Optimum permutation modulation codes and their asymptotic performance (Corresp.)
E. Biglieri, Michele Elia · IEEE Transactions on Information Theory · 1976
Permutation modulation codes are a class of group codes for the Gaussian channel whose codewords are obtained by permuting the components of a given initial vectorXin Euclideann-dimensional space. In this paper, the problem of choosing the components ofXin such a way that the minimum distance between any two codewords is maximized is solved. In particular, a closed-form expression is obtained for this minimum distance and is used to investigate the asymptotic behavior of some selected codes.