Low-density parity-check (LDPC propagation (BP) algorithm achieve a remar close to the Shannon limit at reasonable de Conventionally, each iteration in decoding p steps, the horizontal step and the vertical ste efficient implementation of the adaptive offse algorithm for decoding LDPC codes using the is proposed. Furthermore, the performan algorithm compared with belief-propagation investigated...

In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probab...

In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs wi...

This paper corresponds to a brief survey of LDPC codes. Many error detection and correction codes have been studied. There are vast classes of such codes; some of them are hamming codes, turbo codes, BCH codes and LDPC codes. But among these codes LDPC codes achieve better performance and lower decoding complexity. LDPC codes were originally discovered by Robert G. Gallager. But after the redis...

Binary Low Density Parity Check (LDPC) codes have been shown to have near Shan-non limit performance when decoded using a probabilistic decoding algorithm. The analogous codes deened over nite elds GF(q) of order q > 2 show signiicantly improved performance. We present the results of Monte Carlo simulations of the decoding of innnite LDPC Codes which can be used to obtain good constructions for...

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based a...

A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudorandom nature, and the new codes are quasi-cyclic. Graph isomorphisms and automorphisms are identified and used in an efficient search for good codes. Graphs with girth as large as 12 wer...

A method to construct girth-12 (3,L) quasi-cyclic lowdensity parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes can be arbitrary integers of the form LP, provided that P is larger than a tight lower bound determined by the maximal element within the exponent matrix of t...

It has been widely recognized in the literature that irregular low-density parity-check (LDPC) codes exhibit naturally an unequal error protection (UEP) behavior. In this paper, we propose a general method to emphasize and control the UEP properties of LDPC codes. The method is based on a hierarchical optimization of the bit node irregularity profile for each sensitivity class within the codewo...

In recent years, the amount of digital data which is stored and transmitted for private and public usage has increased considerably. To allow a save transmission and storage of data despite of error-prone transmission media, error correcting codes are used. A large variety of codes has been developed, and in the past decade low-density parity-check (LDPC) codes which have an excellent error cor...