New families of asymptotically optimal codebooks from vectorial dual-bent functions
2026-06-29 • Information Theory
Information Theory
AI summaryⓘ
The authors use a special kind of mathematical function called vectorial dual-bent functions to create groups of code sequences known as codebooks. These codebooks have very low overlap between codes, which is important for clear communication in systems like CDMA and MIMO. The authors show that their codebooks come close to the best possible limit for low overlap and provide exact details about how much overlap exists. Some of their codebooks also use fewer symbols, which can be practical for real-world use.
CodebookCross-correlationWelch boundVectorial dual-bent functionsCDMAMIMOCompressed sensingCoding theoryMaximum cross-correlation amplitude
Authors
Yadi Wei, Jiaxin Wang, Fang-Wei Fu, Wenjuan Yin
Abstract
Codebooks with small maximum cross-correlation amplitudes play an important role in many applications, such as code division multiple access (CDMA) communication systems, multiple-input multiple-output (MIMO) communications, compressed sensing, and coding theory. In this paper, by using vectorial dual-bent functions, we construct several families of codebooks that asymptotically achieve the Welch bound. The maximum cross-correlation amplitudes and the distributions of the cross-correlation amplitudes of the constructed codebooks are explicitly determined. Furthermore, these codebooks have new parameters, and some of them have very small alphabet sizes.