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.

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.

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.

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.

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.