This correspondence presents three algebraic methods for constructing low-density parity-
check (LDPC) codes. These methods are based on the structural properties of finite …

Gallager introduced low-density parity-check (LDPC) codes in 1962, presenting a
construction method to randomly allocate bits in the parity-check matrix subject to certain …

LDPC codes can be described by a bipartite graph called Tanner graph [1], and the girth of a
Tanner graph is the length of the shortest cycle in the graph. Girths in the Tanner graphs of …

For any row weight L, a novel class of (8, L) quasi‐cyclic low‐density parity‐check (QC‐
LDPC) codes is deterministically constructed with girth eight. Compared with a similar …

This paper presents a geometric approach to the construction of low-density parity-check
(LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of …

The use of partial geometries to construct parity-check matrices for binary low-density parity-
check (LDPC) codes has resulted in the design of successful codes with a probability of …

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes.
The liftings are designed to eliminate dominant trapping sets of the base code by removing …

For any column weight J and any row weight L, a novel framework is proposed such that a
girth-eight (J, L) quasi-cyclic low-density parity-check (QC-LDPC) code with any block length …

Near Shannon limit quasi-cyclic low-density parity-check codes Page 1 Near Shannon Limit
Quasi-Cyclic Low-Density Parity-Check Codes Shu Lin, Lei Chen, Jun Xu, and Ivana Djurdjevic …

In the past, several authors have considered quasicyclic LDPC codes whose circulant
matrices in the parity-check matrix are cyclically shifted identity matrices. By composing a …