Variable-Length Coding with Cost Allowing Non-Vanishing Error Probability

Hideki YAGI  Ryo NOMURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.8   pp.1683-1692
Publication Date: 2017/08/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.1683
Type of Manuscript: PAPER
Category: Information Theory
coding with cost,  weak variable-length coding,  coding theorem,  general source,  information spectrum,  

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We consider fixed-to-variable length coding with a regular cost function by allowing the error probability up to any constantε. We first derive finite-length upper and lower bounds on the average codeword cost, which are used to derive general formulas of two kinds of minimum achievable rates. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate under a cost function is also the dominant set for a code attaining the minimum achievable rate under the other cost function. We also give general formulas of the second-order minimum achievable rates.