Combined permutation codes using M-ary modulation for AWGN and fading channels

Modern wireless communication systems require an efficient use of the spectrum. Here we introduce the use of permutation codes (PC) as a combined source coding and channel modulation system using M-ary phase shift keying as the modulation formats. We combine the features of a permutation code vector quantizer and a permutation code as channel modulator. For source coding the permutation code is a class of constant weight vector quantizer, and its rate-distortion performance is near optimal considering practical vector lengths. We obtained the rate-total distortion performance for the combined system when an M-ary PSK modulation formats is used as channel symbols. The performance is obtained using numerical methods for AWGN channel and for frequency nonselective slowly fading channel. We found that the combined system has the advantage over non combined systems of lower encoding delay, and hence simpler transmitter and receiver. Also, we would be able to optimize the overall distortion as a function of the design parameters.