Upper Bounds on the Rate of LDPC Codes for a Class of Finite-State Markov Channels
Pulkit Grover
Ajit Kumar Chaturvedi
Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Feb. 2007
Volume: 53,
Issue: 2
On page(s): 794-804
ISSN: 0018-9448
INSPEC Accession Number: 9301437
Digital Object Identifier: 10.1109/TIT.2006.887511
Current Version Published: 2007-01-22
Abstract
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
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