Asymptotic Bounds In Source-channel Coding
We consider the problem of scalar quantization in the presence of channel noise and develop lower bounds on the mean-squared error between a real-valued hput and its reproduction. Bennett's htegral is an asymptotic formula for the distortion of a scalar quantizer in terms of the source density and the distribution of quantization points (i.e. point density), when the channel is assumed to be noiseless. We look to derive a bound on distortion for the noisy channel channel case that depends on the channel statistics, the source density and the quantizer point density. The lower bounds are derived for the general scalar case and are evaluated for uniform and nonuniform (Gaussian pdfoptimized) scalar quantizers.