Chained Gallager codes

Victor Zyablov, Florian Hug, Rolf Johannesson

Published Jan 1, 2009• 1 citation

Abstract

The ensemble of regular Low-Density Parity-Check (LDPC) codes introduced by Gallager is considered. Using probabilistic arguments a lower bound on the normalized minimum distance is derived. A new code construction, called Chained Gallager codes, is introduced as the combination of two Gallager codes and its error correcting capabilities are studied.

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Chained Gallager codes

Victor Zyablov, Florian Hug, Rolf Johannesson

Published Jan 1, 2009• 1 citation

OpenAlex

Abstract

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An ensemble of

(J,K)

-regular low-density parity- check (LDPC) convolutional codes is introduced and existence-type lower bounds on the minimum distance

d _ {\rm L}

of code segments of finite length

L

and on the free distance

d _{\rm free}

are derived. For sufficiently large constraint lengths

\nu

, the distances are shown to grow linearly with

\nu

and the ratio

d_ {\rm L}/\nu

approaches the ratio

d _{ {\rm free}}/\nu

for large

L

. Moreover, the ratio of free distance to constraint length is several times larger than the ratio of minimum distance to block length for Gallager's ensemble of (J,K)-regular LDPC block codes.