A Deterministic Construction and Density Evolution Analysis for Generalized Product Codes

Abstract

Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. In this tutorial paper, we review a deterministic construction for GPCs that has been previously proposed by the authors together with an accompanying density evolution (DE) analysis. The DE analysis characterizes the asymptotic performance of the resulting GPCs under iterative bounded-distance decoding of the component codes over the binary erasure channel. As an application, we discuss the analysis and design of three different classes of GPCs: spatially-coupled PCs, symmetric GPCs, and GPCs based on component code mixtures.