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IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB)

Variable LLR scaling in LDPC min-sum decoding under horizontal shuffled structure

Kang Zhao, Yin Xu, Dazhi He, Yunfeng Guan, Wenjun Zhang

Published Jun 1, 2016• 3 citations
Publisher

Abstract

LDPC was first proposed in 1962, after that considerable achievements have been made both in decoding algorithms and also in the structure of the decoder. In terms of decoding algorithm, from belief propagation (BP) to min-sum (MS), then normalized MS (NMS) and finally to a more performance oriented variable MS (VMS) algorithm. In terms of the decoder structure, there are mainly two, flooding and shuffled structure (FS and SS), and flooding structure is mainly used in the past and the selection of variable factors in FS VMS has already been studied in the literature. As is known, the horizontal shuffled structure (HSS) are more hardware friendly and now widely deployed, thus to apply VMS algorithm to HSS has an important meaning for the industry. However, there is no effective method for the selection of variable factors in HSS VMS. Based on the study of FS VMS, this paper describes how to apply the generalized mutual information (GMI) based metric to HSS VMS reasonably and proposes the modified GMI based formula. Simulation results on a certain DVB-S2's LDPC code show that, by using modified formula for HSS VMS, we can obtain 0.13dB gain over HSS NMS and the performance is only 0.1dB away from that of HSS BP in terms of bit error rate (BER) at level 1e-7. And simulation results on a certain DVB-T2's LDPC code show that, by using modified formula for HSS VMS, we can obtain 0.04dB gain over HSS NMS and the performance is only 0.06dB away from that of HSS BP in terms of bit error rate (BER) at level 1e-7.

DOI
10.1109/bmsb.2016.7521937

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•Apr 1, 2014•1 citation
LDPC was first proposed in 1962, after that considerable achievements have been made both in decoding algorithms and also in the structure of the decoder. In terms of decoding algorithm, from belief propagation (BP) to min-sum (MS), then normalized MS (NMS) and finally to a more performance oriented variable MS (VMS) algorithm. In terms of the decoder structure, there are mainly two, flooding and shuffled structure (FS and SS), and flooding structure is mainly used in the past and the selection of variable factors in FS VMS has already been studied in the literature. As is known, the horizontal shuffled structure (HSS) are more hardware friendly and now widely deployed, thus to apply VMS algorithm to HSS has an important meaning for the industry. However, there is no effective method for the selection of variable factors in HSS VMS. Based on the study of FS VMS, this paper describes how to apply the generalized mutual information (GMI) based metric to HSS VMS reasonably and proposes the modified GMI based formula. Simulation results on a certain DVB-S2's LDPC code show that, by using modified formula for HSS VMS, we can obtain 0.13dB gain over HSS NMS and the performance is only 0.1dB away from that of HSS BP in terms of bit error rate (BER) at level 1e-7. And simulation results on a certain DVB-T2's LDPC code show that, by using modified formula for HSS VMS, we can obtain 0.04dB gain over HSS NMS and the performance is only 0.06dB away from that of HSS BP in terms of bit error rate (BER) at level 1e-7.
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.
Min Sum algorithm simplifies the non-linear check node operation of Belief Propagation algorithm via linear approximation, which greatly reduces the complexity of realization of decoder but degrades the performance as well. The resulting sub-optimality could be tempered via scaling of LLRs, e.g. fixed optimal scaling applied to Min Sum output resulting in the Normalized Min Sum algorithm, and variable scaling schemes gradually appear in literature. In this paper, we study the variable scaling decoding algorithm, and propose to generate variable scaling sequences via generalized mutual information (GMI) metric. Simulation results on real LDPC codes for different decoding algorithms have shown that our GMI metric performs better than the variable scaling scheme appearing in literature, and meanwhile improves substantially in terms of BER over the conventional Normalized Min Sum algorithm.
Implementing a belief propagation (BP) based LDPC decoder requires high degrees of parallelism using many component soft-in soft-output (SISO) decoding units to perform message passing from variable nodes to check nodes or vice versa. An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the complete parallel message-passing operation. The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes new techniques to improve three key elements of a GHSBP decoding algorithm, namely, the grouping method, the decoding schedule and the log-likelihood updating formulae. The (check nodes) grouping method and decoding schedule optimize certain design criterion. The new normalized min-sum updating formula with a self-adjustable correction (scaling) factor offers better nonlinear approximation. Numerical performance of new GHSBP algorithms that include part or all three new techniques indicate that the combination of the proposed grouping and decoding schedule yields a faster convergence rate and our modified min-sum algorithm gives performance superior to that of the conventional min-sum and normalized min-sum algorithm and is very close to that of the sum-product algorithm.
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.
Normalized Min-Sum Algorithms (NMSA) are extensively employed in trading LDPC (Low Density Parity Check) decoders due to their low complexity and reasonable performance close to the performance of sum product algorithm in terms of Error Rate. Our work is focused on the enhancement of error rate performances of NMS algorithm for the decoding of LDPC decoding. In this context we have proposed a Layered Normalized Min-Sum algorithm (LNMS), which employs an adaptive normalization factor to ameliorate the reliability of the information transmitted during the decoding process. To perform this analysis study LDPC coded communication system has been examined over Weibull fading channels and was analyzed for different decoding techniques by the help of comparative computer simulations. Simulation results indicate that the proposed decoding algorithm can achieve better Bit Error Rate (BER) performances closer to SP algorithm with the preservation of the principal characteristics of the MS algorithm.
Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it provides efficient and high-throughput implementation of LDPC decoders. Variable-Node Layered Belief Propagation (VL-BP) algorithm and their reduced-complexity derivatives for LDPC codes are presented. The VL-BP algorithm is a modification of Belief Propagation algorithm (BP), where the variable nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. Some simplifications can also be made to lower the complexity of both BP and CL-BP algorithms, and particularly the complexity of the check node update rule. In this paper, we consider Variable Node Layered BP (VL-BP) algorithm and propose an optimized min-sum VL-BP (MS VL-BP) algorithm for decoding LDPC code which has better performance not only from MS VL-BP algorithm but also from BP algorithm. In this decoding method, unlike other layered algorithms, we consider for the first layer a set of variable nodes that has a low value of the intrinsic information. Simulation results show that good performance can be achieved, and which can even be improved by the addition of either a normalization term or an additive offset term.