MAP detection of binary sources over discrete Markov channels

A source with memory as well as a memoryless source with a non-uniform distribution are sources with redundancy. If a discrete alphabet source is a uniformly distributed i.i.d. random process, it contains a maximal amount of information and exhibits no redundancy. Its entropy rate is then maximized and is equal to log₂ q bits/sample, where q is the source alphabet size. The amount of redundancy a q-ary alphabet source possesses is equal to the difference between log₂ q and its entropy rate. The authors consider a binary source with an inherent redundancy that they make no attempt to eliminate. The source is directly transmitted over a discrete noisy channel. The objective is to design an optimum receiver which fully utilizes the source redundancy in order to combat the impairments introduced by the channel noise