Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates
Journal article, 2017

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. We consider a deterministic construction of GPCs (as opposed to randomized code ensembles) and analyze the asymptotic performance over the binary erasure channel under iterative decoding. Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, blockwise braided codes, and staircase codes. It is assumed that the component codes can correct a fixed number of erasures and that the length of each component code tends to infinity. We show that this setup is equivalent to studying the behavior of a peeling algorithm applied to a sparse inhomogeneous random graph. Using a convergence result for these graphs, we derive the density evolution equations that characterize the asymptotic decoding performance. As an application, we discuss the design of irregular GPCs, employing a mixture of component codes with different erasure-correcting capabilities.

Author

Christian Häger

Chalmers, Signals and Systems, Kommunikationssystem, informationsteori och antenner, Communication Systems

Henry D. Pfister

Duke University

Alexandre Graell i Amat

Chalmers, Signals and Systems, Kommunikationssystem, informationsteori och antenner, Communication Systems

Fredrik Brännström

Chalmers, Signals and Systems, Kommunikationssystem, informationsteori och antenner, Communication Systems

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 63 7 4357-4378 7890389

Signal Recovery: Compressed Sensing meets Coding Theory

Swedish Research Council (VR), 2012-01-01 -- 2015-12-31.

Areas of Advance

Information and Communication Technology

Subject Categories

Telecommunications

Communication Systems

DOI

10.1109/TIT.2017.2689783