  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.
