Burst Detection and Correction for Gilbert Codes and its QC-LDPC Extensions

The article discusses the issue of determining the location of an error burst based on the structure of a block-permutation low-density parity-check code. Quasi-cyclic low-density parity-check codes with a small number of blocks are considered, making it possible to correct the longest possible bursts within this construction. Through experimentation, the maximum, minimum, and average number of attempts was estimated when determining the start position of the error burst. The features of determining the location of a packet in block-permutation low-density parity-check codes are revealed. The proposed method is based on using majority decoding techniques and allows reducing the average number of attempts to locate a burst from hundreds to units for the codes under consideration. Using the packet detection method, which is based on the analysis of the structure of the parity-check matrix, algorithms for decoding Gilbert and extended Gilbert codes have been proposed, ensuring the correction of bursts within their error-correction capabilities. The process of decoding extended Gilbert codes utilizes list decoding in a supercode, with a criterion for selecting the error vector based on the syndrome.