Average Stopping Set Weight Distributions of Redundant Random Ensembles
Wadayama, T.
Nagoya Inst. of Technol., Nagoya;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Nov. 2008
Volume: 54,
Issue: 11
On page(s): 4991-5004
ISSN: 0018-9448
INSPEC Accession Number: 10299650
Digital Object Identifier: 10.1109/TIT.2008.929973
Current Version Published: 2008-10-21
Abstract
In this paper, redundant random ensembles are defined and their average stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with linearly dependent rows. These linearly dependent rows significantly reduce the number of stopping sets (SS) of small size. Upper and lower bounds on the average SS weight distribution of the redundant random ensembles are proved based on a combinatorial argument. Asymptotic forms of these bounds reveal asymptotic behavior of the average SS weight distributions. From these bounds, a tradeoff between the number of redundant rows (corresponding to decoding complexity of belief propagation on binary erasure channel) and the average SS weight distribution (corresponding to decoding performance) can be derived.
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