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International Symposium INFOTEH-JAHORINA (INFOTEH)

Performance of Self-Corrected Min-Sum Decoding Algorithm for Decoders with Quantized Input

Aleksei Kharin, Igor Volkov, Aleksei Ovinnikov, Evgeny A. Likhobabin, Vladimir V. Vityazev

Published Mar 1, 2019• 1 citation
Publisher

Abstract

In this paper we explore the Min-Sum decoding algorithm for LDPC codes with self-correction (SC-MS) modification and how it affects the error correction performance for quantized input data. Three levels of quantization are observed: 3-, 2- and 1-bit.It was shown that the self-corrected modification significantly improves the performance of Min-Sum decoding algorithm with quantized input in comparison with basic Min-Sum decoding algorithm. Convergence of the algorithm is also better than for basic Min-Sum algorithm.Results of error correction performance and convergence are presented for two codes: CCSDS (8176, 7156) and IEEE 802.3an (2048, 1723) LDPC. The results are also presented for the SC APP-based and basic Min-Sum decoding algorithms.

DOI
10.1109/infoteh.2019.8717757

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In this paper we explore the Min-Sum decoding algorithm for LDPC codes with self-correction (SC-MS) modification and how it affects the error correction performance for quantized input data. Three levels of quantization are observed: 3-, 2- and 1-bit.It was shown that the self-corrected modification significantly improves the performance of Min-Sum decoding algorithm with quantized input in comparison with basic Min-Sum decoding algorithm. Convergence of the algorithm is also better than for basic Min-Sum algorithm.Results of error correction performance and convergence are presented for two codes: CCSDS (8176, 7156) and IEEE 802.3an (2048, 1723) LDPC. The results are also presented for the SC APP-based and basic Min-Sum decoding algorithms.
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 paper, we analyze the performance of quantized offset min-sum (MS) decoding algorithm and propose an optimally quantized offset MS algorithm for a flexible low-density parity-check (LDPC) decoder. It is known that the offset MS decoding algorithm is implemented with simplified hardware complexity and achieves good decoding performance. However, the finite precision effects in decoding LDPC codes result in performance different from floating point. The performance degradation is caused by different dynamic ranges of input data at high signal-to-noise ratio (SNR). The proposed offset MS algorithm uses the received data directly instead of log-likelihood ratio (LLR) data as the intrinsic information. It can achieve better performance than the conventional one since its offset factor is more effective at a wide range of SNR and the intrinsic information is quantized more robustly since it is independent of channel information. Also, it is possible for the proposed scheme to use a same quantization scheme for a flexible LDPC decoder, which can decode several kinds of LDPC codes. Simulation results show that our optimally quantized offset MS algorithms with 5-bits for (1728, 864) and (1728, 1296) irregular LDPC codes achieve better performance compared with the conventional offset MS algorithms with 6-bits quantization scheme.
This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.
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.
It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.
The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly outperform, the ideal belief-propagation algorithm at observed error rates.