Bandwidth compression for continuous amplitude channels based on vector approximation to a continuous subset of the source signal space

Two methods for transmission of a continuous amplitude source signal over a continuous amplitude channel with a power constraint are proposed. For both methods, bandwidth reduction is achieved by mapping from a higher dimensional source space to a lower dimensional channel space. In the first system, a source vector is quantized and mapped to a discrete set of points in a multidimensional PAM signal constellation. In the second system the source vector is approximated with a point in a continuous subset of the source space. This operation is followed by mapping the resulting vector to the channel space by a one-to-one continuous mapping resulting in continuous amplitude channel symbols. The proposed methods are evaluated for a memoryless Gaussian source with an additive white Gaussian noise channel, and offer significant gains over previously reported methods. Specifically, in the case of two-dimensional source vectors, and one-dimensional channel vectors, the gap to the optimum performance theoretically attainable is less than 1.0 dB for a wide range of channel signal-to-noise ratios.