On the pseudocodeword weight and parity-check matrix redundancy of linear codes

Christine A. Kelley, Deepak Sridhara

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

10 Scopus citations

Abstract

The minimum pseudocodeword weight wmin of a linear graph-based code is more influential in determining decoding performance when decoded via iterative and linear programming decoding algorithms than the classical minimum distance dmin under standard maximum-likelihood decoding. Moreover, unlike the minimum distance which is unique to the code regardless of representation, the set of pseudocodewords, and therefore also the minimum pseudocodeword weight, depends on the graph representation used in decoding as well as on the communication channel. This means that a judicious choice of parity-check matrix is crucial for realizing the best potential of any graph-based code. In this paper, we introduce the notion of pseudoweight redundancy for the memoryless binary symmetric channel (BSC). Analogous to the stopping redundancy in the literature, this parameter gives the smallest number of rows needed for a parity-check matrix to have dmin = w min. We provide some upper bounds on the BSC-pseudoweight redundancy and illustrate the concept with some results for Hamming codes, tree-based and finite geometry LDPC codes, Reed-Muller codes and Hadamard codes.

Original languageEnglish (US)
Title of host publication2007 IEEE Information Theory Workshop, ITW 2007, Proceedings
Pages1-6
Number of pages6
DOIs
StatePublished - Dec 1 2007
Event2007 IEEE Information Theory Workshop, ITW 2007 - Lake Tahoe, CA, United States
Duration: Sep 2 2007Sep 6 2007

Publication series

Name2007 IEEE Information Theory Workshop, ITW 2007, Proceedings

Other

Other2007 IEEE Information Theory Workshop, ITW 2007
CountryUnited States
CityLake Tahoe, CA
Period9/2/079/6/07

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ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems
  • Information Systems and Management

Cite this

Kelley, C. A., & Sridhara, D. (2007). On the pseudocodeword weight and parity-check matrix redundancy of linear codes. In 2007 IEEE Information Theory Workshop, ITW 2007, Proceedings (pp. 1-6). [4313040] (2007 IEEE Information Theory Workshop, ITW 2007, Proceedings). https://doi.org/10.1109/ITW.2007.4313040