Quaternary Constant-Amplitude Codes for Multicode CDMA

TL;DR

This paper explores the construction of quaternary constant-amplitude codes over Z_4 for multicode CDMA systems, providing new methods to achieve error correction and constant amplitude properties for all positive integer lengths.

Contribution

It introduces novel constructions of quaternary constant-amplitude codes using bent functions and algebraic codes, applicable for all positive integer lengths, including odd m where binary codes cannot exist.

Findings

Existence of quaternary constant-amplitude codes for all positive m

Construction methods using bent functions and algebraic codes

Mappings from binary to quaternary codes provided

Abstract

A constant-amplitude code is a code that reduces the peak-to-average power ratio (PAPR) in multicode code-division multiple access (MC-CDMA) systems to the favorable value 1. In this paper quaternary constant-amplitude codes (codes over Z_4) of length 2^m with error-correction capabilities are studied. These codes exist for every positive integer m, while binary constant-amplitude codes cannot exist if m is odd. Every word of such a code corresponds to a function from the binary m-tuples to Z_4 having the bent property, i.e., its Fourier transform has magnitudes 2^{m/2}. Several constructions of such functions are presented, which are exploited in connection with algebraic codes over Z_4 (in particular quaternary Reed-Muller, Kerdock, and Delsarte-Goethals codes) to construct families of quaternary constant-amplitude codes. Mappings from binary to quaternary constant-amplitude codes are presented as well.