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.

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基于离散消息传递的不规则LDPC码设计与译码

我们考虑基于信息最优对称查找表 (LUT) 的低密度奇偶校验 (LDPC) 码的离散消息传递 (MP) 解码。建立了离散消息标签和相关对数似然比值（根据密度演化分布定义）之间的联系。这种联系产生了消息标签上的代数结构，并导致将 LUT 解码解释为量化置信传播的一种形式。然后，我们将代数结构用于低复杂度 LUT 解码器设计。通过考虑联合 LUT 设计中的度分布，我们的 LUT 解码框架是第一个也适用于不规则 LDPC 码的框架。我们利用 LUT 解码和置信传播之间的关系来获得稳定性条件和针对 LUT 解码优化的不规则 LDPC 代码设计。