Estimates for the growth of inverse determinant sums of quasi-orthogonal and number field lattices

TL;DR

This paper analyzes the growth of inverse determinant sums in quasi-orthogonal codes, showing they grow logarithmically, which is significantly slower than in comparable number field codes, impacting space-time code performance analysis.

Contribution

It provides a new analysis of inverse determinant sum growth for quasi-orthogonal codes, demonstrating a logarithmic growth rate distinct from number field codes.

Findings

Inverse determinant sums grow logarithmically in quasi-orthogonal codes.

Growth rate is significantly lower than in number field codes.

Results impact the analysis of space-time code performance.

Abstract

Inverse determinant sums appear naturally as a tool for analyzing performance of space-time codes in Rayleigh fading channels. This work will analyze the growth of inverse determinant sums of a family of quasi-orthogonal codes and will show that the growths are in logarithmic class. This is considerably lower than that of comparable number field codes.