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...

Quantum low-density parity check (LDPC) codes such as generalized toric codes with finite rate suggested by Tillich and Zémor offer an alternative route for quantum computation. Here, we study LDPC codes and show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, has a finite error threshold. Based on that, we conclude that quantu...

-Low-density Parity-check (LDPC) code a very promising near-optimal error correction code(ECC), is being widely considered in next generation industry standards. In this paper, two simple iterative low complexity algorithms for decoding LDPC codes have been explained. These algorithms are implemented using real additions only and also not dependent on power spectral density. The survey paper pr...

This paper investigates the performance of image transmission with unequal error protection (UEP) schemes based on irregular Low-Density Parity-Check (LDPC) codes. Firstly, the UEP is achieved by mapping different bits of the image bytes to different positions of LDPC codes, i.e. the more important bits in the image are mapped to the variable node with higher degrees in irregular LDPC codes, af...

An algorithm for constructing parity-check matrices of nonbinary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of t...

 Abstract— A modified log domain decoding algorithm of Low density parity check (LDPC) codes over GF(q) using permutation to simplify the parity check equation is presented in this paper which is different from the conventional log domain decoding algorithm of Low Density Parity Check (LDPC) codes over GF(q) [11]. Modified Log domain is mathematically equivalent to the conventional log domain ...

Abstract: Two different ways of obtaining generalized low-density parity-check codes are considered. Lower bounds on the minimum distance, stopping distance, and pseudodistance are derived for these codes using graph based analysis. These bounds are generalizations of Tanner’s bit-oriented and parity-oriented bound for simple LDPC codes. The new bounds are useful in predicting the performance o...

In this paper, overlapped circular spatially-coupled low-density parity-check codes (OC-LDPC) are proposed and their modified coupled codes are derived, which show better performance compared with the spatially-coupled low-density parity-check (SC-LDPC) codes. It is known that the SC-LDPC codes show asymptotically good performance when the chain length is sufficiently large. However, a large ch...

Low-Density Parity Check codes are a special class of linear block codes widely used in communication and disk storage systems, due to their Shannon limit approaching performance and their favourable structure. A special class of LDPC codes, called QC-LDPC codes, allows for efficient hardware implementations of encoding and decoding algorithms by exploiting the structure of the Parity Check Mat...

The multi-edge type LDPC codes, introduced by Richardson and Urbanke, present the general class of structured LDPC codes. In this paper, we derive the average weight distributions of the multi-edge type LDPC code ensembles. Furthermore, we investigate the asymptotic exponential growth rate of the average weight distributions and investigate the connection to the stability condition of the densi...