Shannon-Kotel'nikov Mappings for Analog Point-to-Point Communications

In this paper an approach to joint source-channel coding (JSCC), named Shannon-Kotel'nikov mappings (S-K mappings), is presented. S-K mappings are (piecewise) continuous, direct source-to-channel mappings operating directly on amplitude continuous, discrete time signals. These mappings include several existing JSCC schemes. There exist many interesting approaches to analog and semi-analog JSCC in the literature that provide both excellent performance as well as robustness to variations in noise level. However, no common theory describing their behavior on a general basis exists at the moment. The objective of this paper is to introduce a general theoretical framework for analysis of analog (and semi-analog) mappings. This framework will enable calculation of distortion when applying such schemes on point-to-point links, reveal more about their fundamental nature, and provide conditions indicating how such mappings should be constructed in order to perform well at low and arbitrary complexity and delay. Since this problem is very difficult we are not attempting to provide a complete theory at this stage, but rather establish a starting point from which future research can be developed. The paper considers memoryless sources with an arbitrary continuous unimodal density function and memoryless Gaussian channels. Most results are valid for good channels.