About the Joint Correcting of Error Bursts and Independent Errors Using LDPC Codes

This article discusses the application of low-density parity-check (LDPC) codes for error correction, with a focus on the joint correction of both grouped and independent errors in communication and data storage systems. The error correction capabilities of LDPC codes with different constructions were estimated when correcting single error bursts and independent errors. Experiments showed that correcting even a single independent error significantly reduces the correctable burst length. A specialized sliding window list decoder designed for joint correction of burst and independent errors was introduced. It uses a single burst correction decoder with certain events and list decoding for independent single errors. The problem of reducing the list size was addressed based on the majority logic principle. However, reducing the list size increases the decoding error probability. Estimates of decoding error probabilities when simultaneously correcting burst and independent single errors are provided, considering burst lengths beyond the code correcting capability. Different strategies for selecting the number of blocks in the block-permutation construction of LDPC codes for burst-only and joint burst-independent error decoding are analyzed. Experiments show that for a fixed code length and rate, the code with three stripes of blocks provides better performance in this case.