Recent advances in coding theory have produced two classes of codes, turbo codes and low-density parity-check (LDPC) codes, which approach the Shannon limit of channel capacity while admitting efficient implementations of message encoding and decoding in software. Theoretic results about the latter have been shown to apply to the former, hence we examine the evolution of LDPC codes from their o...

− Low density parity-check codes are one of the hottest topics in coding theory nowadays. Equipped with very fast encoding and decoding algorithms (probabilistically,) LDPC are very attractive both theoretically and practically. In this paper, I present a throughout view of LDPC. I discuss in detail LDPC’s popular decoding algorithm: belief propagation. I also present some noticeable encoding a...

This paper mainly about the study on one of the widely used error correcting codes that is Low parity check Codes (LDPC). In this paper, the Regular LDPC code has been discussed The LDPC codes explained in this paper is about the Regular Binary LDPC codes or the Gallager. Keywords—LDPC, channel coding.

We look at the intersection of convolutional codes with high rate low-density parity-check codes. Threshold values are obtained with EXIT charts. Simulations show a gain of 1.5dB over a standard deepspace code.

In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagatio...

Analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. We construct -codes whose T...

This article explains the design and implementation of both regular and irregular LDPC codes as carried out by me at the Institute of Communications Engineering, Technical University of Munich. The design of a good irregular LDPC code needs a pair of distributions to be specified. This article discusses a randomized construction which attempts to form a parity check matrix whose row and coloumn...

We develop a belief-propagation-based joint decoding and channel state estimation algorithm for low-density parity check codes on fading channels with memory. The excellent empirical performance of LDPC codes on the AWGN channel and the possibility of arranging the code memory relative to the channel correlation suggests that LDPC codes have the potential to perform well on fading channels with...

For high density magnetic recording channels and memory systems, low-density parity-check (LDPC) codes with probabilistic decoding are replacing Reed-Solomon (RS) codes or Bose-Chaudhuri-Hocquenghem (BCH) codes with conventional algebraic decoding. The main benefit of LDPC codes over the RS and BCH codes is that LDPC codes can provide lower error probabilities than equivalent conventional codes...

Motivated by the potential to reuse the decoder architecture, and thus reduce circuit space, we explore the use of iterative encoding techniques which are based upon the graphical representation of the code. We design codes by identifying associated encoder convergence constraints and also eliminating some well known undesirable properties for sum-product decoding such as 4-cycles. In particula...