| Error control decoding techniques fall into two broad classes: hard decision decoding and soft decision decoding. Soft decision decoding offers substantially improved performance over the hard decision techniques over most channels. However, in the case of error control decoding of block codes, computationally efficient soft decision techniques have not yet been discovered. The resurgence of interest in parallel processing and artificial neural networks in the early 1980's offers the promise of providing efficient mechanisms for performing soft decision decoding. Three-layer multilayer perceptrons can build arbitrary decision regions for any finite set of input and output pair of points. Soft decision decoders form decision regions that are the Voronoi cells of the code words for the code in question. This dissertation reveals certain fundamental relationships between neural network classification and soft decision decoding based upon the Voronoi cell construction of an arbitrary list of points. A new type of network, the maximally robust neural network, is introduced. Given an arbitrary set of inputs and desired outputs, the maximally robust neural network withstands the maximum amount of noise while still yielding the desired reliable performance. This network design is extended, and construction rules for a maximally robust soft decision decoder are presented. This new decoder, the Voronoi decoder, is shown to perform ideal soft decision decoding of some well-known codes including the Hamming codes, Golay codes, and Reed-Muller codes. |
