Optimum Overflow Thresholds in Variable-Length Source Coding Allowing Non-Vanishing Error Probability

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 exces...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 65; no. 12; pp. 8213 - 8221
Main Authors: Nomura, Ryo, Yagi, Hideki
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Channel coding
Codes
Coding
Conferences
Decoding
Entropy
Error probability
general source
Infimum
Lower bounds
overflow probability
Permissible error
Probability
Source coding
Thresholds
variable-length source coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2920417