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arXiv:1512.00210 · Asilomar Conference on Signals, Systems and Computers (ACSSC)

Quantized message passing for LDPC codes

Michael Meidlinger, Alexios Balatsoukas‐Stimming, Andreas Peter Burg, Gerald Matz

Published Nov 1, 2015• 29 citations
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Abstract

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.

DOI
10.1109/acssc.2015.7421419

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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.
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.
In this paper, we propose a finite alphabet message passing algorithm for LDPC codes that replaces the standard min-sum variable node update rule by a mapping based on generic look-up tables. This mapping is designed in a way that maximizes the mutual information between the decoder messages and the codeword bits. We show that our decoder can deliver the same error rate performance as the conventional decoder with a much smaller message bit-width. Finally, we use the proposed algorithm to design a fully unrolled LDPC decoder hardware architecture.
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.
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.
Compared with the sum-product algorithm (SPA) with high decoding complexity for low-density parity-check (LDPC) codes, its approximated version, the min-sum algorithm (MSA), reduces the computational complexity at the cost of slight performance degradation. In order to compensate the oversized check-node messages in the MSA, the effect of clipping on variable-node messages is investigated under two-bit resolution. Our results show that the performance of clipped MSA degrades at the high bit error rate (BER) and increases at the low BER as clipping threshold enlarges. Based on these results, we propose a modified quantized MS decoding algorithm where the adaptive clipping threshold is applied on the variable-node messages according to the number of unsatisfied checks per-iteration. The adaptive rule is designed for easy hardware implementations. Numerical results show that the proposed algorithm has considerable improvement in performance compared with the MSA under two-bit precision. And it can achieve the performance near the SPA for some short-length LDPC codes.
Very high data rates and decoding computational complexity place strict constraints in 5G and 6G communications. In this paper, non-uniform Quantized Decoding algorithm is proposed for Low-density Parity Check codes (LDPC). In the proposed algorithm, the check node updating process is carried out using quantization, which reduces complexity. The Sum Product Algorithm (SPA) is iterative message passing decoding techniques offer the optimal performance for LDPC codes. Implementations use message-passing decoding with more precision, results extremely high complexity. In Iterative, message-passing (MP), trapping sets and absorbing sets causes low error floor. In this article non-uniform quantization proposed to overcome dynamic range of values over uniform quantization. Simulation results provide coding gain increases closer to of 0.5 dB in higher SNR and has good error floor at 10−5.