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...

In this paper we consider low-density parity-check (LDPC) codes for the classic bursty channel. We present lower bounds on the maximum resolvable erasure burst length, Lmax, for arbitrary LDPC codes and then present constructions for LDPC codes with good burst erasure correction performance for channels with and without the presence of noise in the guard band.

This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging f...

In the past decade, a significant progresshas been reported in the field of error control coding. In particular, the innovation ofturbo codes and rediscovery of LDPC codes have been recognized as two significant breakthroughs in this field. The distinct features of these capacity approaching codes have enabled them to be widely proposed and/or adopted in existing wireless standards. Furthermore...

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...

This paper resumes our recent advances in the analysis and design of Spatially-Coupled LDPC (SC-LDPC) codes, used for transmission over nonergodic channels, in particular over the block-fading channel and over the block erasure channel. It has been shown that: a) SC-LDPC codes are naturally suitable for nonergodic channel transmission and are robust to packet errors/erasures; b) it is possible ...

Low Density Parity Check (LDPC) codes have attracted current researchers due to their excellent performance and capability of parallel decoding. One major criticism concerning LDPC codes has been their apparent high encoding complexity and memory inefficient nature due to large parity check matrix. This led the researchers to move into a memory efficient LDPC called Quasi-Cyclic (QC)-LDPC which...

This paper presents the H-ARQ techniques comparison for OFDM systems with a new family of non-binary LDPC codes which has been developed within the EU FP7 DAVINCI project. The punctured NB-LDPC codes have been used in a simulated model of the transmission system. The link level performance has been evaluated in terms of spectral efficiency, codeword error rate and average number of retransmissi...

I n this report we study the decoding algorithms for a family of codes called LDPC codes used over the binary erasure channel (BEC). LDPC codes are able to work at rates near Shannon capacity with linear time decoding algorithms. Those linear time decoding algorithms sometimes fail even when Gaussian elimination would still be able to restore the codeword. In this report we try to experimentall...

LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. However, traditional means of comparing block and convolutional codes tied to the implementation complexity of trellisbased decoding are irrelevant for message-passing decoders. In this paper, we undertake a comparison of LDPC...