TY - GEN

T1 - The stopping redundancy hierarchy of cyclic codes

AU - Hehn, Thorsten

AU - Laendner, Stefan

AU - Milenkovic, Olgica

AU - Huber, Johannes B.

PY - 2006

Y1 - 2006

N2 - We extend the framework for studying the stopping redundancy of a linear block code by introducing and analyzing the stopping redundancy hierarchy. The stopping redundancy hierarchy of a code represents a measure of the trade-off between performance and complexity of iteratively decoding a code used over the binary erasure channel. It is defined as an ordered list of positive integers in which the ith entry, termed the i-Th stopping redundancy, corresponds to the minimum number of rows in any parity-check matrix of the code that has stopping distance at least i. In particular, we derive lower and upper bounds for the i-Th stopping redundancy of a code by using probabilistic methods and Bonferroni-Type inequalities. Furthermore, we specialize the findings for cyclic codes, and show that parity-check matrices in cyclic form have some desirable redundancy properties. We also propose to investigate the influence of the generator codeword of the cyclic parity-check matrix on its stopping distance properties.

AB - We extend the framework for studying the stopping redundancy of a linear block code by introducing and analyzing the stopping redundancy hierarchy. The stopping redundancy hierarchy of a code represents a measure of the trade-off between performance and complexity of iteratively decoding a code used over the binary erasure channel. It is defined as an ordered list of positive integers in which the ith entry, termed the i-Th stopping redundancy, corresponds to the minimum number of rows in any parity-check matrix of the code that has stopping distance at least i. In particular, we derive lower and upper bounds for the i-Th stopping redundancy of a code by using probabilistic methods and Bonferroni-Type inequalities. Furthermore, we specialize the findings for cyclic codes, and show that parity-check matrices in cyclic form have some desirable redundancy properties. We also propose to investigate the influence of the generator codeword of the cyclic parity-check matrix on its stopping distance properties.

UR - http://www.scopus.com/inward/record.url?scp=84940654773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940654773&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84940654773

T3 - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

SP - 1271

EP - 1280

BT - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

PB - University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering

T2 - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

Y2 - 27 September 2006 through 29 September 2006

ER -