Generalized and Extended Product Codes
Mario Blaum, Steve Hetzler
TL;DR
This paper introduces Generalized Product Codes, unifying existing coding schemes, and explores extending product codes with global parities, providing bounds and optimal constructions for various global parity counts.
Contribution
It presents a unification of Product and II codes, studies extending product codes with global parities, and derives bounds and optimal code constructions.
Findings
Upper bound on minimum distance of extended product codes
Explicit codes with 1, 2, and 3 global parities meeting the bound
Discussion of tradeoffs between optimality and field size
Abstract
Generalized Product (GPC) Codes, an unification of Product Codes and Integrated Interleaved (II) Codes, are presented. Applications for approaches requiring local and global parities are described. The more general problem of extending product codes by adding global parities is studied and an upper bound on the minimum distance of such codes is obtained. Codes with one, two and three global parities whose minimum distances meet the bound are presented. Tradeoffs between optimality and field size are discussed.
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Taxonomy
TopicsAdvanced Data Storage Technologies · DNA and Biological Computing · Coding theory and cryptography