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In variable-length coding, the probability of codeword length per source letter being above (resp. below) a prescribed threshold is called the overflow (resp. the underflow) probability. In this paper, we show that the infimum achievable threshold given the overflow probability exponent *r* always coincides with the infimum achievable fixed-length coding rate given the error exponent *r*, without any assumptions on the source. In the case of underflow probability, we also show the similar results. From these results, we can utilize various theorems and results on the fixed-length coding established by Han for the analysis of overflow and underflow probabilities. Moreover, we generalize the above results to the case with overflow and underflow probabilities of codeword cost.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.10 pp.2457-2465

- Publication Date
- 2001/10/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Shannon Theory

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Osamu UCHIDA, Te Sun HAN, "The Optimal Overflow and Underflow Probabilities of Variable-Length Coding for the General Source" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 10, pp. 2457-2465, October 2001, doi: .

Abstract: In variable-length coding, the probability of codeword length per source letter being above (resp. below) a prescribed threshold is called the overflow (resp. the underflow) probability. In this paper, we show that the infimum achievable threshold given the overflow probability exponent *r* always coincides with the infimum achievable fixed-length coding rate given the error exponent *r*, without any assumptions on the source. In the case of underflow probability, we also show the similar results. From these results, we can utilize various theorems and results on the fixed-length coding established by Han for the analysis of overflow and underflow probabilities. Moreover, we generalize the above results to the case with overflow and underflow probabilities of codeword cost.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_10_2457/_p

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@ARTICLE{e84-a_10_2457,

author={Osamu UCHIDA, Te Sun HAN, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={The Optimal Overflow and Underflow Probabilities of Variable-Length Coding for the General Source},

year={2001},

volume={E84-A},

number={10},

pages={2457-2465},

abstract={In variable-length coding, the probability of codeword length per source letter being above (resp. below) a prescribed threshold is called the overflow (resp. the underflow) probability. In this paper, we show that the infimum achievable threshold given the overflow probability exponent *r* always coincides with the infimum achievable fixed-length coding rate given the error exponent *r*, without any assumptions on the source. In the case of underflow probability, we also show the similar results. From these results, we can utilize various theorems and results on the fixed-length coding established by Han for the analysis of overflow and underflow probabilities. Moreover, we generalize the above results to the case with overflow and underflow probabilities of codeword cost.},

keywords={},

doi={},

ISSN={},

month={October},}

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TY - JOUR

TI - The Optimal Overflow and Underflow Probabilities of Variable-Length Coding for the General Source

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2457

EP - 2465

AU - Osamu UCHIDA

AU - Te Sun HAN

PY - 2001

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E84-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 2001

AB - In variable-length coding, the probability of codeword length per source letter being above (resp. below) a prescribed threshold is called the overflow (resp. the underflow) probability. In this paper, we show that the infimum achievable threshold given the overflow probability exponent *r* always coincides with the infimum achievable fixed-length coding rate given the error exponent *r*, without any assumptions on the source. In the case of underflow probability, we also show the similar results. From these results, we can utilize various theorems and results on the fixed-length coding established by Han for the analysis of overflow and underflow probabilities. Moreover, we generalize the above results to the case with overflow and underflow probabilities of codeword cost.

ER -