Blind channel equalization of encoded data over galois fields

In communication systems, the study of elements and structures defined over Galois fields are generally limited to data coding. However, in this work, a novel perspective that combines data coding and channel equalization is considered to compose a simplified communication system over the field. Besides the coding advantages, this framework is able to restore distortions or malfunctioning processes, and can be potentially applied in network coding models. Interestingly, the operation of the equalizer is possible from a blind standpoint through the exploration of the redundant information introduced by the encoder. More specifically, we define a blind equalization criterion based on the matching of probability mass functions (PMFs) via the Kullback-Leibler divergence. Simulations involving the main aspects of the equalizer and the criterion are performed, including the use of a genetic algorithm to aid the search for the solution, with promising results.