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Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates

Christian Häger (Institutionen för signaler och system, Kommunikationssystem) ; Henry D. Pfister ; Alexandre Graell i Amat (Institutionen för signaler och system, Kommunikationssystem) ; Fredrik Brännström (Institutionen för signaler och system, Kommunikationssystem)
IEEE Transactions on Information Theory (0018-9448). Vol. 63 (2017), 7, p. 4357-4378.
[Artikel, refereegranskad vetenskaplig]

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.

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Denna post skapades 2017-06-03. Senast ändrad 2017-09-07.
CPL Pubid: 249582


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Institutioner (Chalmers)

Institutionen för signaler och system, Kommunikationssystem (1900-2017)


Informations- och kommunikationsteknik

Chalmers infrastruktur



Denna publikation är ett resultat av följande projekt:

Signal Recovery: Compressed Sensing meets Coding Theory (VR//2011-5961)