Permutation modulation is a class of group codes for the Gaussian channel. A group code is a set of vectors obtained by a group of orthogonal matrices operating on an initial vector. An important problem is to find the initial vector yielding the largest minimum Euclidean distance between two vectors. This problem is solved for permutation modulation. The performance of such optimized permutation modulation is analyzed. Compared to binary antipodal signals and PSK (phase-shift keying), it typically requires 2.5-4 dB less energy for the same minimum distance. >
