Polymer Expansions for Cycle LDPC Codes

Column Weight Two and Three LDPC Codes with High Rates and Large Girths

In this paper, the concept of the broken diagonal pair in the chess-like square board is used to define some well-structured block designs whose incidence matrices can be considered as the parity-check matrices of some high rate cycle codes with girth 12. Interestingly, the constructed regular cycle codes with row-weights t, 3 ≤ t ≤ 20, t 6= 7, 15, 16, have the best lengths among the known regu...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Nonbinary Quasi-Cyclic LDPC Cycle Codes with Low-Density Systematic Quasi-Cyclic Generator Matrices

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the propose...

Search Based Weighted Multi-Bit Flipping Algorithm for High-Performance Low-Complexity Decoding of LDPC Codes

In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...

A Cycle Search Algorithm Based on a Message-Passing for the Design of Good LDPC Codes

A cycle search algorithm based on a message-passing in a Tanner graph is proposed for designing good LDPC codes. By applying the message-passing algorithm with a message alphabet composed of only two messages to a cycle search, we can perform a cycle search with less computational complexity than tree-based search algorithms. Also, the proposed algorithm can be easily implemented by using an ex...