凸最適化と min-sum 復号によるLDPC符号の反復復号法

Homayoon Hatami, David G. M. Mitchell, Daniel J. Costello +1 more

It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.

智章 老木, Tomoaki Oiki, 隆太郎 松本 +3 more

Hironori Uchikawa, 康祐 原田, 康彦 田邉

Homayoon Hatami, David G. M. Mitchell, Daniel J. Costello +1 more

For decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs), i.e., in the “waterfall region” of the bit error rate curve. This paper demonstrates that, for quantized decoders, MSA actually outperforms AMSA and OMSA in the “error floor” region, and that all three algorithms suffer from a relatively high error floor. This motivates the introduction of a modified MSA that is designed to outperform MSA, AMSA, and OMSA across all SNRs. The new algorithm is based on the assumption that trapping sets are the major cause of the error floor for quantized LDPC decoders. A performance estimation tool based on trapping sets is used to verify the effectiveness of the new algorithm and also to guide parameter selection. We also show that the implementation complexity of the new algorithm is only slightly higher than that of AMSA or OMSA. Finally, the simulated performance of the new algorithm, using several classes of LDPC codes (including spatially coupled LDPC codes), is shown to outperform MSA, AMSA, and OMSA across all SNRs.

祐貴 河内, 洋史 榎, 宏太郎 渡辺 +1 more

Bin Dai, Rongke Liu, Zhiyuan Yan

In this paper, we propose two novel min-sum (MS) decoding algorithms based on deep learning for polar codes, an offset min-sum (OMS) and a scaling offset min-sum (SOMS) algorithm. The parameters of both algorithms are different from iteration to iteration, and are obtained by training over a deep neural network. Our simulation results show that the OMS algorithm has roughly the same error performance as a previously proposed multiple scaling min-sum (MSMS) algorithm, and that the SOMS algorithm performs better than all existing BP-based algorithms. Since the OMS algorithm requires only an addition as opposed to a multiplication in the MSMS algorithm, the OMS algorithm is more suitable for hardware implementation. The two proposed decoding algorithms provide a tradeoff between complexity and error performance.