Neural Network Decoders for Linear Block Codes

This paper presents a class of neural networks suitable for the application of decoding error-correcting codes.The neural model is basically a perceptron with a high-order polynomial as its discriminant function. A single layer of high-order perceptrons is shown to be able to decode a binary linear block code with at most 2 weights in each perceptron, where m is the parity length. For some subclass codes, the number of weights needed can be much less. The (2-1,2-1-m) Hamming code can be decoded with only m+1 weights in each perceptron. With the help of genetic algorithms, efficient neural decoders with 2t+1 terms for each bit for some t-error correctable cyclic and BCH codes are obtained. The neural decoders are formulated as a set of parity networks in the first layer followed by a linear perceptron in the second layer, and thus have simple implementations in analogy VLSI technology.