The Comparative Analysis of Single Error Bursts Decoders for Linear Codes

The article considers the problem of correcting single error bursts, taking into account the influence of the structure of the linear block code parity-check matrix on the performance of decoding algorithms. A heuristic algorithm based on the determination of certain events and an algorithm based on dense information sets for correcting single error bursts are considered. Codes based on a block-permutation construction, as well as random linear codes, are selected. Experiments have been conducted to evaluate the computational efficiency and error probability for the codes and decoders under consideration, taking into account the density of the parity-check matrices and the construction of the codes. It is obtained that when using a block-permutation construction, the heuristic algorithm shows a much lower probability of error with an operating time slightly inferior to the decoder based on dense information sets. However, when the structure of the sparse parity-check matrix changes, the decoding complexity increases, and with increasing matrix density, the complexity of the heuristic algorithm tends to exponential even with small burst lengths. For matrices that do not have a block-permutation structure, the algorithm based on dense information sets shows the best error probability and operating time. Thus, based on the comparative analysis carried out, it can be concluded that the task of correcting single error bursts can be solved with polynomial complexity regardless of the structure of the linear code and optimized taking into account this structure.