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Combinatorial properties of good codes for binary autoregressive sources (Corresp.)

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LetMbe a binary autoregressive source to be encoded within a specified Hamming distortiondelta. A binaryn-tuple is calledsigma-central if it is at distanceleq n(delta + sigma)from at least2^{nH(delta - sigma)}typical sequences produced by the sourceM. It is first shown that, in the region where the Shannon rate-distortion bound is achieved, there exist "good codes" consisting only ofsigma-central words. Next, the characterization problem is studied; the basic conjecture is that a central sequence is well-characterized by its level, which is the Hamming weight of an image sequence. The problem is solved for the memoryless source. In general, ifN(k,r)is defined to be the mean number of typicaln-tuples at distanceleq r = n deltafrom then-tuples of levelk=n xi, then it is shown thatn^{-l} log N(k,r)becomes arbitrarily close toH(delta)for an explicitly determined unique value ofxi.

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Information Theory, IEEE Transactions on  (Volume:26 ,  Issue: 3 )