Math @ Duke

Publications [#319399] of Henry Pfister
Papers Published
 Pfister, HD, Finitelength analysis of a capacityachieving ensemble for the binary erasure channel,
Proceedings of the IEEE ITSOC Information Theory Workshop 2005 on Coding and Complexity, ITW2005
(December, 2005),
pp. 166170, ISBN 078039481X [doi]
(last updated on 2018/09/21)
Abstract: In this paper, we consider the finitelength performance of a capacityachieving sequence of irregular repeataccumulate (IRA) code ensembles. We focus on a sequence of bitregular ensembles with degree 3 which was shown to achieve capacity with bounded complexity [9]. To characterize how fast the block length of the code must grow with respect to the truncation point of the degree distribution (i.e., maximum check degree), we compute an upper bound on the average weight enumerator. Based on this analysis, we present a particular truncation sequence that could achieve a minimum distance which grows like n 1/3 even as the gap to capacity goes to zero. We also consider the performance of these codes in the waterfall region by extending the finitelength scaling law [1] from lowdensity paritycheck codes to IRA codes. This shows that the performance near the iterative decoding threshold is well characterized by a suitably scaled Qfunction for large enough block length. Numerical results are given for the scaling parameters of this ensemble sequence and for a few other IRA codes. Unfortunately, the simulation results for the capacityachieving sequence start to match the scaling law only for very large block lengths. © 2005 IEEE.


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