Reliability Analysis of the Sum-Product Decoding Algorithm for the PSK Modulation Scheme
الموضوعات :
Hadi Khodaei Jooshin
1
(University of Tabriz)
Mahdi Nangir
2
(University of Tabriz)
الکلمات المفتاحية: LDPC Codes , BER Performance , SPA , Channel Decoding Algorithm , Rate , Channel Capacity,
ملخص المقالة :
Iteratively decoding and reconstruction of encoded data has been considered in recent decades. Most of these iterative schemes are based on graphical codes. Messages are passed through space graphs to reach a reliable belief of the original data. This paper presents a performance analysis of the Low-Density Parity-Check (LDPC) code design method which approach the capacity of the Additive White Gaussian Noise (AWGN) model for communication channels. We investigate the reliability of the system under Phase Shift Keying (PSK) modulation. We study the effects and advantages of variation in the codeword length, the rate of parity-check matrix of the LDPC codes, and the number of iterations in the Sum-Product Algorithm (SPA). By employing an LDPC encoder prior to the PSK modulation block and the SPA in the decoding part, the Bit Error Rate (BER) performance of the PSK modulation system can improve significantly. The BER performance improvement of a point-to-point communication system is measured in different cases. Our analysis is capable for applying any other iterative message-passing algorithm. The code design process of the communication systems and parameter selection of the encoding and decoding algorithms are accomplished by considering hardware limitations in a communication system. Our results help to design and select paramours efficiently.
[1] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding : Turbo-codes,” In Communications, 1993. ICC ’93 Geneva. Technical Program, Conference Record, IEEE International Conference on,, vol. 2, pp. 1064–1070.
[2] C. E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, 1948, pp. 379–423 and 623–656.
[3] D. J. C. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” IEEE electronics letters 32, no. 18 ,1996, pp. 1645-1646.
[4] D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Transactions on Information Theory, vol. 45, no. 2, Aug 1999, pp. 399–431.
[5] H. Hatami, DG. Mitchell, DJ. Costello, TE. Fuja. “Performance bounds and estimates for quantized LDPC decoders”. IEEE Transactions on Communications. 2019 Nov 13;68(2):683-96.
[6] R.G. Gallager, “Low-density parity-check codes,” IRE Trans. Inf. Theory, 1962, IT-8, pp. 21–28.
[7] B. Rong, Y. Wu and G. Gagnon, “Multi -Layer Iterative LDPC Decoding for Broadband Wireless Access Networks: A Recursive Shortening Algorithm,” IEEE Transactions on Wireless Communications, vol. 12, no. 3, March 2013, pp. 1320–1327.
[8] T. Koike-Akino, K. Kojima, D.S. Millar, K. Parsons, T. Yoshida and T. Sugihara, “Pareto Optimization of Adaptive Modulation and Coding Set in Nonlinear Fiber-Optic Systems,” Journal of Lightwave Technology, Vol. 35, no. 4, February 2017, pp.1041–1049.
[9] R. Xue, H. Yu and Q. Cheng, “Adaptive Coded Modulation Based on Continuous Phase Modulation for Inter-Satellite Links of Global Navigation Satellite Systems,” IEEE Access, vol. 6, April 2018, pp. 20652–20662.
[10] S. Chen, K. Peng, J. Song and Y. Zhang, “Performance Analysis of Practical QC-LDPC Codes: From DVB-S2 to ATSC 3.0,” IEEE Transactions on Broadcasting, vol. 65, no. 1, March 2019, pp. 172–178.
[11] J. Song, C. Zhang, K. Peng, J. Wang, C. Pan, F. Yang, J. Wang, H. Yang, Y. Xue, Y. Zhang, and Z. Yang, “Key Technologies and Measurements for DTMB-A System,” IEEE Transactions on Broadcasting, vol. 65, no. 1, March 2019, pp. 53–64.
[12] S.-K. Ahn, K.-J. Kim, S. Myung, S.I. Park and K. Yang, “Comparison of Low-Density Parity-Check Codes in ATSC 3.0 and 5G Standards,” IEEE Transactions on Broadcasting, vol. 65, no. 3, September 2019, pp. 489-495.
[13] KS. Chan, A. James, S. Rahardja. “Evaluation of a Joint Detector Demodulator Decoder (JDDD) Performance With Modulation Schemes Specified in the DVB-S2 Standard”. IEEE Access. 2019 Jun 19;7:86217-25.
[14] S. Papaharalabos and P. T. Mathiopoulos, “Simplified sum-product algorithm for decoding LDPC codes with optimal performance,” Electronics Letters, vol. 45, no. 2, January 2009, pp. 116-117.
[15] IB. de Almeida, GP. Aquino, LL. Mendes. “Iterative Receiver for Non-Orthogonal Waveforms Based on the Sum-Product Algorithm”. In 16th International Symposium on Wireless Communication Systems (ISWCS) 2019 Aug 27, pp. 38-42.
[16] F. Vatta, A. Soranzo, F. Babich. “More accurate analysis of sum-product decoding of LDPC codes using a Gaussian approximation”. IEEE Communications Letters. 2018 Dec 11;23(2):230-3.
[17] J. Ziv and A. Lempel, “A Universal Algorithm for Sequential Data Compression,” IEEE Transactions on Information Theory, vol. 23, no. 3, May 1997, pp. 337–343.
[18] J. Ziv and A. Lempel, “Compression of Individual Sequences via Variable-Rate Coding,” IEEE Transactions on Information Theory, vol. 24, no. 5, September 1978, pp. 530–536.
[19] J. A. Storer and T. G. Szymanski, “Data Compression via Textual Substitution,” Journal of the ACM, vol. 29, no. 4, October 1982, pp. 928–951.
[20] M. Nangir, H. Behroozi, and M. R. Aref, “A new recursive algorithm for universal coding of integers”. Journal of Information Systems and Telecommunication (JIST), vol. 3, no. 1, Jan 2015, pp. 1–6.
[21] M. Nangir, R. Asvadi, M. Ahmadian-Attari, and J. Chen, “Binary CEO problem under log-loss with BSC test-channel model”, In 2018 29th Biennial Symposium on Communications (BSC), IEEE, Jun 2018, pp. 1–5.
[22] D. Harita, KP. Rajan. “Reliability Variance based Weighted Bit Flipping Algorithms for LDPC”. In 9th International Conference on Cloud Computing, Data Science & Engineering (Confluence), 2019 Jan 10, pp. 593-595.
[23] J. Liu, J. Yuan, J. Sha. “Symbol-Based Algorithms for Decoding Binary LDPC Codes with Higher-Order Modulations”. In IEEE International Symposium on Circuits and Systems (ISCAS) 2019 May 26, pp. 1-5.
[24] R. Tanner, “A recursive approach to low complexity codes,” IEEE Transactions on Information Theory, vol. 27, no. 5, 1981, pp. 533–547.
[25] T. Richardson and R. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Transactions on Information Theory, vol. 47, no. 2, Feb 2000, pp. 638–656.
