# LDPC codes constructed from some combinatorial structures

Šimac, Marina (2017) LDPC codes constructed from some combinatorial structures. Doctoral thesis, Faculty of Science > Department of Mathematics.

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## Abstract

The main subjects of the thesis are LDPC codes constructed from combinatorial structures. Combinatorial structures that have been used for the construction are: $$\mu$$-geodetic graphs obtained from block designs, strongly regular graphs with parameters $$(v, k, 0, 1)$$, and block designs with parameters $$(45, 5, 1)$$. In the thesis we have constructed a family of LDPC codes using $$\mu$$-geodetic graphs obtained from block $$(v, k, \lambda)$$ designs. We have shown that the Tanner graphs of LDPC codes constructed from $$\mu$$-geodetic graphs obtained from block designs with $$k=3$$ are free of cycles of length four, and we have analyzed properties of the constructed codes. We have examined a connection between the parameters of the constructed codes and the parameters of the initial design. The existence and the structures of absorbing sets in the Tanner graphs of the constructed codes have been analyzed. Analysis of structures of the absorbing sets enabled us to determine the exact number of the absorbing sets of certain size using parameters of the initial design. For construction of LDPC codes we have used strongly regular graphs with parameters $$(v, k, 0, 1)$$ since the Tanner graph of the corresponding LDPC code is free of cycles of length four. We have examined the existence and the structures of absorbing sets in the Tanner graphs of the constructed codes. LDPC codes from some block designs with parameters $$(45, 5, 1)$$ have been constructed. Simulation results for the constructed LDPC codes have been presented.

Item Type: Thesis (Doctoral thesis) Rukavina, Sanja 2017 105 NATURAL SCIENCES > Mathematics Faculty of Science > Department of Mathematics Iva Prah 05 May 2017 10:36 05 May 2017 10:36 http://digre.pmf.unizg.hr/id/eprint/5510