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 codewords, 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 affected by independent random errors, this strategy requires a small number of patterns to obtain a good identification with high probability of the code from the noisy data.