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...

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...

In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes hybrid LDPC codes. Although efficient optimization techniques exist for binary LDPC codes and more recently for non-binary LDPC codes, they both exhibit drawbacks due to different reasons. Our goal is to capitalize on t...

In this paper, we present a construction method of non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an extension of Felström and Zigangirov construction [1] for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary convolutional code is also discussed. The proposed rate-compatible code is designed from one single mother (2,4)-reg...

Gallager introduced LDPC codes in 1962, presenting a construction method to randomly allocate bits in a sparse parity-check matrix subject to constraints on the row and column weights. Since then improvements have been made to Gallager’s construction method and some analytic constructions for LDPC codes have recently been presented. However, analytically constructed LDPC codes comprise only a v...

A mutual information inspired nonbinary coded modulation design with non-uniform shaping is proposed. Instead of traditional power of two signal constellation sizes, we design 5-QAM, 7-QAM and 9-QAM constellations, which can be used in adaptive optical networks. The non-uniform shaping and LDPC code rate are jointly considered in the design, which results in a better performance scheme for the ...

Low density parity check (LDPC) codes are one of the best error correcting codes in today’s coding world and are known to approach the Shannon limit. As with all other channel coding schemes, LDPC codes add redundancy to the uncoded input data to make it more immune to channel impairments. In addition to coding, the best modulation techniques available today are MSK (Minimum Shift Keying) and G...

The literature survey has been carried out in 3 phases. The first phase focussed on LDPC Codes .The 2 nd Phase on Projective Geometry and Majority Logic decoding and the 3 rd phase on p-adic extension of PG LDPC Codes. In the first phase, the introduction to LDPC Codes, their construction,comparision is done in the references from [1],[9]-[21].The decoding methodologies and various techniques a...

—In this paper, MIMO (Multiple-Input-Multiple Output) system based on turbo equalization techniques which LDPC (Low Density Parity Check) codes were outer code and STTC (Space Time Trellis Code) were employed as an inner code are studied. LDPC decoder and STTC decoder are connected through the interleaving and de-interleaving that updates each other's information repeatedly. On the receiver si...

OF THE THESIS Properties of LDGM-LDPC codes With Applications to Secrecy Coding by Manik Raina Thesis Directors: Professor Predrag Spasojević The ensemble of low-density generator-matrix/low-density parity-check (LDGM-LDPC) codes has been proposed in literature. In this thesis, an irregular LDGM-LDPC code is studied as a sub-code of an LDPC code with some randomly punctured outputbits. It is sh...