Cutoff rate for fixed-composition coding over energy constrained AWGN channels

Abstract

Shannon showed that, under an energy constraint, the ensemble of shell constrained codes optimizes the cutoff rate for AVVGN channels. Unfortunately, this ensemble is not very practical since its input alphabet is the entire real line. In this thesis, we consider the ensemble of fixed-composition codes which satisfy the shell constraint and have a finite input alphabet. For a certain four-letter symrnetric input alphabet, the cutoff rates for ensembles of fixed-composition codes of blocklengths ii]) to 10 are compnti'd for tlie AVVGN channel at various signal-to-noise ratios. Also an asymptotic analysis of these cutoff rates is carried out a.s blocklenghth tends to infinity. These results are compared with the cutoff rates optimized over the independentletters code ensemble, which is the ensemble ordinarily used in [>ractice. The results of this comparison show that, for relatively moderate signal-to-noise ratios, it is possible to achieve cutoff rates within 1-2% of the optimum value by using fixed-composition codes; whereas, with iudepeiideiit-letters codes, one can get at most within 9-10% of the optimum value. Thus, fixed-composition codes can provide significant improvements in cutoff rate in practice, cispiicially for moderate to high signal-to-noise ratios.