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IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

On irregular LDPC codes with quantized message passing decoding

Michael Meidlinger, Gerald Matz

Published Jul 1, 2017• 23 citations
Publisher

Abstract

Irregular low-density parity-check (LDPC) codes are among the best codes currently known. Unfortunately, the performance of existing codes may deteriorate substantially with practical finite-precision decoder implementations. This motivates us to extend our previous work on finite-alphabet decoders based on look-up tables (LUTs) to irregular LDPC codes. We devise a joint design of the LUTs used for different node degrees and present a strategy to optimize the degree distribution (DD) of the LDPC code under LUT decoding. Numerical simulations show that with 4-bit LUT decoding the resulting codes outperform state-of-the-art codes with floating point min-sum (MS) decoding.

DOI
10.1109/spawc.2017.8227780

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Irregular low-density parity-check (LDPC) codes are among the best codes currently known. Unfortunately, the performance of existing codes may deteriorate substantially with practical finite-precision decoder implementations. This motivates us to extend our previous work on finite-alphabet decoders based on look-up tables (LUTs) to irregular LDPC codes. We devise a joint design of the LUTs used for different node degrees and present a strategy to optimize the degree distribution (DD) of the LDPC code under LUT decoding. Numerical simulations show that with 4-bit LUT decoding the resulting codes outperform state-of-the-art codes with floating point min-sum (MS) decoding.
We consider discrete message passing (MP) decoding of low-density parity check (LDPC) codes based on information-optimal symmetric look-up table (LUT). A link between discrete message labels and the associated log-likelihood ratio values (defined in terms of density evolution distributions) is established. This link gives rise to an algebraic structure on the message labels and leads to an interpretation of LUT decoding as a form of quantized belief propagation. We then exploit the algebraic structure for low-complexity LUT decoder designs. Our LUT decoding framework is the first to also apply to irregular LDPC codes by taking into account the degree distribution in a joint LUT design. We exploit the relation between LUT decoding and belief propagation to obtain stability conditions and irregular LDPC code designs optimized for LUT decoding. The resulting decoders outperform floating-point precision min-sum decoders at LUT resolutions as low as 3 bit s for regular codes and 4 bits for irregular codes.
We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic criterion. We show that even with message resolutions as low as 3 bits, the proposed algorithm can achieve better error rates than a floating-point min-sum decoder. Moreover, we study in detail the effect of different decoder design parameters, like the design SNR and the LUT tree structure on the performance of our decoder, and we propose some complexity reduction techniques, such as LUT re-use and message alphabet downsizing.
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.
In practical implementations, message passing decoding of LDPC codes has to be implemented with finite precision, i.e., the messages are quantized with a small number of bits. This results in a significant performance degradation with respect to decoding with high-precision messages. Recently, we have proposed so-called information bottleneck decoders to design finite-precision decoders with error-correction performance close to high-precision belief-propagation decoding. Earlier works solely focus on the design of information bottleneck decoders for regular LDPC codes or specifically optimized irregular LDPC codes. In this paper, we extend the concept of information bottleneck decoders to irregular LDPC with arbitrary degree distribution. We show that this extension is not straightforward and requires an additional information-optimum step. Therefore, we devise a novel intermediate construction step which we call message alignment. Exemplary numerical simulations using an irregular LDPC code taken from the IEEE 802.11 standard show that incorporating message alignment in the construction yields a 4-bit information bottleneck decoder which performs only 0.15 dB worse than a double-precision belief propagation decoder and outperforms a min-sum decoder.
In this paper, we propose a general framework of the mutual infomration-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes, which can outperform the state-of-the-art lookup table (LUT) decoder by using simple mappings and fixed-point additions for the node updates. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and it can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm, leading to the MIM quantized BP (MIM-QBP) decoder and the MIM quantized MS (MIM-QMS) decoder, respectively. In particular, we approximate the check node (CN) update of the MIM-QBP decoder by a max-product operation and obtain the MIM-QMS decoder, which simplifies the decoder design and requires less resource consumption. To avoid the precision degradation, we introduce a dynamic reconstruction method to optimize the variable node update for different iterations. Some practical aspects of the proposed decoders such as the design and decoding complexity are also discussed. Simulation results show that the MIM-QBP decoder outperforms the LUT decoders in the waterfall region with both 3-bit and 4-bit precision. Moreover, the 4-bit MIM-QMS decoder can even surpass the floating-point BP decoder in the error-floor region.
The Belief-propagation (BP) algorithm is a powerful decoder for LDPC codes. However, the BP algorithm requires the high complexity of the check node operation. Therefore, in the previous works, a lookup table (LUT)-based decoder has been proposed for LDPC codes. In this work, we propose the LUT design for protograph LDPC codes. Our LUT design can support the parallel edge, variable node with degree-1 and punctured variable node. As a result, the coding losses of 2-, 3- and 4-bit quantization of LUT decoder are 1.6, 0.5 and 0.1 dB compared to BP algorithm.