The Minimum Distance of Turbo-Like Codes

Authors: Louay Bazzi, Mohammad Mahdian, and Daniel Spielman.

Bibliographic Information: Submitted to IEEE Transaction on Information Theory, 2003.

Abstract

We derive worst-case upper bounds on the minimum distance of parallel concatenated Turbo codes, serially concatenated Turbo codes, repeat-accumulate codes, repeat-convolute codes, and generalizations of these codes obtained by allowing non-linear and large-memory constituent codes. We show that parallel-concatenated Turbo codes and repeat-convolute codes with sub-linear memory are asymptotically bad. We also show that depth-two serially concatenated codes with constant-memory outer codes and sub-linear-memory inner codes are asymptotically bad. In contrast, we prove that depth-three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good. We also show how to construct interleavers for Turbo codes with two-branches that maximize their minimum distance up to a constant factor.

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Daniel A. Spielman

Last modified: Fri Aug 3 02:13:15 EDT 2001