Low Density Parity Check Codes originally invented by Gallagher and subsequently rediscovered by multiple groups 30 years later has become the best known error correcting code in a variety of situations. In this paper, we review regular and irregular LDPC codes. We describe a number of message passing decoders for decoding these codes and explain their operation via examples. Density evolution,...

Leveraging the advanced coherent optical communication technologies, this paper explores the feasibility of using four-dimensional (4D) nonbinary LDPC-coded modulation (4D-NB-LDPC-CM) schemes for long-haul transmission in future optical transport networks. In contrast to our previous works on 4D-NB-LDPC-CM which considered amplified spontaneous emission (ASE) noise as the dominant impairment, t...

The design of a class of well-structured low-density parity-check (LDPC) codes, namely linear interleaver based concatenated zigzag (LICZ) codes, is investigated. With summary distances as the design metric, short LICZ codes with large minimum distances can be constructed. Moreover, an efficient cycle-based method is proposed to compute the minimum distances of LICZ codes. Simulation results sh...

LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing throughput is achieved by allocating a sufficient number of processing elements (PEs). Supporting multiple heterogeneous LDPC codes on a parallel decoder poses seri...

The class of low-density parity-check (LDPC) codes was introduced by Gallager in his thesis in 1961 [2]. Until the invention of turbo codes, they were largely neglected, but received a lot of interest lately, due to the possibility of designing LDPC codes within 0.0045 dB of the Shannon limit. We review in this project techniques used to analyze the performance of LDPC codes under a message-pas...

Introduction: Multilevel coding (MLC) was proposed by Imai and Hirawaki [1] as a bandwidth-efficient coded modulation scheme designed for protecting each bit of a non-binary symbol with the aid of binary codes, while maintaining different target bit error rates (BERs). Parallel independent decoding (PID) [2] is employed as an efficient decoding strategy with reduced decoding delay, where there ...

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...

Abstract – In this paper a formal theory, construction methods, and a random ensemble approach for low-density parity-check convolutional codes (including turbo-codes) are presented. The principles of iterative decoding of low-density parity-check (LDPC) convolutional codes are given, and an iterative algorithm for decoding of homogeneous LDPC convolutional codes is described. Some simulation r...

This paper is concerned with a family of concatenated tree (CT) codes. CT codes are special low-density paritycheck (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and...

Aiming at seeking a low complexity decoder of the low-density parity-check (LDPC) codes, we present one modified multi-bit flipping (MMBF) algorithm. For those LDPC codes whose parity check matrices have light column weight, both the bootstrap step and a novel delay-handling step are included in MMBF, based on one framework which is the combination of conventional PWBF and IWBF. On the other ha...