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Mediterranean Conference on Embedded Computing (MECO)

Efficient BP-based Decoding Algorithms for QC-LDPC Codes

Konstantin Zavertkin, Anastasia Panarina, Aleksei Ovinnikov, Evgeny A. Likhobabin

Published Jun 7, 2021• 1 citation
Publisher

Abstract

In this paper we propose to use a self-correction technique with two computationally efficient LDPC decoding algorithms: QRCBP and adjusted min-sum. It is shown that using such a technique allows to improve performance of this algorithms both in error floor and waterfall regions. Also comparison with other BP-based simplified decoding algorithms is presented for three quasi-cyclic LDPC codes.

DOI
10.1109/meco52532.2021.9460244

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In this paper we propose to use a self-correction technique with two computationally efficient LDPC decoding algorithms: QRCBP and adjusted min-sum. It is shown that using such a technique allows to improve performance of this algorithms both in error floor and waterfall regions. Also comparison with other BP-based simplified decoding algorithms is presented for three quasi-cyclic LDPC codes.
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.
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.
Low-density parity-check (LDPC) codes have attracted tremendous attention for their excellent error-correction performance and inherent fitness for high-parallelism implementation. With great complexity reduction and friendly for hardware implementation, the min-sum (MS) decoding algorithm for LDPC codes gains widespread applications in practical. In the MS decoding algorithm, finding the first two minima among input variable-to-check messages is the most complex part. To further reduce the complexity of the MS decoding algorithm, an efficient single-minimum (single-min) based layered MS decoding for quasi-cyclic LDPC (QC-LDPC) codes is proposed in this paper. It is found that statistically the difference between the first minimum and second minimum increases as the decoding becomes more convergent. Accordingly, in the proposed single-min scheme, the second minimum is approximately derived based on the first minimum and an index indicating the convergence degree. Besides, some other metrics that are easily obtained are used to refine the second minimum. Simulation results show that the proposed method can significantly improve the error-correction performance and lower the average number of iterations, compared with the state-of-the-art single-min based MS decoding algorithms.
Low-density parity-check (LDPC) have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost , time, power and bandwidth requirements of target applications. Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important subclass of LDPC codes that are known as one of the most effective error controlling methods. Quasi cyclic codes are known to possess some degree of regularity. Many important communication standards such as DVB-S2 and 802.16e use these codes. The proposed Optimized Min-Sum decoding algorithm 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.Proposed decoder is well matched for VLSI implementation and will be implemented on Xilinx FPGA family
Compared with the BP decoding algorithm,the min-sum decoding algorithm has higher error floor for LDPC codes over the binary symmetric channel(BSC).In order to solve this problem,a modified algorithm is presented.The proposed algorithm can reduce memory overhead and accelerate the convergence of decoding algorithm by using the thought of multi-level quantification and considering the knowledge both extra messages for each node and received values from the channel,respectively.Simulation results show that the improved min-sum algorithm with three or four levels approach and even surpass floating-point BP decoding algorithm in frame error rate(FER) performance over the BSC.
This paper presents a different decoding techniques for Quasi-Cyclic (QC) Low Density Parity Check (LDPC) code. QC-LDPC code is proposed to reduce the complexity of the Low Density Parity Check code while obtaining the similar performance. The encoding and decoding processes of these codes are easy to simplify and implement. The algorithm used for encoding and decoding are based on matrices and implemented on MATLAB for simulation results. In this paper decoding technique QC-LDPC is introduced and compare the performance of LDPC and QC-LDPC. The decoding techniques is conducted by different algorithms such as Bit Flipping (BF), Belief Propagation (BP) Log, Belief Propagation (BP) Probabilistic (Prob), Belief Propagation (BP) Log Simple.