The paper is devoted to the search for an effective decoding method for a new class of binary erasure-correcting codes. The codes in question are set by an encoding matrix with restrictions on column weights (MRSt codes). To work with the constructed codes, a decoder based on information aggregates and a decoder based on the belief propagation are used, adapted for the case of erasures. Experiments have been carried out to determine the decoding speed and correcting ability of these methods in relation to the named classes of noise-resistant codes. In the case of MRSt codes, the decoder, based on the principle of spreading trust, significantly benefits in speed compared to the decoder for information aggregates, but loses slightly in terms of corrective ability.

Keywords: channels with erasure, distributed fault-tolerant data storage systems, code with equal-weight columns, decoder based on information aggregates, decoder based on the belief propagation, RSt code, MRSt code

Unintentional errors occur in all data transmission channels. The standard way to deal with them is to use noise-resistant codecs based on the use of algebraic error correction codes. There are transmission channels in which a special type of error occurs – erasures, i.e. a type of error in which the location of the error is known, but its value is not known. Coding theory claims that error-control methods can be applied to protect data from erasure, however, these statements are not accompanied by details. This work fills this gap. Algorithms for correcting erasures using arbitrary decoders for error correcting codes are constructed. Lemmas about the correctness of the constructed algorithms are formulated, some estimates of the probability of successful decoding are obtained.

Keywords: channels with erasures, noise-resistant code, algebraic code, error correction code decoder, erasure correction algorithm