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Weak variable-length source coding

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1 Author(s)
Te Han ; Graduate Sch. of Inf. Syst., Univ. of Electro-Commun., Tokyo, Japan

Given a general source X={Xn}n=1, source coding is characterized by a pair (φn, ψn) of encoder φn, and decoder ψn , together with the probability of error εn≡Pr{ψnn(Xn ))≠Xn}. If the length of the encoder output φ n(Xn) is fixed, then it is called fixed-length source coding, while if the length of the encoder output φn (Xn) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error εn is required to asymptotically vanish (i.e., limn→∞εn=0), whereas in the context of variable-length source coding the probability of error εn is required to be exactly zero (i.e., εn =0∀n=1, 2, ...). In contrast to these, we consider the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., limn→∞εn =0), and establish several fundamental theorems on this new subject

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 4 )