Perfect Space-Time Codes with Minimum and Non-Minimum Delay for Any Number of Antennas

TL;DR

This paper introduces the construction of perfect space-time codes with minimum and non-minimum delay for any number of antennas, extending their optimal properties beyond previously known dimensions.

Contribution

It presents a novel method to construct perfect space-time codes for all antenna configurations, including minimum and non-minimum delay variants.

Findings

Constructed perfect codes for all channel dimensions.

Achieved full rate, full diversity, and non-vanishing determinant.

Extended optimal code properties to new antenna configurations.

Abstract

Perfect space-time codes were first introduced by Oggier et. al. to be the space-time codes that have full rate, full diversity-gain, non-vanishing determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping of the constellation. These defining conditions jointly correspond to optimality with respect to the Zheng-Tse D-MG tradeoff, independent of channel statistics, as well as to near optimality in maximizing mutual information. All the above traits endow the code with error performance that is currently unmatched. Yet perfect space-time codes have been constructed only for 2,3,4 and 6 transmit antennas. We construct minimum and non-minimum delay perfect codes for all channel dimensions.