Summary
The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
2018
Session Number:We-PM-2-3
Session:
Number:We-PM-2-3.3
Generalized Fano-Type Inequality for Countably Infinite Systems with List-Decoding
Yuta Sakai,
pp.759-763
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.We-PM-2-3.3
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Summary:
This study investigates generalized Fano-type inequalities in the following senses: (i) the alphabet X of a random variable X is countably infinite; (ii) instead of a fixed finite cardinality of X, a fixed X-marginal distribution is given; (iii) information measures are generalized from the conditional Shannon entropy H(X | Y) to a general type of conditional information measures h?φ(X | Y) without explicit form; and (iv) the average probability of error is defined on list-decoding rules. As a result, we give tight upper bounds on such generalized conditional information measures for a fixed X-marginal, a fixed list size, and a fixed tolerated probability of error. Then, we also clarify a sufficient condition, which the Fano-type inequalities are sharp, on the cardinality of the alphabet Y of a side information Y. Resulting Fano-type inequalities can apply to not only the conditional Shannon entropy but also the Arimoto’s and Hayashi’s conditional Renyi entropies. All of the proofs in this study can be found in arXiv:1801.02876 [19].