b software. In general BCH codes demonstrate better performance than Hamming code and Cyclic code for both BPSK and QPSK. Keywords: Additive White Gaussian Noise (A WGN) channel, Bose-Chaudhuri-Hocquenghem code (BCH), Hamming code, Cyclic code, energy per bit to noise power spectral density ratio (EblNo), Bit Error Rate (BER), codeword length (N), message length (K), error-correction capability (t). I. INTRODUCTION In digital communication, one of the most important technical issues which are synchronization problem and the error correction code used in this research are BCH code, cyclic code and hamming code which is these code have their unique advantage that suited to modify this problem. This is because the codes have the ability to recover the synchronization problem since this code is selfsynchronizable [1]. Owing to this reason, the codes have been choosing in order to study the performance of BPSK and QPSK apply in communication system. Since, this research is study the performance of phase shift keying modulation, it is necessary to find the most suitable channel that use to propagate the signal. Basically, channel is fall into three types which are fading channels, channels in which the noise stems from the others and A WGN channel. As the author compared all the three type of channels, the best suite channel for communication system is A WGN channel. This is because in the practical world is that A WGN never infinite in bandwidth. Thus, the destruction process is successfully safe since the receiver or measuring instrument has finite bandwidth [2]. In communications, the additive white Gaussian noise (A WGN) channel model is one in which the only impairment with a linear addition of wideband or white noise with a constant spectral density (expressed as watts per hertz of bandwidth) and a Gaussian distribution of amplitude. The model does not account for the phenomena of fading, frequency selectivity, interference, nonlinearity or dispersion [2]. However, it produces simple and tractable mathematical models which are useful for gaining insight into the underlying behavior of a system before these other phenomena are considered [1]. This paper analyzes the performance of BCH code, cyclic code and hamming code in A WGN fading channel using BPSK and QPSK as the modulation scheme. The study is mainly focuses on three type of error correction code without considering the time taken in each of the coded bits retransmission and other fading effects. This paper also investigates more parameters which affect the performance of the coding. The Hamming Encoder block creates a Hamming code with message length K and codeword length N. The number N must have the form 2M-I, where M is an integer greater than or equal to 3. Hamming codes can detect up to two simultaneous bit errors, and correct single-bit errors; thus, reliable communication is possible when the Hamming distance between the transmitted and received bit patterns is less than or equal to one. By contrast, the simple parity code cannot correct errors, and can only detect an odd number of /$ IEEE 178

errors [3]. Cyclic code are the subset of the class linear codes of linear codes that satisfy the every codeword c= (c1,...,cn), then the word (cn,cl,.

The input must contain exactly K elements. The output is a vector of length N For a given codeword length N, only specific message lengths K are valid for a BCH code.

This research purposely to analyze and simulate the performance of BPSK and QPSK using three types of error coding namely Hamming code, BCH code and Cyclic code.

2 errors [3]. Cyclic code are the subset of the class linear codes of linear codes that satisfy the every codeword c= (c1,...,cn), then the word (cn,cl,...,cn-l), obtained by a cycle shifts of the elements of C, is also code word. The BCH Encoder block creates a BCH code with message length K and codeword length N. The input must contain exactly K elements. The output is a vector of length N For a given codeword length N, only specific message lengths K are valid for a BCH code. No known analytic formula describes the relationship among the codeword length, message length, and error-correction capability [4]. This research purposely to analyze and simulate the performance of BPSK and QPSK using three types of error coding namely Hamming code, BCH code and Cyclic code. Besides, it also compares both BPSK and QPSK in order to yield the best performances in the term of BER as well as EblNo. Furthermore, the performance of three types of error coding in term of symbol error correcting capability (t) is also highlighted for both BPSK and QPSK. A comparison between simulated BER and theoretical BER has been made as illustrated in Figure 3. The BER value as EblNo varies from OdB to lodb. At OdB, simulated BER is and theoretical BER is , which comprised slightly difference values of At 10dB, the simulated BER is 3.00E-06 and the theoretical BER is 3.87E-06, which comprised a difference of 8.72E-07. Since the difference between the simulated BER and theoretical BER is insignificant, it can be observed that, the value of the theoretical BER is comparable to the simulated BER. B. Performance of a Communication System (using QPSK) without Error Correcting Codes. l.ooe+oo BER vs without coding (QPSK) II. METHODOLOGY I.OOE-OI This research begins with the construction of the block diagram of the communication system. This block diagram play an important role in order to make sure this project is satisfied with the communication system. The simulation was divided into four parts: simulation without block codes, simulation with hamming code, simulation with cyclic code and simulation with BCH code using the BPSK and QPSK modulator/demodulator. During this research, all simulations process representing the performance both BPSK and QPSK is done using software known as Matlab simulink. a: w co BER vs without coding (BPSK) 100E.00 I 0 100E E E'()3 100E'()4 100E'()S _BERlsimulated) -+(BER theory) Figure 1: BER performance of BPSK without error correcting codes III. RESULTS AND DISCUSSION A. Performance of a Communication System of BPSK without Error Correcting Codes "'<---- Eb/N. eer(simulated) eer (t'leory) Figure 2: The BER performance of QPSK without error correcting codes. By referring to Figure 2, at OdB, the simulated BER is and theoretical BER The slight difference between simulated BER and the theoretical BER is While, at lodb, the simulated BER is and the theoretical BER is , which comprised a difference of Still, the difference between the simulated BER and theoretical BER is insignificant, thus, it can be observed that, the value of the theoretical BER is comparable to the simulated BER. C. Performance of communication system of BPSK without and with error correcting codes using Hamming code BER Vs between without codes and Hamming codes 1.00E.. OO I,nOE-OI 1.00E-OS 1.00E E-08 -t--witoutcodes t-iamming{7,4) -a-hamming(63.57) Figure 3: BER vs () of a communication System (using BPSK) without error correcting codes, 179

Hamming code (7,4) and hamming code(63,57). From the graph in Figure 3, the results demonstrate that the BPSK using Hamming code (63, 57) has the lowest BER compared to others.

Peiformance of communication system of QPSK without and with error correcting codes using Hamming code.

By referring to graph in Figure 5, at 0 db, the BCH (31,11,5) coding demonstrated the highest value of 0.1481, which is followed by BCH (7,4,1) and without coding.

3 Hamming code (7,4) and hamming code(63,57). From the graph in Figure 3, the results demonstrate that the BPSK using Hamming code (63, 57) has the lowest BER compared to others. The BER for BPSK using Hamming (63, 57) is at OdB and 2.00E-08 at lodb. Thus, it can be observed that BPSK using hamming (63, 57) demonstrate better performance than others. D. Peiformance of communication system of QPSK without and with error correcting codes using Hamming code. BER Vs between without codes and Hamming Codes Figure 5: BER vs (EhINo) of a communication System (using BPSK) without error correcting codes, BCH code (7,4, I) and BCH code(31,11,5). By referring to graph in Figure 5, at 0 db, the BCH (31,11,5) coding demonstrated the highest value of , which is followed by BCH (7,4,1) and without coding. While, at 10dB, BCH (31,11,5) exhibited the lowest BER of O. The BER values of BCH (7,4,1) and without coding exhibited values of and 3.00E-06 respectively. Thus, it can be observed that BCH (31,11,5) has better performance than BCH (7,4,1) and without code. The higher error correction capability, t, will produce the better performance in communication system. 1.00E+OO 1.UUt:.-Ul J F. Peiformance of communication system of QPSK without and with error correcting codes using BCH code -+-without codes 1-lamming(7,4)...-tlamming(G3,57) BER vs without code and BCH code for QPSK 1.00[ E E-01 E!:!f:_ wlthoutcode Figure 4: BER vs (EhINo) of a communication System (using QPSK) without error correcting codes, Hamming code (7,4) and hamming code(63,57). By referring to graph in Figure 4, the performance of Hamming (7,4), Hamming (63, 57) and without codes are observed in term of BER. At OdB, Hamming (7, 4) is the highest BER compare to the others. At some point when EblNo reach 8dB, the value of Hamming (63, 57) and without code is almost the same which is and respectively. At lodb, the value of BER of Hammings (63, 57) demonstrated the least performance compared to Hamming (7, 4) and without code. Thusm, it can be observed that Hamming (63, 57) gives a better BER values. E. Peiformance of communication system of BPSK without and with error correcting codes using BCH code. BER vs Between without code and BCH code 1.00[-03 J 1.00E-05 -' ::: Eb ""N::-O----- BCH(7,4,l) -.-SCH ( ) Figure 6: BER vs (EhINo) of a communication System (using QPSK) without error correcting codes, BCH code (7, 4, I) and BCH code (63, 36, and 5). By referring to graph in Figure 6, at OdB, the highest BER value is BCH (7,4,1) with and the lowest BER is without code which is At lodb, the simulated BER of BCH (63,36,5) demonstrated the lowest value compared to the BER of BCH(7,4,1) and without code. The value BER of BCH (63,36,5) at lodb is 7.00E-05 and value of BCH(7,4,I) and without code are and respectively. This proves that when the higher value of t, the better performance of BER. G. Peiformance of communication system of BPSK without and with error correcting codes using cyclic code. 1.00E-01 l.00e-03 without code BCH (7,4,1) l.00e-05 -a-bch (31,11,5) l.00e E-(J8 180

BER vs without code and Cyclic code for BPSK l.ooe+oo l.ooe-01 l.ooe-02 BER vs () of a communication System (QPSK) for Hamming code, Cyclic code and BCH code. 1.OOE-tOO TI---- 1.OOE-Ol 10 11 t----:,.

ooe-07.. qpsk Ha"mlng(63,57,1) l00f-ol Figure 7: BER vs (EbINo) of a communication System (using BPSK) without error correcting codes, cyclic code (7, 4, 1) and cyclic code (15, 7, 2).

It can be observed that the values of BER of EblNo from OdB to 6dB is almost the similar to each other. Similarly, with value of t is being compared for t equal to 1 and t equal to 2 respectively.

Peiformance of communication system of QPSK without and with error correcting codes using cyclic code 1.OOE-OS..I.

4 BER vs without code and Cyclic code for BPSK l.ooe+oo l.ooe-01 l.ooe-02 BER vs () of a communication System (QPSK) for Hamming code, Cyclic code and BCH code. 1.OOE-tOO TI OOE-Ol t----:,.=_---- ffi "" l.ooe-03 without l.ooe-04 _cyclic code (7,4,1) 1.ooE02 -+-qpsk BCH(7,4,1) _qpsk 8CH(63,36,5) l.ooe-os -a-cycliccode (15,7,2) l.ooe-06 -a-qpsk cyclic code (31,H'::;) -qpslcrychc(/.4.1) -qpsk IlaTlming(7,4,l) l.ooe-07.. qpsk Ha"mlng(63,57,1) l00f-ol Figure 7: BER vs (EbINo) of a communication System (using BPSK) without error correcting codes, cyclic code (7, 4, 1) and cyclic code (15, 7, 2). By referring to graph in Figure 7, BPSK also has been compared for various value of symbol error correcting capability, t in term of BER. It can be observed that the values of BER of EblNo from OdB to 6dB is almost the similar to each other. Similarly, with value of t is being compared for t equal to 1 and t equal to 2 respectively. The fact that the higher value of t will cause the better performance in term of BER that has been achieved for Cyclic code (15,7,2) with 3.00E-07 at lodb while at OdB. H. Peiformance of communication system of QPSK without and with error correcting codes using cyclic code 1.OOE-OS..I...-- Figure 9: BER vs (EbINo) of a communication System (QPSK) for Hamming code, Cyclic code and BCH code_ By referring to graph in Figure 9, the results show that the best performance occurs when the communication system uses a BCH code with N=63, K=36 and t=5 with QPSK modulator/demodulator. BER vs () of a communication System (BPSK) for Hamming code, Cyclic code and BCH code. l.ooe+oo, l.u<jt-<n l.wt.()1 bpsk BCr(31,ll.l) BER vs without and Cyclic Code for QPSK m... l.wt.-<h bpsk 0Icl;c(7,4,1) l.wt.()l -bp,kqci;c(15,7,l1 l.00f-o\ bpk HdlUlllillg(7,4.1) l.ode-01 t-----"...,riiib.:, (lOF-Oh 1.00F-07 l.otlf-or _bpk Hdllunil1g(63,57,1).. bpsk BCr(7.4,1) l.00e ' l.ode \--- l.00[-04 -' ,-, [b/no wi!h:>ut _cyciiccodep,l,l) -a-cycli::codc (31.21,5) Figure 8: BER vs (EbINo) of a communication System (using QPSK) without error correcting codes, cyclic code (7, 4, 1) and cyclic code (31, 21, 5). By referring to graph in Figure 8, it can be observed that the smallest value of BER is when using Cyclic code (31, 21, 5). 1. Peiformance Comparison between Communication System with BCH Code, cyclic code and with Hamming Code Using BPSK modulator/demodulator and QPSK modulator/demodulator. Figure 10: BER vs (EbINo) of a communication System (BPSK) for Hamming code, Cyclic code and BCH code_ As in Figure 10, the results show that the best performance occurs when the communication system uses a BCH code with N=31, K=l1 and t=5 with BPSK modulator/demodulator. In general, the BCH codes are better than Hamming code and Cyclic code. This is because Hamming codes and Cyclic code are capable of detecting and correcting single errors only whereas BCH codes are capable of detecting and correcting multiple errors. IV. CONCLUSION The simulation shows that the performance of QPSK and BPSK is dependent on several factors. The symbol error correcting, t, codeword length, N and message length, K. Based on the result obtained, it can be concluded that the best performance is graded when the value of t is increased. The best performance occur when communication system use a BCH code with N=31, K=l1 and t=5 with BPSK 18 1

5 modulator or demodulator. The higher of value of N, K and t is better the performance and in general BCH codes are better than Hamming code and cyclic code Hence, the objective of this research is successfully achieved in which is success to analyze and simulates the performance of BPSK and QPSK using different types of error correcting codes through A WO N channel. For instance, the order phase shift keying modulation is determined the quality of the modulation process and also determine the capacity data that can be transfer. As the order of PSK is increase, the performance will be degraded since the order of constellation is more susceptible to noise. Besides, the symbol-error correcting capability (t) also give some impact to the performance of PSK since this research apply error correction code as the encode/decode technique. [15] M.A. Kousa and A.H. Mugaibel, "Puncturing effects on turbo codes," IEE Pme. Commun. Vol. 149, No 3, June 2002 [16] M. Liinaharja, "Studies On the Performance of Some ARQ Schemes," Helsinki University of Technology Communications Laboratory Tech. Rep. T54, 2006 [17] S. Falahati, P. Frenger, P. Orten, T. Ottosson and A. Svensson, "Convolutional Coding and ARQ Schemes for Wireless Communications," in Proc. IEEE Nordic Radio Symposium, Saltsjobaden, Sweden, October 1998, pp203-21o. [18] P. Robertson, E. Villebrum and P. Hoher, "A comparison of optimal and suboptimal MAP decoding algorithms operating in the Log-domain", Int. Conf. on Communications, pp , 1995 [19] S. Lin and D. 1. Costello, "Error Control Coding: Fundamentals and Applications," 2nd ed. Prentice Hall, [20] M. Kouraichi, O. B. Belghith, A. Kachouri and L. Kamoun, "Evaluation of SOYA algorithm in Turbo code", IEEE Transactions on Information Theory, pp , March REFERENCES [I] keying#quadrature ha seshift_ keying_.28qpsk.29 [2] Vishakan Ponnampalam, Branka Vucetic, "Maximum Likelihood Decoding Of Reed Solomon Codes," ISIT 1998, Cambridge MA, USA, August 16-August 21. [3] MacWilliams, F. J. and Sloane, N.1. A. The Theory of Error Correcting Codes. Amsterdam, Netherlands: North-Holland, [E-book] Available at [4] Jorge Castineira Moreira and Patrick Guy Farrell, Essentials of Error Control Coding.Argentina: wiley and Son, 2006.[Ebook] Available at [5] Andre Neubauer, Jurgen Freudenberger, and volken Kuhn. Coding Theory Algorithms, Architectures and Application.England: Wiley and son, [E-book] Available at [6] U. Elisabeth, "Hybrid ARQ Using Serially Concatenated Block Codes for Real-Time Communication - An Iterative Decoding Approach," Licentiate Thesis, Chalmers University of Technology, Sweden, 2001 [7] K. Oteng-Amoako, 1. Yuan, S. Nooshabadi, "Selective Hybrid ARQ turbo schemes with various Combining methods in Fading Channels," in Proceeding of Workshop on Modelling and Optimisation on Mobile Ad Hoc Networking and Computing (Wiopt03), France, 2003 [8] F. Chiti, R. Fantacci, F. Versaci, "Turbo soft combining hybrid ARQ techniques: theory and application to 3G wireless networks," in Annales des Telecommunications, 2005, v:60, n:i-2, pp: [9] L. Bahl, 1. Jelinek, 1. Raviv, and F. Raviv, "Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate," IEEE Trans. on Information Theory, vol. IT-20, pp , Feb [10] G. D. Forney, "The Viterbi Algorithm," Proc. Of the IEEE, vol. 61, pp , Mar [II] Tsg-Ran WgI#17, "Performance Comparison of Hybrid-ARQ Schemes," Motorola, Stockholm, Sweden, Tech. Rep. TSGRI # 17(00)1396-Adhoc#24-HSDPA, [12] A. Banerjee, D. 1. Costello Jr., T. E. Fuja, "Performance of hybrid ARQ schemes using turbo trellis coded modulation for wireless channels," University of Notre Dame, [13] T. M. Kim, H. Shin, and J. H. Lee, "A novel error detection scheme for Turbo coded hybrid ARQ," in Proc. of the IEEE VTC 2002-Fall, Vancouver, Canada, Sept , pp , [14] T. Rodrigues, R. D. Souza, M. E. Pellenz, "Hybrid ARQ Scheme Based on Recursive Convolutional Codes and Turbo Decoding", IEEE Transactions on Communications,

Performance Evaluation and Comparative Analysis of Various Concatenated Error Correcting Codes Using BPSK Modulation for AWGN Channel

Performance Evaluation and Comparative Analysis of Various Concatenated Error Correcting Codes Using BPSK Modulation for AWGN Channel International Journal of Electronics and Communication Engineering. ISSN 0974-2166 Volume 5, Number 3 (2012), pp. 235-244 International Research Publication House http://www.irphouse.com Performance Evaluation