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 moreMetadata
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)