A.P. Ratushin1, E.I. Balunin2, M.V. Vlasov3, D.S. Khrapkov4

1–4 Military University of Radio Electronics (Cherepovets, Russia)

1–4 vure_nio@mil.ru

Modern distributed code structures continue to develop and are optimized through the use of protograph-based parity-check matrices. A protograph can be constructed from a small base matrix with several elements which expanding the code to large block lengths, allows for low encoder complexity while maintaining the property of a linear minimum distance and a fast decoding procedure. These properties are manifested due to the structural features of the parity-check matrices involved in the low-density coding procedure.

The article presents an analytical description of the structural features in the formation of parity-check matrices of effective low-density codes.

The conducted analysis of the structure of parity-check matrices of low-density codes showed that the weight coefficients of the rows and columns are determined by the basic matrix of the protograph, and the positions of the units in the submatrices are set by rearranging the edges between the corresponding variables and check nodes of the Tanner graph. Edge permutation is most often performed using a quasi-cyclic algorithm for generating submatrices. The structure of the parity-check matrices depends on the following facts: the length of the information sequence to be encoded; the subclass of the protograph; the rate of code; coefficients extensions calculated in accordance with the requirements of the PEG and ACE algorithms.

The presented analytical description of the structural features of low-density codes embedded in the formation of parity-check matrices will allow us to build models of distributed code structures based on protographs.

Ratushin A.P., Balunin E.I., Vlasov M.V., Khrapkov D.S. Structural specificity of quasi-cyclic parity-check matrix of low-density protograph-based codes. Electromagnetic waves and electronic systems. 2024. V. 29. № 6. P. 34−39. DOI: https://doi.org/10.18127/ j15604128-202406-04 (in Russian)

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