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arXiv:1510.04589 · SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems

A fully-unrolled LDPC decoder based on quantized message passing

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

Published Oct 1, 2015• 35 citations
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Abstract

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.

DOI
10.1109/sips.2015.7345024

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IEEE International Symposium on Circuits and Systems proceedings•May 1, 2007•14 citations
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 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.
A recent result has shown connections between statistical learning theory and channel quantization. In this paper, we present a practical application of this result to the implementation of LDPC decoders. In particular, we describe a technique for designing the message-passing decoder mappings (or lookup tables) based on the ideas of channel quantization. This technique is not derived from sum-product algorithm or any other LDPC decoding algorithm. Instead, the proposed algorithm is based on an optimal quantizer in the sense of maximization of mutual information, which is inserted in the density evolution algorithm to generate the lookup tables. This algorithm has low complexity since it only employs 3-bit messages and lookup tables, which can be easily implemented in hardware. Two quantized versions of the min-sum decoding algorithm are used for comparison. Simulation results for a binary-input AWGN channel show 0.3 dB and 1.2 dB gains versus the two quantized min-sum algorithms. On the binary symmetric channel also a gain is seen.
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 class of finite alphabet iterative decoder (FAID), called mutual information-maximizing quantized belief propagation (MIM-QBP) decoder, for decoding regular low-density parity-check (LDPC) codes. Our decoder follows the reconstruction-calculation-quantization (RCQ) decoding architecture that is widely used in FAIDs. We present the first complete and systematic design framework for the RCQ parameters, and prove that our design with sufficient precision at node update is able to maximize the mutual information between coded bits and exchanged messages. Simulation results show that the MIM-QBP decoder can always considerably outperform the state-of-the-art mutual information-maximizing FAIDs that adopt two-input single-output lookup tables for decoding. Furthermore, with only 3 bits being used for each exchanged message, the MIM-QBP decoder can outperform the floating-point belief propagation decoder at the high signal-to-noise ratio regions when testing on high-rate LDPC codes with a maximum of 10 and 30 iterations.
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.
In this paper, we propose an efficient message passing architecture for permutation matrices based LDPC code decoders. Min-sum algorithm is reformulated to facilitate significant reduction of routing complexity and memory usage. For a (2048, 1723) (6, 32) LDPC code with 4-bit quantization, 54% outgoing wires per variable node unit and 90% outgoing wires per check node unit can be saved. To further reduce hardware complexity, an optimized nonuniform quantization scheme using only 3 bits to represent each message has been investigated. The simulation result shows that it has only 0.25dB performance loss from the floating-point SPA