Dynamics and performance analysis of analog iterative decoding for low-density parity-check (LDPC) codes

• Published in: IEEE transactions on communications Vol. 54; no. 1; pp. 61 - 70
• Main Authors: Hemati, S., Banihashemi, A.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Analog circuits; Analog decoding; Applied sciences; Asymptotic properties; asynchronous iterative methods; Belief propagation; belief propagation (BP); Code standards; Codes; Coding, codes; Decoders; Decoding; Dynamic tests; Dynamics; dynamics of iterative decoding; Exact sciences and technology; Floods; Gaussian distribution; Information, signal and communications theory; Iterative algorithms; Iterative decoding; Iterative methods; low-density parity-check (LDPC) codes; Mathematical models; min-sum (MS); Parity check codes; Performance analysis; Signal and communications theory; Steady-state; Strontium; Studies; successive relaxation (SR); successive substitution (SS); sum-product; Telecommunications and information theory; Bit error rate; belief propagation (BP); Data transmission; successive substitution (SS); Iterative method; Decoding; successive relaxation (SR); dynamics of iterative decoding; asynchronous iterative methods; iterative decoding; low-density parity-check (LDPC) codes; min-sum (MS); Analog decoding; Relaxation method; Parity check codes; Performance analysis; sum-product
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2005.861668

Conventional iterative decoding with flooding or parallel schedule can be formulated as a fixed-point problem solved iteratively by a successive substitution (SS) method. In this paper, we investigate the dynamics of a continuous-time (asynchronous) analog implementation of iterative decoding, and show that it can be approximated as the application of the well-known successive relaxation (SR) method for solving the fixed-point problem. We observe that SR with the optimal relaxation factor can considerably improve the error-rate performance of iterative decoding for short low-density parity-check (LDPC) codes, compared with SS. Our simulation results for the application of SR to belief propagation (sum-product) and min-sum algorithms demonstrate improvements of up to about 0.7 dB over the standard SS for randomly constructed LDPC codes. The improvement in performance increases with the maximum number of iterations, and by accordingly reducing the relaxation factor. The asymptotic result, corresponding to an infinite maximum number of iterations and infinitesimal relaxation factor, represents the steady-state performance of analog iterative decoding. This means that under ideal circumstances, continuous-time (asynchronous) analog decoders can outperform their discrete-time (synchronous) digital counterparts by a large margin. Our results also indicate that with the assumption of a truncated Gaussian distribution for the random delays among computational modules, the error-rate performance of the analog decoder, particularly in steady state, is rather independent of the variance of the distribution. The proposed simple model for analog decoding, and the associated performance curves, can be used as an "ideal analog decoder" benchmark for performance evaluation of analog decoding circuits.