The main subjects of the thesis are LDPC codes constructed from combinatorial structures. Combinatorial structures that have been used for the construction are:
μ-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
μ-geodetic graphs obtained from block
(v,k,λ) designs. We have shown that the Tanner graphs of LDPC codes constructed from
μ-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.
Absorbing sets, a class of combinatorial structures of the Tanner graph representation of a low-density parity-check (LDPC) code, are known to influence the performance of the code under message passing iterative decoding. In this paper, we study the smallest absorbing sets of LDPC codes constructed from projective planes and Euclidean planes. The lower bounds on the parameters of smallest absorbing sets given by Dolecek are proven to be tight for these two families of LDPC codes. We also analyze the combinatorial properties of the smallest absorbing sets and give conditions necessary and sufficient for a set of bit nodes in the Tanner graph to be a smallest absorbing set. For LDPC codes from projective planes, we further give a condition necessary and sufficient for a smallest absorbing set to be a fully absorbing set. In addition, we show that these smallest absorbing sets are asymptotically not stable, which may explain to some extent the good performance as well as the low error floor expectation of these two families of LDPC codes.