TY - GEN

T1 - Relationship between source resolvability with normalized f-divergence and fixed-length coding

AU - Nomura, Ryo

N1 - Funding Information:
This work is supported in part by JSPS KAKENHI Grant Number JP18K04150 and Waseda University Grant for Special Research Projects (Project number: 2020C-528).
Publisher Copyright:
©2021 IEEE

PY - 2021/4/11

Y1 - 2021/4/11

N2 - This paper deals with the relationship between the source resolvability problem (or resolvability problem for short) and the fixed-length source coding problem. In the literature, optimum achievable rates in the resolvability problem (optimum resolvability rate) with respect to the variational distance as well as the Kullback-Leibler (KL) divergence, have already been analyzed. The relationship between the optimum resolvability rate and the optimum rate of the fixed-length source coding has also been clarified in each cases. In particular, it has been reported that the optimum source resolvability rate with respect to the normalized KL divergence has a close relationship with the optimum fixed-length source coding rate with the correct decoding exponent. Recently, the optimum resolvability rate with respect to a class of f-divergences has been analyzed. This result can be considered as a generalization of the optimum resolvability rate with respect to the unnormalized KL divergence. However, unnormalized f-divergences has not been considered yet in the resolvability problem. Hence, in this paper, we consider the resolvability problem with respect to a class of unnormalized f-divergences. In particular, we derive the relationship between the optimum resolvability rate with a class of normalized fdivergences and the optimum rate of the fixed-length source coding.

AB - This paper deals with the relationship between the source resolvability problem (or resolvability problem for short) and the fixed-length source coding problem. In the literature, optimum achievable rates in the resolvability problem (optimum resolvability rate) with respect to the variational distance as well as the Kullback-Leibler (KL) divergence, have already been analyzed. The relationship between the optimum resolvability rate and the optimum rate of the fixed-length source coding has also been clarified in each cases. In particular, it has been reported that the optimum source resolvability rate with respect to the normalized KL divergence has a close relationship with the optimum fixed-length source coding rate with the correct decoding exponent. Recently, the optimum resolvability rate with respect to a class of f-divergences has been analyzed. This result can be considered as a generalization of the optimum resolvability rate with respect to the unnormalized KL divergence. However, unnormalized f-divergences has not been considered yet in the resolvability problem. Hence, in this paper, we consider the resolvability problem with respect to a class of unnormalized f-divergences. In particular, we derive the relationship between the optimum resolvability rate with a class of normalized fdivergences and the optimum rate of the fixed-length source coding.

KW - F-divergence

KW - Fixed-length Coding

KW - General source

KW - Random number generation

KW - Source resolvability

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U2 - 10.1109/ITW46852.2021.9457657

DO - 10.1109/ITW46852.2021.9457657

M3 - Conference contribution

AN - SCOPUS:85113310429

T3 - 2020 IEEE Information Theory Workshop, ITW 2020

BT - 2020 IEEE Information Theory Workshop, ITW 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2020 IEEE Information Theory Workshop, ITW 2020

Y2 - 11 April 2021 through 15 April 2021

ER -