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

Ryo Nomura, Hideki Yagi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number8727916
Pages (from-to)8213-8221
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number12
Publication statusPublished - 2019 Dec


  • Error probability
  • General source
  • Overflow probability
  • Variable-length source coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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