Unitary Space-Time Group Codes: Diversity Sums From Character Tables

Diversity sum, which is calculated from the Frobenius norm of the difference of two distinct elements in a signal constellation, is the significant parameter to predict a unitary space-time constellation having good performance in low signal-to-noise ratio (SNR). In this correspondence, we propose a method to compute the diversity sum of a unitary group constellation using a character table. Our proposed analysis is simple, requiring only, a lookup of the character table. We illustrate our method for the finite special linear groups SL2, and compare codes with high diversity sum against fixed point free groups at low SNR. We also introduce the notion of a faithful group constellation. that is, one whose diversity sum is greater than 0. Faithful group constellations may be obtained from any nontrivial character of a group. We describe the method to do so in this correspondence and illustrate it with the example of the finite projective special linear group PSL2.