Estimation of error-correction performance for self-orthogonal codes

The article discusses the problem of improving the reliability of data transmission over noisy channels, the effective solution of which is associated with the use of error-correcting coding. The multithreshold methods for decoding self-orthogonal codes proposed earlier by the authors are among the best in terms of efficiency and complexity of implementation both in classical channels with independent errors and in channels with erasures. At the same time, in a number of problems related to the design of multithreshold decoders and the construction of the used self-orthogonal codes, it is required to evaluate their efficiency at a high noise level. The known analytical estimates are valid for low noise levels and are not suitable for this. The aim of this work is to obtain lower bounds on the error and erasure probability in channels with independent errors and erasures for multithreshold decoders, taking into account the structure of self-orthogonal codes and decoder parameters. In this work, new analytical bounds on the error probability of multithreshold decoders are obtained for a binary symmetric channel and a channel with erasures. When deriving these estimates, the structure of the generating polynomial of the used code was taken into account, which determines the dimensions of the checks used by the threshold element, and the parameters of the decoder. The research results presented in the work showed that these bounds are in good agreement with the results of computer modeling even with a high noise level in the channel. The use of the proposed bounds in the design of multithreshold decoders will make it possible to construct more efficient self-orthogonal codes, including those with parallel concatenation, which ensure the operation of multithreshold decoders near the channel capacity.