Steiner system signal sets over the Gaussian channel

Steiner systems constitute an example of codes that achieve asymptotic error-free transmission for the Gaussian channel. In contrast to simplex and orthogonal codes which also have this property, these codes make more efficient use of the bandwidth by reducing the required dimensionality to generate the M signals. Tight upper bounds for the symbol error probability are derived for coherent and noncoherent detection that include previously reported results as special cases. The relative bandwidth efficiency with respect to orthogonal codes is presented, and a combined performance plot is given that allows a meaningful comparison between the different coding schemes considered.<>