Frequency designed COSET codes for spectrally constrained channels

Abstract

Summary form only given, as follows. The authors present a design method by which good coset codes can be used with channels that have severe intersymbol interference or spectral shaping constraints. The spectral shaping is achieved by using large block lengths in combination with a discrete (finite-length) Fourier transform to decompose the constrained channel into several independent subchannels. Energy and bit allocation methods are designed for application to the group of subchannels using optimal signal sets in four and eight dimensions, so that good coset codes can be used with the group to obtain coding gains close to the maximum. The authors consider both notch codes and codes for channels with finite-length intersymbol interference patterns (partial response), but for which the channel transfer is best specified in the frequency domain. Partial response channels are an important subclass of the channels considered. A method of cyclic extension of the transform is used to ensure independence of the subchannels. The codes derived are unusually powerful and also flexible in the specification of frequency characteristic, at the price of a substantial increase in the number of (time-domain) levels that are input to the channel.