Capacity-achieving codes for finite-state channels with maximum-likelihood decoding
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
Capacity-achieving codes for channels with memory with maximum-likelihood decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
| Hi-index | 754.90 |
In this correspondence, we consider the class of finite-state Markov channels (FSMCs) in which the channel behaves as a binary symmetric channel (BSC) in each state. Upper bounds on the rate of LDPC codes for reliable communication over this class of FSMCs are found. A simple upper bound for all noninverting FSMCs is first derived. Subsequently, tighter bounds are derived for the special case of Gilbert-Elliott (GE) channels. Tighter bounds are also derived over the class of FSMCs considered. The latter bounds hold almost-surely for any sequence of randomly constructed LDPC codes of given degree distributions. Since the bounds are derived for optimal maximum-likelihood decoding, they also hold for belief propagation decoding. Using the derivations of the bounds on the rate, some lower bounds on the density of parity check matrices for given performance over FSMCs are derived