TY - JOUR

T1 - Optimum overflow thresholds in variable-length source coding allowing non-vanishing error probability

AU - Nomura, Ryo

AU - Yagi, Hideki

N1 - Funding Information:
Manuscript received October 6, 2018; revised May 18, 2019; accepted May 21, 2019. Date of publication June 3, 2019; date of current version November 20, 2019. This work was supported in part by JSPS KAKENHI under Grant JP16K06340, Grant JP18H01438, Grant JP17K00020, and Grant JP18K04150. This paper was presented at the 2017 IEEE Information Theory Workshop [1].

PY - 2019/12

Y1 - 2019/12

N2 - The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem, the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds, we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. Finally, we apply the general formula derived in this paper to the case of stationary memoryless sources.

AB - The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem, the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds, we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. Finally, we apply the general formula derived in this paper to the case of stationary memoryless sources.

KW - Error probability

KW - General source

KW - Overflow probability

KW - Variable-length source coding

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U2 - 10.1109/TIT.2019.2920417

DO - 10.1109/TIT.2019.2920417

M3 - Article

AN - SCOPUS:85077499370

VL - 65

SP - 8213

EP - 8221

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 12

M1 - 8727916

ER -