I.V. Sviridova − Senior Lecturer, 

Department of Design and Production of Radio Equipment, 

Voronezh State Technical University (Voronezh, Russia)

E-mail: ri-ss-ka@mail.ru

A.V. Bashkirov − Dr.Sc. (Eng.), Associate Professor, 

Head of Department of Design and Production of Radio Equipment, 

Voronezh State Technical University (Voronezh, Russia)

E-mail: fabi7@mail.ru

S.Y. Beletskaya − Dr.Sc. (Eng.), Professor, 

Department of Computer-Aided Design and Information Systems, 

Voronezh State Technical University (Voronezh, Russia)

E-mail: su_bel@mail.ru

S.I. Panychev − Dr.Sc. (Eng.), Associate Professor, Leading Research Scientist,  Center for System Research and Development,

JSC «Scientific and Technical Center for Electronic Warfare» (Voronezh, Russia)

E-mail: pany4ev@mail.ru

N.V. Astakhov − Ph.D. (Eng.), Associate Professor,

Department of Design and Production of Radio Equipment, 

Voronezh State Technical University (Voronezh, Russia) E-mail: kokakoller@gmail.com

Formulation of the problem. R. Gallagher proposed codes with a low density of parity checks (LDPC), as well as several decoding algorithms with messaging, among which the trust propagation algorithm (BP), as you know, has the best performance. The excellent performance of message-decoding LDPC codes has made them reliable candidates for error correction in many digital communications systems. As a linear block code, the LDPC code may be represented by a Tanner graph. Given the Tanner graph for the LDPC code, it was shown that an iterative implementation of BP, which happens as if there are no loops on the graph, gives impressive results. In fact, it is well known that if the Tanner graph does not have a cycle, then BP converges to a posteriori probability for variable nodes. However, in many applications, LDPC codes are short to intermediate in length (from several hundred to several thousand bits), and the assumption of a loop without a loop is unacceptable.

Purpose. Explore two very simple modifications of the trust propagation algorithm (BP), which provide a slight improvement in BP performance, especially for short and intermediate block lengths.

Results. Two modified versions of the trust propagation algorithm are presented, a normalized and biased algorithm, in which the reassessment of message reliability is compensated by the multiplicative and additive correction factors, respectively. The simulation results show that both algorithms work more or less the same during optimization, and both of them provide a slight performance improvement compared to the standard trust propagation algorithm. The proposed algorithms, called “normalized BP” and “biased BP”, reduce the absolute value of outgoing messages of the logarithmic likelihood coefficient (LLR) in the variable nodes using the multiplicative coefficient and the additive coefficient, respectively.

Practical significance. A normalized confidence propagation algorithm with a fixed correction factor can be easily implemented (without additional transistors) by scaling the transistors in the current pipelines used in the analog implementation of the confidence propagation algorithm.

Sviridova I.V., Bashkirova A.V., Beletskaya S.Y., Panycheva S.N., Astakhova N.V. Improving belief propagation on graphs with cycles. Radiotekhnika. 2020. V. 84. № 6(12). P. 37−41. DOI: 10.18127/j00338486-202006(12)-07.

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