A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good...

Binary LDPC coded relay systems have been well studied previously with the assumption of infinite codeword length. In this paper, we deal with non-binary LDPC codes which can outperform their binary counterpart especially for practical codeword length. We utilize non-binary LDPC codes and recently invented non-binary coding techniques known as multiplicative repetition to design the low-rate co...

A new approach for encoding one class of quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed. The proposed encoding method is applicable to parity-check matrices having dual-diagonal parity structure with single column of weight three in the parity generation region. Instead of finding the parity bits directly, the proposed method finds parity bits through vector correction. While...

We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Shor-Steane (CSS) construction do not need to satisfy the dual-containing property as long as pre-shared entanglement is available to both sender and receiver. We c...

This paper presents a construction of low-density parity-check (LDPC) codes based on the incidence matrices of oval designs. The new LDPC codes have regular parity-check matrices and Tanner graphs free of 4-cycles. Like the finite geometry codes, the codes from oval designs have parity-check matrices with a large proportion of linearly dependent rows and can achieve significantly better minimum...

Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexibl...

To meet the demands of different high bandwidth service, OFDM-PON has been considered as one of the candidates for NG-PON2. In this paper, downstream transmission performance based on LDPC-OFDM coding PON system is studied. The simulation results show that employing the LDPC-OFDM coding in PON system can achieve 10 Gb/s downstream transmission. The transmission performance of the LDPC-OFDM syst...

In this paper, a new variant of the McEliece cryptosystem, based on Low-Density Parity-Check (LDPC) codes, is studied. Random-based techniques allow to design large families of LDPC codes with equivalent error correction capability; therefore, in principle, such codes can substitute Goppa codes, originally used by McEliece in his cryptosystem. Furthermore, Quasi-Cyclic (QC) LDPC codes can be ad...

Iterative decoding of Low Density Parity Check (LDPC) codes using the Parity Likelihood Ratio (PLR) algorithm have been proved to be more efficient compared to conventional Sum Product Algorithm (SPA). However, the nature of PLR algorithm tends to put numerious pieces of data to this decoder and perform computation intensive operations, which is a major challenge for building a practical real-t...

In this paper, a repeater system is studied which is basically used for the relay in the cellular communication. The LDPC (Low Density Parity Check) code is introduced into DFE (decision feedback equalizer) in the receiver for the BER (bit error rate) performance. For the better quality of service (QoS) and the higher convenience, the wireless repeater was considered for the relay system. In th...