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International Symposium on Turbo Codes and Iterative Information Processing

Min-Sum decoding of irregular LDPC codes with adaptive scaling based on mutual information

Florence Alberge

Published Sep 1, 2016• 8 citations
Publisher

Abstract

Min-Sum decoding (MS) is an alternative to belief propagation decoding with substantially lower complexity. MS often results in an overestimation of the log likelihood ratio (LLR) in particular in the early stage of the iterative process. A linear post-processing is usually performed as a compensation. With regular low density parity check codes (LDPC), a fixed scaling of the LLR yields sufficiently good results. In contrast, adaptive strategies are mandatory with irregular codes. It is well known that the scaling factor is an increasing function of the reliability of the LLR. In most of the publications, the scaling factor is envisioned as a function of both the iteration number and the signal-to-noise ratio. It is proposed here to use the mutual information between extrinsics as a measure of the reliability of the LLR. A practical implementation is derived with reasonable complexity. Compared to the literature, the proposed method yields slightly better results in terms of BER and a significant reduction in the number of iterations.

DOI
10.1109/istc.2016.7593079

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Min-Sum decoding (MS) is an alternative to belief propagation decoding with substantially lower complexity. MS often results in an overestimation of the log likelihood ratio (LLR) in particular in the early stage of the iterative process. A linear post-processing is usually performed as a compensation. With regular low density parity check codes (LDPC), a fixed scaling of the LLR yields sufficiently good results. In contrast, adaptive strategies are mandatory with irregular codes. It is well known that the scaling factor is an increasing function of the reliability of the LLR. In most of the publications, the scaling factor is envisioned as a function of both the iteration number and the signal-to-noise ratio. It is proposed here to use the mutual information between extrinsics as a measure of the reliability of the LLR. A practical implementation is derived with reasonable complexity. Compared to the literature, the proposed method yields slightly better results in terms of BER and a significant reduction in the number of iterations.
Min-sum decoding is a low-complexity alternative to the so-called belief propagation and consists in simplification of the nonlinear operation on the log likelihood ratios (LLRs) in the check nodes. The resulting suboptimality may be tempered via appropriate scaling of the LLRs, e.g., the fixed optimal scaling in the normalized min-sum algorithm, and variable scaling algorithms gradually appearing in the literature. However, up to now, none of the papers studied variable scaling both as per iteration and as per different check node degree, due to the prohibitive complexity of multioptimization over space of too many parameters. In this paper, we propose a generalized mutual information (GMI) of LLRs as the criterion to search for the scaling factors for different check node degrees in every iteration in a 1-D thus low-complexity manner. This approach is first analyzed via density evolution, and in addition can be extended to practical LLRs based formulas via Monte Carlo tools to cope with the mismatch issue. Bit error rate simulation results on two low-density parity-check codes show that our proposed GMI metrics have a noticeable gain over the variable scaling schemes that appeared in the literature.
In this paper, a modified normalized Min-Sum algorithm (MNMSA) is proposed for decoding irregular Low Density Parity Check Codes (LDPC) with non-uniform degree distribution. The proposed algorithm provides an efficient decoding scheme to enhance the error performance of an irregular LDPC code without increasing the hardware complexity. An efficient 6- bit quantization scheme is utilized in the proposed algorithm with optimally combined normalization and down scaling factors to resolve the magnitude overestimation issue which occurs during iterative message passing process between the nodes. The simulation results demonstrate that the proposed algorithm achieves good decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without the requirement of complex arithmetic calculations. Compared to other min- sum based decoding algorithms the decoding process of the proposed MNMSA requires only fewer decoding iterations over wide range of signal- to- noise ratio (SNR) to achieve comparable decoding performance to that of Belief Propagation (BP) algorithm without increasing the hardware complexity.
This paper presents a low complexity Min-Sum algorithm for decoding irregular Low-Density Parity-Check (LDPC) codes. In the proposed algorithm, the significant improvement in the error correcting performance without enhancing the hardware complexity is achieved by employing adaptive and optimized normalization factors for both the extrinsic information and log-likelihood ratio data bits respectively. The experimental results demonstrate that the proposed algorithm with 6-bit non-uniform quantization achieves reasonable decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without increasing the hardware complexity by avoiding finite word length effects of soft information.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.
This paper proposes a new min-sum algorithm for low-density parity-check decoding. In this paper, we first define the negative and positive effects of the received signal-to-noise ratio (SNR) in the min-sum decoding algorithm. To improve the performance of error correction by considering the negative and positive effects of the received SNR, the proposed algorithm applies adaptive scaling factors not only to extrinsic information but also to a received log-likelihood ratio. We also propose a combined variable and check node architecture to realize the proposed algorithm with low complexity. The simulation results show that the proposed algorithm achieves up to 0.4 dB coding gain with low complexity compared to existing min-sum-based algorithms.
Low Density Parity Check Codes (LDPC) give groundbreaking performance which is known to approach Shannon's limits for sufficiently large block length. Historically and recently, LDPC have been known to give superior performance than concatenated coding. In the following paper, a proposal to modify the standard Min-Sum (MS) algorithm for decoding LDPC codes is presented. This is done by introduction of a difference to sum ratio factor, κ in the check to bit node updating process. The algorithm is further extended by implementing hard decision of the Bit-Flipping (BF) algorithm over the soft decision of MS algorithm. Simulation results demonstrate that the proposed algorithms are effective in imparting a better performance in terms of a lower bit error rate (BER) at medium to high signal to noise ratio (SNR) when compared to the traditional MS algorithm while adding fair amount of complexity.