Processing math: 25%
New Sequences of Capacity Achieving LDPC Code Ensembles Over the Binary Erasure Channel | IEEE Journals & Magazine | IEEE Xplore

New Sequences of Capacity Achieving LDPC Code Ensembles Over the Binary Erasure Channel

Publisher: IEEE

Abstract:

In this paper, new sequences (\lambda ^{n},\rho ^{n}) of capacity achieving low-density parity-check (LDPC) code ensembles over the binary erasure channel (BEC) is i...View more

Abstract:

In this paper, new sequences (\lambda ^{n},\rho ^{n}) of capacity achieving low-density parity-check (LDPC) code ensembles over the binary erasure channel (BEC) is introduced. These sequences include the existing sequences by Shokrollahi as a special case. For a fixed code rate R , in the set of proposed sequences, Shokrollahi's sequences are superior to the rest of the set in that for any given value of n , their threshold is closer to the capacity upper bound 1- R . For any given \delta , 0 < \delta < 1-R , however, there are infinitely many sequences in the set that are superior to Shokrollahi's sequences in that for each of them, there exists an integer number n_{0} , such that for any n > n_{0} , the sequence (\lambda ^{n},\rho ^{n}) requires a smaller maximum variable node degree as well as a smaller number of constituent variable node degrees to achieve a threshold within \delta -neighborhood of the capacity upper bound 1-R . Moreover, it is proven that the check-regular subset of the proposed sequences are asymptotically quasi-optimal, i.e., their decoding complexity increases only logarithmically with the relative increase of the threshold. A stronger result on asymptotic optimality of some of the proposed sequences is also established.
Published in: IEEE Transactions on Information Theory ( Volume: 56, Issue: 12, December 2010)
Page(s): 6332 - 6346
Date of Publication: 18 November 2010

ISSN Information:

Publisher: IEEE

References

References is not available for this document.