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International Symposium on Turbo Codes and Iterative Information Processing

Optimization of Sign-Preserving Noise-Aided Min-Sum Decoders with Density Evolution

Franklin Cochachin, Emmanuel Boutillon, David Declercq

Published Dec 1, 2018• 2 citations
Publisher

Abstract

The novelty of this paper is to propose a new LDPC decoder called Sign-Preserving Noise-Aided Min-Sum (SP-NA-MS) decoder that improves the decoding performance compared to classical Offset Min-Sum (OMS) decoder when messages are quantized, with only 3 or 4 bits. The particularity of the SP-NA-MS decoder is that the variable-to-check messages are never set to 0, and always carry the sign information. Moreover, the decoder incorporates random perturbation due to deliberate noise injection. The parameters of the SP-NA-MS decoders are optimized in the asymptotic limit of the code length thanks to the Density Evolution (DE) method. The finite-length simulations confirm the conclusions of the DE analysis and gain of up to 0.3 dB in SNR can be obtained compared to regular OMS with same quantization level.

DOI
10.1109/istc.2018.8625309

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The novelty of this paper is to propose a new LDPC decoder called Sign-Preserving Noise-Aided Min-Sum (SP-NA-MS) decoder that improves the decoding performance compared to classical Offset Min-Sum (OMS) decoder when messages are quantized, with only 3 or 4 bits. The particularity of the SP-NA-MS decoder is that the variable-to-check messages are never set to 0, and always carry the sign information. Moreover, the decoder incorporates random perturbation due to deliberate noise injection. The parameters of the SP-NA-MS decoders are optimized in the asymptotic limit of the code length thanks to the Density Evolution (DE) method. The finite-length simulations confirm the conclusions of the DE analysis and gain of up to 0.3 dB in SNR can be obtained compared to regular OMS with same quantization level.
This paper proposes a new finite precision iterative decoder for low-density parity-check (LDPC) codes. The proposed decoder, named Sign-Preserving Min-Sum (SP-MS), significantly improves the decoding performance compared to the classical Offset Min-Sum (OMS) decoder when messages are quantized onq=2q=2q=2, 3, or 4 bits. The particularity of the SP-MS decoder is that messages cannot take the 0 value, and can fully benefit from theqqqbits of precision. The optimization of the SP-MS decoder is investigated in the asymptotic limit of the code length using density evolution (DE). Our study shows that 3-bit SP-MS decoders can achieve the same error-correcting performance as 5-bit OMS decoders, and 2-bit SP-MS decoders outperform 3-bit OMS decoders. The finite-length simulations confirm the conclusions of the DE analysis for several LDPC codes. Our SP-MS decoder shows a signal-to-noise ratio (SNR) gain up to 0.43 dB, with a memory/wire reduction of up to 40%, compared to the OMS decoder. Moreover, the SP-MS decoder converges faster and uses fewer iterations than the OMS decoder, with an improvement of up to 83.3% of the average decoding throughput. On an FPGA, the SP-MS decoder reduces resource utilization by up to 56% compared to the OMS decoder.
In this paper, we define Noise-against-Noise Min-Sum (NAN-MS) decoders as decoders that incorporate a certain amount of random perturbation due to deliberate noise injection. We introduce a noise model which is used to implement quantized NAN-MS decoders, using a limited number of precision bits. The behavior of NAN-MS decoders is investigated in the asymptotic limit of the code length using a noisy version of density evolution (DE). We use the noisy-DE thresholds to analyze and optimize the noise model parameters. We show that a controlled injection of noise allows NAN-MS decoders to achieve better performance than noiseless MS decoders, especially for low precision. The finite-length simulations confirm the conclusions of the DE analysis.
In this paper, we analyze the performance of quantized offset min-sum (MS) decoding algorithm and propose an optimally quantized offset MS algorithm for a flexible low-density parity-check (LDPC) decoder. It is known that the offset MS decoding algorithm is implemented with simplified hardware complexity and achieves good decoding performance. However, the finite precision effects in decoding LDPC codes result in performance different from floating point. The performance degradation is caused by different dynamic ranges of input data at high signal-to-noise ratio (SNR). The proposed offset MS algorithm uses the received data directly instead of log-likelihood ratio (LLR) data as the intrinsic information. It can achieve better performance than the conventional one since its offset factor is more effective at a wide range of SNR and the intrinsic information is quantized more robustly since it is independent of channel information. Also, it is possible for the proposed scheme to use a same quantization scheme for a flexible LDPC decoder, which can decode several kinds of LDPC codes. Simulation results show that our optimally quantized offset MS algorithms with 5-bits for (1728, 864) and (1728, 1296) irregular LDPC codes achieve better performance compared with the conventional offset MS algorithms with 6-bits quantization scheme.
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 this paper, we propose an improvement of the normalized min-sum (MS) decoding algorithm and novel MS decoder architectures with reduced word length using nonuniform quantization schemes for low-density parity-check (LDPC) codes. The proposed normalized MS algorithm introduces a more exact adjustment with two optimized correction factors for check-node-updating computations, while the conventional normalized MS algorithm applies only one correction factor. The proposed algorithm provides a significant performance gain without any additional computation or hardware complexity. The finite word-length analysis in implementing an LDPC decoder is a very important factor since it directly impacts the size of memory to store the intrinsic and extrinsic messages and the overall hardware area in the partially parallel LDPC decoder. The proposed nonuniform quantization scheme can reduce the finite word length while achieving similar performances compared to a conventional quantization scheme. From simulation results, it is shown that the proposed 4-bit nonuniform quantization scheme achieves an acceptable decoding performance, unlike the conventional 4-bit uniform quantization scheme. Finally, the proposed MS decoder architectures by the nonuniform quantization scheme provide significant reductions of 20% and up to 8% for the memory area and combinational logic area, respectively, compared to the conventional 5-bit ones.
It has been shown that under min-sum (MS) decoding, scaling the messages at the output of check nodes can improve the performance of regular low-density parity-check (LDPC) codes. However, for irregular codes designed for the sum-product decoder, linear scaling can hinder the performance. The problem of code design for MS and linear scaling min-sum (LSMS) decoders have been recently investigated. It is shown that the gap to the capacity for LSMS codes is better than MS codes, but compared to sum-product codes the gap is still considerable. In this letter, a modified MS decoding is proposed and studied. We use the stability analysis of density evolution to show that the proposed method allows for a larger fraction of edges connected to degree-2 variable nodes than LSMS codes. Finally, by designing codes based on the modified method, we show that compared to MS and LSMS codes, a smaller gap to the capacity can indeed be achieved while the complexity of decoding remains essentially the same.