Extended symbol correction algorithm for group testing based non-binary error correction codes of minimum distance d_q < 5

摘要

This work presents a new decoding algorithm that extends the error-correction capacity of group testing based (GTB) non-binary error correction codes without modifying the number of parity symbols of the codeword. A list decoding algorithm based on the pattern of the syndromes takes advantage of the parity matrix equation exploiting its structure. The decoding algorithm can be reformulated by detecting superimposed errors (errors that affect to the same parity check equation). The list of superimposed patterns applies the extrinsic information of the non-superimposed locations to correct the errors. The list of non-superimposed locations simply apply a majority-logic pattern. The complexity of the proposed solution is lower, as it does not require complex operations such as multiplications or inversions in the Galois Field and shares the magnitude equations for both cases, keeping the rest of the equations with the same number of comparisons as the original single-symbol error correction algorithm.