Gilbert-Varshamov bound for Euclidean space codes over distance-uniform signal sets. (Correspondence)

In this correspondence, in extension of Piret's bound for codes over phase-shift keying (PSK) signal sets, we investigate the application of the Gilbert-Varshamov (GV) bound to a variety of distance-uniform (DU) signal sets in Euclidean space. It is shown that four-dimensional signal sets matched to binary tetrahedral, binary octahedral, and binary icosahedral groups lead to better bounds compared to the bounds for signal sets matched to dicyclic groups with the same number of signal points and comparable symmetric PSK signal sets. Index Terms--Euclidean space codes, Gilbert-Varshamov (GV) bound, group codes, multilevel construction, signal sets matched to groups, uniform signal sets.