A.A. Ovchinnikov1, A.A. Fominykh2

1 St. Petersburg State University of Aerospace Instrumentation (St. Petersburg, Russia)
 

he existing error-correcting methods for modern communication standards are built on the assumption that the appearing errors are independent. However, in real communication channels, errors are not independent. In such a case, it is said that the channel has a memory. It is known that channel memory, when exploited, allows one to increase the channel capacity. On the one hand, a simple technique called interleaving is used to perform decoding in memory channels, reducing the impact of code redundancy. On the other hand, to achieve the increased channel capacity and exploit the code redundancy and increase, it is required to construct special methods of encoding and decoding.

Low-density parity-check (LDPC) codes are one of the most popular types of error-correcting codes nowadays. The existing decoding algorithms for LDPC, such as a belief propagation algorithm and a bit flipping algorithm, may be used in channels with memory, but the errors will be treated as independent. Thus, the channel memory is not exploited, degrading the system error correcting performance. Therefore, the construction of the decoding methods that take into account the channel memory are of great importance.

The paper presents two novel heuristic decoding methods that solve the problem of ambiguous decisions appearing during the decoding process. The simulations are carried out in a channel with artificial error bursts for random block-permutation LDPC code. The presented decoding algorithms show lower error probability compared to existing decoding methods and allow a reduction in time consumption. The presented algorithms open the prospect for further investigation of possible algorithm modifications.

Ovchinnikov A.A., Fominykh A.A. About two heuristic error burst decoding algorithms for channels with memory using LDPC codes. Achievements of modern radioelectronics. 2022. V. 76. № 12. P. 55–65. DOI: https://doi.org/ 10.18127/j20700784-202212-08 [in Russian]

1. Eckford A.W., Kschischang F.R., Pasupathy S. Analysis of low-density parity-check codes for the Gilbert-Elliott channel. IEEE Transactions on Information Theory. 2005. V. 51. № 11. S. 3872–3889.
2. Eckford A.W., Kschischang F.R., Pasupathy S. On designing good LDPC codes for Markov channels. IEEE Transactions on Information Theory. 2006. V. 53. № 1. S. 5–21.
3. Gilbert E.N. Capacity of a burst‐noise channel. Bell system technical journal. 1960. V. 39. № 5. S. 1253–1265.
4. Elliott E.O. Estimates of error rates for codes on burst-noise channels. The Bell System Technical Journal. 1963. V. 42. № 5.
   S. 19771997.
5. Ryan W., Lin S. Channel codes: classical and modern. Cambridge university press., 2009. 710 p.
6. Gallager R. Low-density parity-check codes. IRE Transactions on information theory. 1962. V. 8. № 1. P. 21–28.
7. Kruk E.A., Ovchinnikov A.A. Tochnaya korrektiruyushchaya sposobnost' kodov Gilberta pri ispravlenii paketov oshibok. Informacionno-upravlyayushchie sistemy. 2016. T. 80. № 1. S. 80–87 [in Russian].
8. Krouk E.A., Ovchinnikov А.А. Block-permutation LDPC codes for distributed storage systems. Smart Innovation, Systems and Technologies. 2015. V. 40. P. 227–238.
9. Hu X.Y., Eleftheriou E., Arnold D.M. Regular and irregular progressive edge-growth tanner graphs. IEEE transactions on information theory. 2005. V. 51. № 1. P. 386–398.
10. Veresova A.M., Ovchinnikov A.A. About one algorithm for correcting bursts using block-permutation LDPC-codes. 2019 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF). IEEE. 2019. P. 1–4.
11. Ovchinnikov A. A., Fominykh A.A. About Some Irregular Degree Distributions of LDPC Codes in Two-State Channels. 2021 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF). 2021. P. 1–4.