Given a general source X = {X-n}(n=1)(infinity), sourcecoding is characterized by a pair (phi(n), psi(n)) of encoder phi(n) and decoder psi(n) together with the probability of error epsilon(n) = Pr{psi(n)(phi(n)(X-n)...
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Given a general source X = {X-n}(n=1)(infinity), sourcecoding is characterized by a pair (phi(n), psi(n)) of encoder phi(n) and decoder psi(n) together with the probability of error epsilon(n) = Pr{psi(n)(phi(n)(X-n)) not equal X-n}. If the length of the encoder output phi(n)(X-n) is fixed, then it is called fixed-lengthsourcecoding, while if the length of the encoder output phi(n)(X-n) is variable, then it is called variable-lengthsourcecoding. Usually, in the context of fixed-lengthsourcecoding the probability of error epsilon(n) is required to asymptotically vanish (i.e., lim(n-->infinity) epsilon(n) = 0), whereas in the context of variable-lengthsourcecoding the probability of error epsilon(n) is required to be exactly zero (i.e., epsilon(n) = 0 For All n = 1, 2,....) In contrast to these, we consider in the present paper the problem of variable-lengthsourcecoding with asymptotically vanishing probability of error (i.e., lim(n-->infinity) epsilon(n) = 0), and establish several fundamental theorems on this new subject.
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