В.A. Gluskin1

1 Central Scientific Research Institute of All-Union Combined Arms and Space Forces of the Ministry of Defense of the Russian Federation (Korolev, Mowsov Region, Russia)

The properties of the matrix whose elements are Hemming distances between binary combinations of a given length are considered. The proof of the statement concerning expediency of using the above matrix as a loss matrix in decoding block codes is presented. The algorithm of factorization of calculation of a product of a binary vector on the above matrix and the modified algorithm of decoding of linear block codes on the basis of criterion of the minimum average risk is offered.

The current state of the telecommunications industry is characterized by a significant increase in the volume of transmitted information. In conditions of limitations on frequency resource, the most important task determining the results of competition of telecommunication equipment manufacturers is the development and implementation of new effective methods of information transmission and reception, allowing to ensure a given level of reliability of message reception in complex conditions of signal and interference environment. One of the promising directions for solving the problem of increasing the reliability of information reception is the development of new models, methods and techniques that allow to remove restrictions in the form of uniform law of probability distribution of symbols of the transmitted message and binomial law of probability distribution of symbols of the error stream in a discrete communication channel, often inadequate to the real situation.

Improving the efficiency of LIS (information transmission systems) is based on trade-offs between frequency and energy efficiency and is reduced to reducing the redundancy of modulation and coding systems. However, entropy coding methods that take into account only the probability distributions of source symbols are not efficient, and codes that take into account statistical relationships are complex and require unacceptable transmission delay when encoding long sequences of symbols. This circumstance determines the potential possibility of using the redundancy of the source of messages to solve the problem of improving the reliability of reception, provided that the transformation carried out by the scrambler, which is now a mandatory element of the information transmission path.

Using peculiarities of MF construction, it is possible to reduce computational complexity of algorithm of decoding of BC on criterion of the minimum average risk approximately in times. Thus, correcting ability of the developed algorithm corresponds to correcting ability of the algorithm given in [2]. In addition, the fast minimum average risk algorithm allows to perform parallel calculations, which can further reduce the computational complexity by a factor of where – the number of parallel branches. depends on the number of pins for data input/output and the number of cells that perform the multiplication operation in the FPGA. In this case, the computational complexity will only depend on.

Gluskin В.A. Fast decoding of block codes by criterion of minimum average risk on the basis of loss matrix factorization. Dynamics of complex systems. 2023. V. 17. № 4. P. 45−55. DOI: 10.18127/j19997493-202304-05 (in Russian)

1. Konyshev M.Yu., Shinakov S. V., Pankratov A. V., Utyanskij E. M. Model' diskretnogo istochnika oshibok v cifrovyh kanalah svyazi. Izv. GTU. Informacionnye sistemy i tekhnologii. 2010. № 5. S. 135–141 (in Russian).
2. Konyshev M.Yu., Pankratov A.V, Shinakov S.V., Baranov S.V. Neparametricheskoe dekodirovanie blokovyh kodov v kanalah s negaussovymi shumami. Telekommunikacii. 2011. № 3. S. 3–9 (in Russian).
3. Kormen T.H., Lejzerson Ch.I., Rivest R.L., Shtajn K. Algoritmy: postroenie i analiz. M.: Izdatel'skij dom «Vil'yams», 2005. 1296 s. (in Russian)
4. Bol'shev A.I., Lom. R.S. O razlichenii gipotez pri funkciyah poter', zavisyashchih ot resheniya. Problemy peredachi informacii. T. XII. Vyp. 2. M.: Nauka i tekhnologii. 1976. S. 43–46 (in Russian).
5. De Grot M. Optimal'nye statisticheskie resheniya. M.: Mir. 1974. 490 s. (in Russian).
6. Zyuko A.G., Fal'ko A.I., Panfilov I.P., BanketV., Ivashchenko P.V. Pomekhoustojchivost' i effektivnost' sistem peredachi informacii. Pod red. A.G. Zyuko. M.: Radio i svyaz'. 1985. 272 s. (in Russian)
7. Bloh E.L., Popov O.V., Turin V.Ya. Modeli istochnika oshibok v kanalah peredachi cifrovoj informacii. M.: Svyaz'. 1971. 312 s. (in Russian)
8. Davydov I.Yu., Kozlov D.A., Shahtanov S.V., Shibaeva M.Yu. Perestanovochnoe dekodirovanie v sisteme kombinacij kodovyh konstrukcij pri ocenke biometricheskih dannyh. Avtomatizaciya processov upravleniya. 2019. № 3 (47). S. 67–74 (in Russian).
9. Gallager R. Teoriya informacii i nadezhnaya svyaz'. M.: Sov. radio. 1974. 720 s. (in Russian)
10. Gladkih A.A., Pchelin N.A., Shahtanov S.V. Minimizaciya ob"ema pamyati kognitivnoj karty dekodera v sisteme poiska ekvivalentnyh kodov. Radiotekhnika. 2018. № 6. S. 38–41 (in Russian).
11. Shein V.V. Obespechenie celostnosti v sistemah hraneniya dannyh na osnove snizheniya vychislitel'noj slozhnosti dekodirovaniya pomekhoustojchivyh kodov. Promyshlennye ASU i kontrollery. 2018. № 5. S. 43–49 (in Russian).