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Average-sense optimality and competitive optimality for almost instantaneous VF codes

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2 Author(s)
H. Yamamoto ; Dept. of Math. Inf., Tokyo Univ., Japan ; H. Yokoo

One-shot coding and repeated coding are considered for the class of almost instantaneous variable-to-fixed length (AIVF) codes, CAIVF, which includes some nonproper VF codes in addition to the class of proper VF codes, CPVF. An algorithm is given to construct the average-sense optimal (a-optimal) AIVF code in one-shot coding that attains the maximum average parse length in CAIVF. The algorithm can also be used to obtain an AIVF code with multiple parse trees, which can attain good performance for repeated coding. Generally, the a-optimal code for one-shot coding and the good code for repeated coding are more efficient than the Tunstall (1967) code in A-ary cases if A⩾3 although they coincide with the Tunstall code in the binary case. The competitively optimal (c-optimal) VF code is also considered for one-shot coding, and it is shown that the c-optimal code does not always exist in CPVF and in CAIVF. Furthermore, whenever the c-optimal code exists, the Tunstall code is c-optimal in CPVF and the a-optimal code obtained by our algorithm is c-optimal in CAIVF if A=2 or 3, but the a-optimal code is not always c-optimal in CAIVF if A⩾4

Published in:

IEEE Transactions on Information Theory  (Volume:47 ,  Issue: 6 )