The decoding quasi-cyclic codes

P. Heijnen, Henk C. A. van Tilborg

Keke Liu, Shu Lin, Khaled Abdel-Ghaffar

Cyclic and quasi-cyclic algebraic LDPC codes constructed based on finite fields, finite geometries, and combinatorial designs can achieve excellent performance in terms of error rate, error floor and rate of decoding convergence with iterative decoding. However, the relatively high density of the parity-check matrix of an algebraic cyclic or quasi-cyclic LDPC code makes the hardware implementation complexity of the decoder quite large, which may be a critical issue in practical applications. This paper presents an effective reduced-complexity algorithm for decoding algebraic cyclic and quasi-cyclic LDPC codes based on the block cyclic structure and cyclic grouping of the rows of their parity-check matrices. The decoding of a code is carried out based on a single small submatrix of the parity-check matrix of the code in a revolving manner. The proposed decoding algorithm significantly reduces the hardware implementation complexity and the size of memory required to store information.

Kanat Abdukhalikov, Tushar Bag, Daniel Panario

Lei Jing, Yongqiang Gao, Jianhui Wang +1 more

A new fast decoding method of Quasi-Cyclic LDPC(QC-LDPC)codes, named semi-serial decoding algorithm, is presented through contraposing the shortcoming of flood decoding method.For the algorithm, the message was updated in a serial sequence of m subsets of check nodes(or variable nodes), while the check nodes(or variable nodes) in the same subset are updated simultaneously. In this way,the decoding speed would be faster than the common serial decoding algorithm several times. An efficient grouping method suitable for the quasi-cyclic LDPC codes based on the circulant architecture is proposed.Simulation results show that,under the same complexiry,the proposed algorithm fastens the decoding speed of quasi-cyclic LDPC codes, meanwhile, it inherits all the merits of the serial massage-passing decoding algorithm. The conclusion is that the speed of the semi-serial decoding method is at least p times than that of the serial one(p is the number of rows of the cyclic permutation matrix in the parity check matrix of quasi-cyclic LDPC codes).

P. Heijnen, Henk van Tilborg, S. Weijs

Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes. Furthermore we present a decoding algorithm for the binary quasi-cyclic codes of rate 1/m.

Chao Chen