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

This work presents an algebraic method for constructing QC-LDPC codes based on the minimum-weight (m-w) codewords of Reed-Solomon (RS) codes over GF(q) with two information symbols.

This letter presents two classes of quasi-cyclic low-density parity-check codes that perform close to the Shannon limit.

The paper presents two classes of quasi-cyclic low-density parity-check (LDPC) codes which perform close to the Shannon limit. The construction of these codes is based on decomposition of circulant matrices constructed from finite geometries.