This paper investigates the theoretical analysis of intrinsic message passing decoding for generalized product codes (GPCs) with irregular degree distributions, a generalization of product codes that allows every code bit to be protected by a minimum of two and potentially more component codes. We derive a random hypergraph-based asymptotic performance analysis for GPCs, extending previous work that considered the case where every bit is protected by exactly two component codes. The analysis offers a new tool to guide the code design of GPCs by providing insights into the influence of degree distributions on the performance of GPCs.

翻译：本文研究具有非规则度分布的广义乘积码（GPCs）的内在消息传递解码理论分析，广义乘积码是乘积码的推广形式，允许每个码字比特至少受两个甚至更多分量码保护。我们推导了基于随机超图的GPCs渐近性能分析，将先前考虑每个比特恰好受两个分量码保护的情形进行了推广。该分析为GPCs的码设计提供了新工具，揭示了度分布对GPCs性能的影响规律。