The design of LDPC codes based on a class of expander graphs is investigated. Graph products, such as the zig-zag product [9], of smaller expander graphs have been shown to yield larger expanders. LDPC codes are designed based on the zigzag product graph of two component Cayley graphs. The results for specific cases simulated reveal that the resulting LDPC codes compare well with other random L...

Low-Density Parity-Check (LDPC) code is one kind of prominent error correcting codes (ECC) being considered in next generation industry standards. The decoder implementation complexity has been the bottleneck of its application. This paper presents a new kind of high-throughput and memory efficient LDPC decoder architecture. In general, more than fifty percent of memory can be saved over conven...

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-...

In this paper, a Joint Source Channel coding scheme based on LDPC codes is investigated. We consider two concatenated LDPC codes, one allows to compress a correlated source and the second to protect it against channel degradations. The original information can be reconstructed at the receiver by a joint decoder, where the source decoder and the channel decoder run in parallel by transferring ex...

Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit error rate (BER) region and p...

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...

This letter investigates the combination of the Chase-2 and sum-product (SP) algorithms for low-density parity-check (LDPC) codes. A simple modification of the tanh rule for check node update is given, which incorporates test error patterns (TEPs) used in the Chase algorithm into SP decoding of LDPC codes. Moreover, a simple yet effective approach is proposed to construct TEPs for dealing with ...

Low-density parity-check (LDPC) codes have been successfully deployed in NAND Flash memory based Solid State Drives (SSDs). As Flash memory scales, and has now advanced from planar architectures to three-dimensional ones, defects in the form of stuck cells have increased. Stuck cells are more difficult to correct using LDPC codes because they typically masquerade as reliable bits, but their per...

Bliss schemes of a run length limited (RLL) codec in combination with an LDPC codec, generate LDPC parity bits over a systematic sequence of RLL channel bits that are inherently redundant as they satisfy e.g. a d = 1 minimum run length constraint. That is the subsequences consisting of runs of length d = 1, viz. . . . 010 . . . and . . . 101 . . ., cannot occur. We propose to use this redundanc...

SUMMARY Low-density parity-check (LDPC) codes are shown to tightly approach the performance of idealized maximum distance separable (MDS) codes over memoryless erasure channels, under maximum likelihood (ML) decoding. This is possible down to low error rates and even for small and moderate block sizes. The decoding complexity of ML decoding is kept low thanks to a class of decoding algorithms, ...