Extended Product and Integrated Interleaved Codes

TL;DR

This paper introduces Extended Product Codes, a new class of codes with added parities, discusses their erasure decoding applications, and explores a special case called Extended Integrated Interleaved codes that improve minimum distance and decoding capabilities.

Contribution

The paper presents the design, bounds, and constructions of Extended Product Codes and introduces Extended Integrated Interleaved codes, unifying and enhancing existing coding schemes.

Findings

EPC codes have an upper bound on minimum distance and meet it in some cases.

EII codes improve minimum distance over II codes with same rate.

EII codes enable decoding on both columns and rows, and facilitate uniform parity distribution.

Abstract

A new class of codes, Extended Product (EPC) Codes, consisting of a product code with a number of extra parities added, is presented and applications for erasure decoding are discussed. An upper bound on the minimum distance of EPC codes is given, as well as constructions meeting the bound for some relevant cases. A special case of EPC codes, Extended Integrated Interleaved (EII) codes, which naturally unify Integrated Interleaved (II) codes and product codes, is defined and studied in detail. It is shown that EII codes often improve the minimum distance of II codes with the same rate, and they enhance the decoding algorithm by allowing decoding on columns as well as on rows. It is also shown that EII codes allow for encoding II codes with an uniform distribution of the parity symbols.