Algebraic and Combinatorial Coding Theory
A.2.3
Lecture
Algebraic Coding Theory II

Constructions of Complex Codebooks Asymptotically Meeting the Welch Bound: A Graph Theoretic Approach

Shohei Satake, Yujie Gu

Date & Time

01:00 am – 01:00 am

Abstract

Complex codebooks with small inner-product correlation have many applications such as in code-division multiple access communications and compressed sensing. It is desirable but difficult to construct optimal codebooks achieving the well-known Welch bound. In this paper, complex codebooks are investigated from a graph theoretic perspective. A connection between codebooks and Cayley sum graphs is established. Based on this, many infinite families of complex codebooks are explicitly constructed, which are asymptotically optimal with respect to the Welch bound. These constructions not only include some known constructions as special cases but also provide flexible new parameters.


Presenters

Shohei Satake

Kumamoto University

Yujie Gu

Tel Aviv University

Session Chair

Parastoo Sadeghi

Australian National University