Construction of LDPC Codes for Single Bursts Correction by Masking

P. 1–5.

Veresova A., Ovchinnikov A.

This paper addresses the problem of constructing
codes for correcting single error bursts. The construction is
based on a block-circulant design of low-density parity-check
codes. For such a design, the maximal correctable burst length
is limited by the block size, which forces consideration of codes
whose parity-check matrix contains only a small number of large
blocks. However, this significantly restricts the attainable sets
of code lengths and code rates, and, aside from a few special
cases, such codes may be turned out to be rather far from
the Reiger bound on the maximum correctable burst length. To
overcome these limitations we introduce a masking procedure and
propose a method for constructing a masking matrix based on
evaluating the burst correcting capability of a code. Experiments
estimating the correcting capability of the proposed codes in
comparison with both the original block-circulant construction
and with random codes defined by dense parity-check matrices
were performed. The proposed methodology provides quasi-
cyclic low-density parity-check codes whose correcting capability
substantially exceeds that of block-circulant codes without zero
subblocks and, for certain parameter choices, approaches the
Reiger bound. The resulting codes also provide greater flexibility
in varying the number and size of blocks, enabling more versatile
adjustment of code lengths and code rates. Finally, the burst
correcting capability of the proposed construction is comparable
to that of codes defined by dense parity-check matrices, while
its quasi-cyclic structure enables more computationally efficient
encoding and decoding procedures.

Keywords: LDPC codes, quasi-cyclic codes, error bursts, Reiger bound

Publication based on the results of: Research and development of methods for increasing the security and reliability of message delivery using code-based post-quantum cryptography in systems with multiple access (2025)

In book

2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), 5-7 Nov. 2025

IEEE, 2025.