Quantization Over Discrete Noisy Channels Under Complexity Constraints

Abstract

A fundamental problem in communication is the transmission of an information source across a communication channel. According to Shannon's separation principle, this problem can be separated (without loss of optimality) into two different, yet similar, problems: source coding and channel coding. This result, however, holds only when complexity and delay are not an issue. In practical situations, complexity plays a major role in many system designs. When complexity is constrained, treating these two problems jointly may prove to be more fruitful than treating them separately.<P>In this work we consider two approaches to joint source-channel coding of discrete-time, continuous- amplitude sources and discrete memoryless channels when complexity is constrained.<P>In the first approach, we consider the analysis and design of two low-complexity vector quantizer - the tree-structured vector quantizer (TSVQ) and the multistage vector quantizer (MSVQ) - when used over a noisy channel. The resulting schemes are called channel-matched TSVQ and channel- matched MSVQ. These schemes are compared with (i) the ordinary TSVQ and MSVQ which are designed for the noiseless channel and (ii) a tandem source-channel coding scheme in which the source and channel codes are designed separately.<P>In the second approach, we assume a low-complexity quantizer (i.e., source code) is given. Because of its low complexity, the quantizer is sub-optimum and hence certain redundancy remains at its output. Our aim is to make use of this redundancy to combat channel noise. We consider two scenarios: (i) the redundancy is in the form of memory and (ii) it is in the form of a non-uniform distribution.<P>In the second case, we propose the use of a rate- one convolutional code to convert the residual redundancy into a usable form. Comparisons are also made with a tandem source- channel coding scheme.