A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound

Zhangti YAN; Zhi GU; Wei GUO; Jianpeng WANG

doi:10.1587/transfun.2021EAL2109

A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound

Zhangti YAN, Zhi GU, Wei GUO, Jianpeng WANG

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Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q²+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.11 pp.1513-1516

Publication Date: 2022/11/01

Publicized: 2022/05/16

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2021EAL2109

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Zhangti YAN
  Southwest Jiaotong University
Zhi GU
  Southwest Jiaotong University
Wei GUO
  Southwest Jiaotong University
Jianpeng WANG
  Southwest Jiaotong University

Keyword

codebook, Levenshtein bound, Ramanujan graph, maximal cross-correlation amplitude

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Zhangti YAN, Zhi GU, Wei GUO, Jianpeng WANG, "A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound" in IEICE TRANSACTIONS on Fundamentals, vol. E105-A, no. 11, pp. 1513-1516, November 2022, doi: 10.1587/transfun.2021EAL2109.
Abstract: Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q²+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2109/_p

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@ARTICLE{e105-a_11_1513,
author={Zhangti YAN, Zhi GU, Wei GUO, Jianpeng WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound},
year={2022},
volume={E105-A},
number={11},
pages={1513-1516},
abstract={Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q²+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.},
keywords={},
doi={10.1587/transfun.2021EAL2109},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1513
EP - 1516
AU - Zhangti YAN
AU - Zhi GU
AU - Wei GUO
AU - Jianpeng WANG
PY - 2022
DO - 10.1587/transfun.2021EAL2109
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2022
AB - Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q²+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.
ER -