Regular LDPC Codes from Semipartial Geometries

Valentina Pepe

Zhimin Zhang

Based on(n,2,k)regular Low Density Parity-Check(LDPC)codes without short cycles,an approach for the geometry construction of(n,3,k)regular LDPC codes with 8-girth is proposed in this paper,which is simple, intuitive and effective.Simulation results show these codes achieved properties much better than those of stochastically constructed regular LDPC codes in AWGN channel.

S. Babvey, Stephen McLaughlin

Xiuli Li, Zhengduo Shan

By considering a class of combinatorial structures, known as strongly regular (a, beta) -geometries, we define a class of low-density parity-check (LDPC) codes. We derive bounds on minimum distance, rank and girth for the codes from strongly regular (a, beta) -geometries, which have not previously been proposed for use with iterative decoding. In further, we present performance results for the class of codes.

Jun Xu, Lei Chen, Ivana Djurdjevic +2 more

Two algebraic methods for systematic construction of structured regular and irregular low-density parity-check (LDPC) codes with girth of at least six and good minimum distances are presented. These two methods are based on geometry decomposition and a masking technique. Numerical results show that the codes constructed by these methods perform close to the Shannon limit and as well as random-like LDPC codes. Furthermore, they have low error floors and their iterative decoding converges very fast. The masking technique greatly simplifies the random-like construction of irregular LDPC codes designed on the basis of the degree distributions of their code graphs

Marina Šimac, Dean Crnković, Sanja Rukavina