On the PMEPR of phase-shifted binary codes

The peak-to-mean envelope power ratio (PMEPR) of a code employed in orthogonal frequency-division multiplexing (OFDM) systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift. Motivated by some previous designs of phase shifts using suboptimal methods, the following question is considered in this paper. For a given binary code, how much PMEPR reduction can be achieved when the phase shifts are taken from a 2(h)-ary phase-shift keying (PSK) constellation? A lower bound on the PMEPR is established, m which is related to the covering radius of the binary code. Most notably, a small covering radius of the binary code precludes a significant PMEPR reduction. The bound is then applied to some well understood codes, including BCH codes and their duals, Reed-Muller codes, and convolutional codes. It appears that some previously obtained (presumably not optimal) results attain or approach our bound.