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5 Compression
5.9.2 The Rate-Distortion Function
Let us assume that the information is produced by a discrete memoryless
source. By this we mean that the successive symbols generated by the source
are independent and identically distributed, i.e., &(aj) does not depend on
time. Next, we assume the channel to be a discrete memoryless channel,
which means that the channel processes successive letters of an input word
(i.e.,
an input sequence of symbols) independently of one another. Note that
The expected value of (191) (or, equivalently, (194)) is called the average
mutual information between the source X and the receiver Y and is denote ...