New Binary Encoding Schemes of Positive Integers

Yoko MIYAKAWA; Yuichi SAITOH; Hideki IMAI

New Binary Encoding Schemes of Positive Integers

Yoko MIYAKAWA, Yuichi SAITOH, Hideki IMAI

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We propose five classes of variable length codes for encoding positive integers: One is a class of codes having constant Hamming weight. The other four classes of codes have a prefix and a suffix in a codeword. The prefix indicates the weight or the length of the suffix and variable length constant weight codes are used for the prefixes and the suffixes of some of these codes. For encoding of these codes we can use Schalkwijk's algorithm. It is shown that some of the proposed codes are universal and asymptotically optimal in the meaning that P. Elias has defined. We compare them with other known codes from the viewpoints of the length of the codewords corresponding to integers 2^M (M=0, 1, , 30) and the average codeword length for two sources: 26 letters in English sentences and the geometrically distributed positive integers. The results shows that some of the proposed codes which are universal and asymptotically optimal are more efficient than the known codes.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.9 pp.2504-2512

Publication Date: 1991/09/25

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

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Yoko MIYAKAWA
Yuichi SAITOH
Hideki IMAI

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Yoko MIYAKAWA, Yuichi SAITOH, Hideki IMAI, "New Binary Encoding Schemes of Positive Integers" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 9, pp. 2504-2512, September 1991, doi: .
Abstract: We propose five classes of variable length codes for encoding positive integers: One is a class of codes having constant Hamming weight. The other four classes of codes have a prefix and a suffix in a codeword. The prefix indicates the weight or the length of the suffix and variable length constant weight codes are used for the prefixes and the suffixes of some of these codes. For encoding of these codes we can use Schalkwijk's algorithm. It is shown that some of the proposed codes are universal and asymptotically optimal in the meaning that P. Elias has defined. We compare them with other known codes from the viewpoints of the length of the codewords corresponding to integers 2^M (M=0, 1, , 30) and the average codeword length for two sources: 26 letters in English sentences and the geometrically distributed positive integers. The results shows that some of the proposed codes which are universal and asymptotically optimal are more efficient than the known codes.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e74-a_9_2504/_p

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@ARTICLE{e74-a_9_2504,
author={Yoko MIYAKAWA, Yuichi SAITOH, Hideki IMAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Binary Encoding Schemes of Positive Integers},
year={1991},
volume={E74-A},
number={9},
pages={2504-2512},
abstract={We propose five classes of variable length codes for encoding positive integers: One is a class of codes having constant Hamming weight. The other four classes of codes have a prefix and a suffix in a codeword. The prefix indicates the weight or the length of the suffix and variable length constant weight codes are used for the prefixes and the suffixes of some of these codes. For encoding of these codes we can use Schalkwijk's algorithm. It is shown that some of the proposed codes are universal and asymptotically optimal in the meaning that P. Elias has defined. We compare them with other known codes from the viewpoints of the length of the codewords corresponding to integers 2^M (M=0, 1, , 30) and the average codeword length for two sources: 26 letters in English sentences and the geometrically distributed positive integers. The results shows that some of the proposed codes which are universal and asymptotically optimal are more efficient than the known codes.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - New Binary Encoding Schemes of Positive Integers
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2504
EP - 2512
AU - Yoko MIYAKAWA
AU - Yuichi SAITOH
AU - Hideki IMAI
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1991
AB - We propose five classes of variable length codes for encoding positive integers: One is a class of codes having constant Hamming weight. The other four classes of codes have a prefix and a suffix in a codeword. The prefix indicates the weight or the length of the suffix and variable length constant weight codes are used for the prefixes and the suffixes of some of these codes. For encoding of these codes we can use Schalkwijk's algorithm. It is shown that some of the proposed codes are universal and asymptotically optimal in the meaning that P. Elias has defined. We compare them with other known codes from the viewpoints of the length of the codewords corresponding to integers 2^M (M=0, 1, , 30) and the average codeword length for two sources: 26 letters in English sentences and the geometrically distributed positive integers. The results shows that some of the proposed codes which are universal and asymptotically optimal are more efficient than the known codes.
ER -