From Sidon sequence over ZP, two classes of type-1 (J = 3;L) QC-LDPC codes are explicitly proposed with block length L2P and with girth at least ten. For the first method, any Sidon sequence over ZP(P odd) with cardinality no smaller than L (L odd) corresponds to a class of type-1 (3, L) QC-LDPC codes with girth at least ten. For the second one, any Sidon sequence over ZP(P prime) with cardinality no smaller than L (L arbitrary) corresponds to a class of type-1 (3, L) QC-LDPC codes with girth at least ten. Compared with the method from 3-D lattices, which can also generate type-1 QC-LDPC codes with girth at least ten, the main advantage of the new methods is that the construction process is much simpler, and L is not necessarily a prime integer. Simulation results show that the new type-1 QC-LDPC codes outperform the girth-8 QC-LDPC codes constructed by Sidon sequence or the earliest sequence, and perform almost as well as Bocharova's shortest girth-12 QC-LDPC codes.From Sidon sequence over ZP, two classes of type-1 (J = 3;L) QC-LDPC codes are explicitly proposed with block length L2P and with girth at least ten. For the first method, any Sidon sequence over ZP(P odd) with cardinality no smaller than L (L odd) corresponds to a class of type-1 (3, L) QC-LDPC codes with girth at least ten. For the second one, any Sidon sequence over ZP(P prime) with cardinality no smaller than L (L arbitrary) corresponds to a class of type-1 (3, L) QC-LDPC codes with girth at least ten. Compared with the method from 3-D lattices, which can also generate type-1 QC-LDPC codes with girth at least ten, the main advantage of the new methods is that the construction process is much simpler, and L is not necessarily a prime integer. Simulation results show that the new type-1 QC-LDPC codes outperform the girth-8 QC-LDPC codes constructed by Sidon sequence or the earliest sequence, and perform almost as well as Bocharova's shortest girth-12 QC-LDPC codes.

IEEE Information Theory Workshop (ITW)Nov 1, 201410 citations

(7,K) GIRTH-8 QC-LDPC CODES WITH AN EXPLICIT CONSTRUCTION

M. Majdzadeh, Mohammad Gholami, Gh. Raeisi

Recently, for each row weight $K$ and column-weight $J$ , $3le J< K$ , several classes of $(J,K)$ quasi-cyclic (QC) low-density parity-check (LDPC) codes with girth 8 have been constructed explicitly such that their corresponding lower-bounds on the size of circulant permutation matrices (CPMs) have been considered small as possible. In this paper, for $J=7$ , a class of $(7,K)$ QC-LDPC codes with girth 8 is generated by an explicit method such that the lower-bounds of the constructed codes remarkably are better than the state-of-the-art bound $(K-1)(K^2+K)+1$ .Recently, for each row weight $K$ and column-weight $J$, $3le J< K$, several classes of $(J,K)$ quasi-cyclic (QC) low-density parity-check (LDPC) codes with girth 8 have been constructed explicitly such that their corresponding lower-bounds on the size of circulant permutation matrices (CPMs) have been considered small as possible. In this paper, for $J=7$, a class of $(7,K)$ QC-LDPC codes with girth 8 is generated by an explicit method such that the lower-bounds of the constructed codes remarkably are better than the state-of-the-art bound $(K-1)(K^2+K)+1$.

Journal of Algebraic SystemsJan 1, 20222 citations

A Study on QC-LDPC codes with girth 8 or 10 for broadband communications

Wataru Matsumoto, Yoshikuni Miyata, Hideo Yoshida

IEICE Technical Report; IEICE Tech. Rep.Sep 27, 20071 citation

Design of good QC-LDPC codes without small girth in the p-plane

Ling-jun, Kong, Yang Yang +1 more

Journal of Systems Engineering and ElectronicsJan 1, 20110 citations

Some explicit constructions of type-II, III, IV, V QCLDPC codes with girth 6

Farzaneh Abedi, Mohammad Gholami

Multi-type quasi-cyclic (QC) low-density parity-check (LDPC) codes can be considered as multiple-edge protograph QC-LDPC codes having some advantages in the minimum Hamming distance bound over single-edge protograph codes or type-I QC-LDPC codes when the base matrices have the same size. In this paper, we investigate a class of multi-type QC-LDPC codes whose parity-check matrices contain just one blockrow of circulants and we obtain the generator matrix of such codes in general form. Using the permutation arrays and defining injection arrays, we present a new approach to construct a class of high-rate type-I QC-LDPC codes with girth 6 from the constructed 4-cycle free multi-type QC-LDPC codes. In continue, for 2 ≤ w ≤ 6, some type-w QC-LDPC codes with girth 6 are constructed explicitly such that the constructed codes are flexible in terms of rate and length. To the best of our knowledge, for w = 5,6, this is the first paper which deals with the explicit construction of type-w QC-LDPC codes with girth 6 and high rates. Moreover, for w = 3,4, the constructed type-w QC-LDPC codes have better (6,8)-cycle multiplicities than the codes with minimum achievable length recently constructed by cyclic difference families (CDFs). Simulation results show that the binary and non-binary constructed codes outperform the constituent underlying QC-LDPC codes.Multi-type quasi-cyclic (QC) low-density parity-check (LDPC) codes can be considered as multiple-edge protograph QC-LDPC codes having some advantages in the minimum Hamming distance bound over single-edge protograph codes or type-I QC-LDPC codes when the base matrices have the same size. In this paper, we investigate a class of multi-type QC-LDPC codes whose parity-check matrices contain just one blockrow of circulants and we obtain the generator matrix of such codes in general form. Using the permutation arrays and defining injection arrays, we present a new approach to construct a class of high-rate type-I QC-LDPC codes with girth 6 from the constructed 4-cycle free multi-type QC-LDPC codes. In continue, for 2 ≤ w ≤ 6, some type-w QC-LDPC codes with girth 6 are constructed explicitly such that the constructed codes are flexible in terms of rate and length. To the best of our knowledge, for w = 5,6, this is the first paper which deals with the explicit construction of type-w QC-LDPC codes with girth 6 and high rates. Moreover, for w = 3,4, the constructed type-w QC-LDPC codes have better (6,8)-cycle multiplicities than the codes with minimum achievable length recently constructed by cyclic difference families (CDFs). Simulation results show that the binary and non-binary constructed codes outperform the constituent underlying QC-LDPC codes.

China CommunicationsMay 1, 20204 citations

Recently, for each row weight

K

and column-weight

J

3le J< K

, several classes of

(J,K)

quasi-cyclic (QC) low-density parity-check (LDPC) codes with girth 8 have been constructed explicitly such that their corresponding lower-bounds on the size of circulant permutation matrices (CPMs) have been considered small as possible. In this paper, for

J=7

, a class of

(7,K)

QC-LDPC codes with girth 8 is generated by an explicit method such that the lower-bounds of the constructed codes remarkably are better than the state-of-the-art bound

(K-1)(K^2+K)+1