‎s‎. ‎kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (qc) low-density parity-check (ldpc)‎ ‎codes‎, ‎i.e‎. ‎tanner $(3,5)$ of length $5p$‎, ‎where $p$ is a prime of‎ ‎the form $15m+1$‎. ‎in this paper‎, ‎by extension this method to‎ ‎tanner $(3,7)$ codes of length $7p$‎, ‎where $p$ is a prime of the‎ ‎form $21m‎+ ‎1$‎, ‎the girth values of tanner $(3,7...

A constant challenge in Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes lies on flexible code lengths and rates, conditioned by good error performance. This paper presents an optimal construction method of QC-LDPC Codes on the basis of graphical model and search algorithm. Utilizing the proposed scheme, we can construct adaptable QC-LDPC codes whose girths are no less than 12, and column ...

Hamming code-based LDPC (H-LDPC) block codes are obtained by replacing the single parity-check constituent codes in Gallager’s LDPC codes with Hamming codes. This paper investigates the asymptotic performance of ensembles of random H-LDPC codes, used over the binary symmetric channel and decoded with a low-complexity hard-decision iterative decoding algorithm. It is shown that there exist H-LDP...

Low-density parity-check (LDPC) coded orthogonal-frequency-division multiplexing (OFDM) is studied as an efficient coded modulation technique suitable for fiber-optics communication systems. We show that in long-haul fiber optics communications LDPC-coded OFDM increases spectral efficiency and requires simple equalization to deal with chromatic dispersion. LDPC-coded OFDM is also a promising po...

In this paper, overlapped circular spatially-coupled low-density parity-check codes (OC-LDPC) are proposed and their modified coupled codes are derived, which show better performance compared with the spatially-coupled low-density parity-check (SC-LDPC) codes. It is known that the SC-LDPC codes show asymptotically good performance when the chain length is sufficiently large. However, a large ch...

This paper presents a construction of very high-rate low-density parity-check (LDPC) codes based on the incidence matrices of unital designs. Like the projective geometry and oval designs, unital designs exist with incidence matrices which are significantly rank deficient. Thus high-rate LDPC codes with a large number of linearly dependent parity-check equations can be constructed. The LDPC cod...

This paper resumes our recent advances in the analysis and design of Spatially-Coupled LDPC (SC-LDPC) codes, used for transmission over nonergodic channels, in particular over the block-fading channel and over the block erasure channel. It has been shown that: a) SC-LDPC codes are naturally suitable for nonergodic channel transmission and are robust to packet errors/erasures; b) it is possible ...

If the degree distribution is chosen carefully, the irregular LDPC codes can outperform the regular ones. In this paper, we proposed an LDPC coded BICM scheme in image transmission system to improve both efficiency and reliability. Simulation results show that LDPC codes are good coding schemes over fading channel in image communication with lower system complexity. Simultaneously, irregular co...

In this study, a new method for constructing low-density parity-check (LDPC) codes is presented. This construction is based on permutation matrices which come from a finite abstract group and hence the codes constructed in this manner are called group permutation low-density parity-check (GP-LDPC) codes. A necessary and sufficient condition under which a GP-LDPC code has a cycle, is given and s...