Low-Density Parity-Check (LDPC) codes have gained lots of popularity due to their capacity achieving/approaching property. This work studies the iterative decoding also known as message-passing algorithms applied to LDPC codes. Belief propagation (BP) algorithm and its approximations, most notably min-sum (MS), are popular iterative decoding algorithms used for LDPC and turbo codes. The thesis ...

In this paper, a Low-Density Parity-Check (LDPC) coded Orthogonal Frequency-Division Multiplexing (OFDM) wireless communication system based on IEEE 802.11a standard is studied and a simplified LDPC decoding initialization algorithm is proposed. Simulation results showed that this algorithm is effective and can fasten decoding procedure. Appling this algorithm the LDPC decoding performance is s...

The evaluation of the minimum distance of low-density parity-check (LDPC) codes remains an open problem due to the rather large dimension of the parity check matrix H associated with any practical code. In this article, we propose an effective modification of the error impulse (EI) technique for computation of the minimum distance of the LDPC codes. The EI method is successfully applied to sub-...

A numerical method has recently been presented to determine the noise thresholds of low density parity-check (LDPC) codes that employ the message passing decoding algorithm on the additive white Gaussian noise (AWGN) channel. In this paper, we extend this technique to the uncorrelated flat Rayleigh fading channel. Using a nonlinear code optimization technique, we optimized irregular LDPC codes ...

Low-density parity check codes (LDPC codes) were introduced by Gallager [2] and have received intensive study in the last few years, as advances in technology have made their implementation far more practical than when they were originally proposed. Basically, an LDPC code is a binary linear block code defined by a sparse m × n parity-check matrix H . Equivalently such a code can be thought of ...

In this paper, we present a construction method of non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an extension of Felström and Zigangirov construction [1] for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary convolutional code is also discussed. The proposed rate-compatible code is designed from one single mother (2,4)-reg...

Among the recent advances in the area of low-density parity-check (LDPC) codes, protograph-based LDPC codes have the advantages of a simple design procedure and highly structured encoders and decoders. These advantages can also be exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. In this dissertation we provide analytical tools which aid the design of protographbased ...

An information reconciliation method for continuous-variable quantum key distribution with Gaussian modulation that is based on non-binary low-density paritycheck (LDPC) codes is presented. Sets of regular and irregular LDPC codes with different code rates over the Galois fields GF(8), GF(16), GF(32), and GF(64) have been constructed. We have performed simulations to analyze the efficiency and ...

Binary low-density parity-check (LDPC) codes perform very well on magnetic recording channels (MRCs) with additive white Gaussian noise (AWGN). However, an MRC is subject to other impairments, such as media defects and thermal asperities. Binary LDPC codes may not be able to cope with these impairments without the help of a Reed–Solomon code. A better form of coding may be -ary LDPC codes, whic...

Low-Density Parity Check (LDPC) codes are linear block codes which perform closer to Shannon‟s limit. It is defined by the parity check matrix (PCM) which contains only a few ones in comparison to the number of zeros (sparsity). Stochastic based computation is a method to design lowprecision digital circuits. In stochastic computing, probabilities are encoded by random sequences of bits. In thi...