A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound

Zhangti Yan,Zhi Gu,Wei Guo,Jianpeng Wang

IEICE transactions on fundamentals of electronics, communications and computer sciences/IEICE transactions on fundamentals of electronics, communications and computer science（2022）

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摘要

Codebooks with small maximal cross-correlation ampli-tudes 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 = q(2) +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.

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关键词

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

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