Complementary Sets, Generalized Reed-Muller Codes, and Power Control for OFDM

TL;DR

This paper explores the use of generalized Reed-Muller codes and complementary sets to design OFDM schemes with low peak-to-mean envelope power ratio, improving power control and code performance.

Contribution

It generalizes the concept of complementary sets for q-phase sequences and introduces new OFDM coding schemes based on generalized Reed-Muller codes.

Findings

Sequences lie in complementary sets of size 2^{k+1}

Provides tight PMEPR bounds for small k

Codes often outperform existing constructions

Abstract

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2^m lies in a complementary set of size 2^{k+1}, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2^m. A new 2^h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them.