A New Error-Correcting Syndrome Decoder with Retransmit Signal Implemented with an Hardlimit Neural Network

Still today the problem of counting the errors of a noisy received word is an open problem in literature. This means that when we use an error correcting code we cannot control if the number of errors of the received noisy word is greater than the error correction capability of the code of k errors, k=(d-1)/2, where d is the minimum Hamming distance of the code. The main advantage of our proposal results from the introduction of the Retransmit signal when the syndrome decoder detects an ambiguity situation and cannot correct the noisy word. These ambiguity situations occur when happens one more error than the error correction capability of the error correcting code. This property of the error correcting syndrome scheme allows increasing the error correction capability of an error correcting code by one error at a little increment of bandwidth or delay in the transmission. Although there are some proposals of implementation of error-correcting decoders with neural networks in literature our work is completely different in what concerns three main aspects. First we propose the implementation of the retransmit signal based on the detection of ambiguity of the minimum Hamming distance between the received word and each of the codewords, i.e. when there are more than one codeword at the minimum Hamming distance to the too noisy received word. Second we use a constructive approach that does not need training. And finally we use hardlimit neurons that can be implemented in hardware by a single transistor in a high gain setup. We begin with two exhaustive simulation experiments where we introduced all manners of occurrence of two errors in all codewords of two codes with minimum Hamming distances 3 and 4, respectively, which only guarantee all possible one error good corrections, to show how the ambiguities arise in the decoding process. Next we present the building blocks of the error correcting decoder based in hardlimit multilayered perceptrons and then we assembled all them out and show an example for an error correcting decoder for a four codewords error correcting code. Finally we discuss the advantages of our proposal and the consequences of the introduction of the Retransmit signal and define possible ways of evolution of our work.