New families of asymptotically optimal codebooks from vectorial dual-bent functions
This work provides new codebook constructions for applications like CDMA and compressed sensing, but the improvement is incremental over existing asymptotically optimal codebooks.
The paper constructs several families of codebooks using vectorial dual-bent functions that asymptotically achieve the Welch bound, with explicitly determined maximum cross-correlation amplitudes and distributions. Some codebooks have new parameters and very small alphabet sizes.
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.