Trellis coding for high signal-to-noise ratio Gaussian noise channels

Abstract

It is known that under energy constraints it is best to have each code word of a code satisfy the constraint with equality, rather than have the constraint satisfied only in an average sense over all code words. This suggests the use of fixed-composition codes on additive Gaussian noise channels, for which the coding gains achievable by this method are significant, especially in the high signal-to-noise-ratio case. The author examines the possibility of achieving these gains by using fixed-composition trellis codes. Shell-constrained trellis codes are promising in this regard, since they can be decoded by sequential decoding at least at rates below the computational cutoff rate.