Shifted inverse determinant sums and new bounds for the DMT of space-time lattice codes

TL;DR

This paper develops a general framework for analyzing shifted inverse determinant sums in space-time lattice codes, providing new bounds that relate to the diversity-multiplexing trade-off and decoding performance across all multiplexing gains.

Contribution

It introduces a comprehensive approach to study shifted sums for all multiplexing gains, extending previous low-gain analyses, and derives bounds that link these sums to key code properties.

Findings

Bounds characterize the diversity-multiplexing trade-off.

Shifted sums relate to decoding performance and SNR thresholds.

Framework applies to all multiplexing gains, not just low.

Abstract

This paper considers shifted inverse determinant sums arising from the union bound of the pairwise error probability for space-time codes in multiple-antenna fading channels. Previous work by Vehkalahti et al. focused on the approximation of these sums for low multiplexing gains, providing a complete classification of the inverse determinant sums as a function of constellation size for the most well-known algebraic space-time codes. This work aims at building a general framework for the study of the shifted sums for all multiplexing gains. New bounds obtained using dyadic summing techniques suggest that the behavior of the shifted sums does characterize many properties of a lattice code such as the diversity-multiplexing gain trade-off, both under maximum-likelihood decoding and infinite lattice naive decoding. Moreover, these bounds allow to characterize the signal-to-noise ratio thresholds corresponding to different diversity gains.