Permutation codes for the Gaussian broadcast channel with two receivers

A deterministic coding scheme for reliable transmission over the Gaussian broadcast channel with two receivers is considered. The coding scheme is based upon Slepian´s permutation mudulation codes. It is shown that it is relatively easy for both receivers to accomplish maximum likelihood detection even though one receiver must instrument a composite hypothesis test. Bounds on the performance of various codes are given. The parameters of the codes are chosen in order to achieve the best performance. The performance of these best codes are compared with results predicted by random coding and with time sharing of ordinary permutation codes.