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Mediterranean Conference on Embedded Computing (MECO)

Self-corrected UMP-APP decoding of LDPC codes

Vladimir V. Vityazev, Evgeny A. Likhobabin

Published Jun 1, 2016• 5 citations
Publisher

Abstract

In this paper we propose a very simple but powerful self-correction method for the UMP-APP decoding of LDPC codes. Like self-corrected min-sum decoding, our method does not try to correct the check node processing approximation, but it modifies the variable node processing by erasing unreliable messages. Monte-Carlo simulations show that the proposed self-corrected UMP-APP decoding performs better then common UMP-APP decoding. Estimation of the complexity and average number of iteration for self-corrected UMP-APP algorithm are also shown.

DOI
10.1109/meco.2016.7525774

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In this paper we propose a very simple but powerful self-correction method for the UMP-APP decoding of LDPC codes. Like self-corrected min-sum decoding, our method does not try to correct the check node processing approximation, but it modifies the variable node processing by erasing unreliable messages. Monte-Carlo simulations show that the proposed self-corrected UMP-APP decoding performs better then common UMP-APP decoding. Estimation of the complexity and average number of iteration for self-corrected UMP-APP algorithm are also shown.
In this paper we propose a very simple but powerful self-correction method for the min-sum decoding of LPDC codes. Unlike other correction methods known in the literature, our method does not try to correct the check node processing approximation, but it modifies the variable node processing by erasing unreliable messages. However, this positively affects check node messages, which become symmetric Gaussian distributed, and we show that this is sufficient to ensure a quasi-optimal decoding performance. Monte-Carlo simulations show that the proposed self-corrected min-sum decoding performs very close to the sum-product decoding, while preserving the main features of the min-sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low-Density Parity-Check (LDPC) code is a linear block code approaching the Shannon limit. The improvement of the decoding performance of LDPC codes is a hot research direction today. To improve the decoding performance of the self-correcting min-sum (SCMS) algorithm, an improved self-correcting min-sum (ISCMS) algorithm is proposed based on this algorithm. In the iterative decoding process of the ISCMS algorithm, the update rule of the check node (CN) is optimized to the update rule of the CN of the IOMS algorithm, which improves the accuracy of decoding from the processing of the CN. Simulation results show that the proposed ISCMS algorithm has better error performance and convergence performance than the SCMS algorithm with a small increase in computational complexity.
The min-sum (MS) and approximate-min* (a-min*) algorithms are alternatives of the belief propagation (BP) algorithm for decoding low-density parity-check (LDPC) codes. To lower the BP decoding complexity, both algorithms compute two magnitudes at each check node (CN) and pass them to the neighboring variable nodes (VNs).In this work we propose a new algorithm, ga-min*, that generalizes the MS and a-min* in terms of number of incoming messages to a CN.We analyze and demonstrate a condition to improve the performance when applying self-correction to the ga-min*. Simulations on 5G LDPC codes show that the proposed decoding algorithm yields comparable performance to the a-min* with a significant reduction in complexity, and it is robust against LLR mismatch.
In this paper we explore the impact of self-correction (SC) modification on performance of a posteriori probability (APP) based decoding algorithm for LDPC codes. Influence of self-correction technique was investigated for decoders with 3, 2 and 1 bit input quantization. It was shown that performance of decoders with quantized input can be significantly improved in comparison with regular APP-based decoding algorithm, and in some cases with Min-Sum algorithm. Convergence of algorithm is almost the same as for Min-Sum decoding. Performance and convergence results are presented for two CCSDS (8176, 7156) and IEEE 802.3an (2048, 1723) LDPC codes for APP-based, SC APP-based and Min-Sum decoding algorithms.
In this work, we introduce a very simple technique that improves the performance of the belief propagation (BP) and BP-based decoders in waterfall and error-floor regions. Unlike other techniques known in literature, this technique does not explicitly use any trapping sets elimination algorithm, but it modifies the variable node processing by erasing unreliable messages. However, this modification positively affects on the overall decoder performance, and reduces the error floors. At the same time self-correction have insignificant contribution in total computational complexity of LDPC decoder. Moreover it is shown, that such a modification can be used for any BP-based decoding algorithm.