Capacity of block transmission systems with quantized inputs and outputs

A common inaccuracy that is made when computing the capacity of digital channels, is to assume that the inputs and outputs of the channel are analog Gaussian random variables and then based upon that assumption, invoke the Shannon capacity bound for an additive white Gaussian noise (AWGN) channel. In a channel utilizing a finite set of inputs and outputs, clearly the inputs and outputs are not Gaussian distributed and Shannon bound is not exact. In this paper we study the capacity of a block transmission AWGN channel with quantized inputs and outputs given the simultaneous constraints that the channel is frequency selective and there exists an average power constraint P at the transmitter. The channel is assumed known at the transmitter. In [13] we show supporting simulation results consequent upon the theoretical framework developed in this paper as well as the results obtained by applying the framework to a practical example.