Linear Codes Interpolation from Noisy Patterns by means of a Vector Quantization Process

An algorithm inferring a boolean linear code from noisy patterns received by a noisy channel, under the assumption of uniform occurrence distribution over the code-words, and an upper bound to the amount of data are presented. A vector quantizer is designed from the noisy patterns, choosing the obtained codebook as code approximation. It is shown both theoretically and experimentally that, when the data are aaected by independent random errors, this strategy requires a small number of patterns to obtain a good identiication with high probability of the code from the noisy data.