Lower Bounds on Maximum Signal-to-Noise Ratios for Digital Communication Over the Gaussian Channel

This paper considers the performance of a class of digital communication systems wherein a uniformly distributed stationary process from an analog source is sampled and quantized and transmitted by means of a generalized form of pulse-code modulation (PCM). It is shown that output signal-to-noise ratios may be obtained which increase exponentially as a function of the channel signal-to-noise ratio in the bandwidth of the source. Lower bounds on the maximum exponent for an optimized system are obtained for conventional PCM, for coded PCM with no coding delay and for coded PCM with arbitrarily large delay. Improved performance is obtained at the cost of considerable expansion of the modulated bandwidth over the source bandwidth. Expressions for the bandwidth expansion for these systems are also obtained. Mention is made of the similarity of these exact results for digital systems to recent approximate results for analog modulation systems.