A class of block codes with expanded signal-sets for PSK-modulation

The authors deal with a block coding approach to channel codes in which the redundancy is obtained not from parity symbols, but by expanding the channel signal constellation. Such codes are well suited for the bandlimited channel because the data rate and the bandwidth are unaffected. For transmission of m information bits/symbol they use the signal set 2^m+1-PSK. The signal set is given the structure of the finite field GF(2^m+1). The code is defined by a square generator matrix over the finite field. A good subclass of codes is obtained by giving the matrix a cyclic structure. A computer search results in codes with coding gains of the order of 0.2-6.0 dB over uncoded modulation for code lengths up to 12 symbols