New results on the minimum distance of repeat multiple accumulate codes

Jörg Kliewer, Kamil S. Zigangirov, Daniel J. Costello

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

Abstract

In this paper we consider the ensemble of codes formed by a serial concatenation of a repetition code with mul-tiple accumulators through uniform random interleavers. Based on finite length weight enumerators for these codes, asymptotic expressions for the minimum distance and an arbitrary number of accumulators larger than one are derived. In accordance with earlier results in the literature, we irst show that the minimum distance of RA codes can grow, at best, sublinearly with the block length. Then, for RAA codes and rates of 1/3 or smaller, it is proved that these codes exhibit linear distance growth with block length. where the gap to the Gilbert-Varshamov bound can be made arbitrarily small by increasing the number of accumulators beyond two. In order to address rates larger than 1/3, random puncturing of a low-rate mother code is introduced. We show that in this case the resulting ensemble of EAA codes asymptotically achieves linear distance growth close to the Gilbert-Varshamov bound. This holds even for very high rate codes.

Original languageEnglish (US)
Title of host publication45th Annual Allerton Conference on Communication, Control, and Computing 2007
PublisherUniversity of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages1097-1102
Number of pages6
ISBN (Electronic)9781605600864
StatePublished - 2007
Externally publishedYes
Event45th Annual Allerton Conference on Communication, Control, and Computing 2007 - Monticello, United States
Duration: Sep 26 2007Sep 28 2007

Publication series

Name45th Annual Allerton Conference on Communication, Control, and Computing 2007
Volume2

Other

Other45th Annual Allerton Conference on Communication, Control, and Computing 2007
CountryUnited States
CityMonticello
Period9/26/079/28/07

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Networks and Communications

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