The Low Density Parity Check (LDPC) codes have been widely acclaimed in recent years for their nearcapacity performance, they have not found their way into many important applications. For some cases, this is due to their increased decoding complexity relative to the classical coding techniques. For other cases, this is due to their inability to reach very low bit error rates at low signal-to-n...

We present a technique for designing low-density parity-check (LDPC) code matrices for the MCS-1 to MCS-4 coding schemes of GSM. We demonstrate that these codes have significant performance gains over randomly constructed LDPC codes in the GSM setup. The new codes also show significant gains in performance over the conventional MCS-1 to MCS-4 GSM coding schemes when compared in terms of the bit...

• low density parity check (LDPC) codes are error correction codes • represented by two probability distributions λ and ρ • desired properties: – high code rate r ∈ R+ → fraction of redundancy present in the code – high noise threshold g ∈ R+ → the largest noise up to which the original code can be reconstructed from its noisy version without any loss of information • LDPC codes can be decoded ...

This paper presents a novel quantum signature scheme by using quantum quasi-cyclic low density parity check (QC-LDPC) codes and quantum hash function. We construct quantum public keys by using quantum QC-LDPC Codes. Decoding general linear codes is NP-complete problem. The security of our scheme relies on the fact that NP-complete problem can not be solved on quantum Turing machines. Based on t...

Error detection in memory applications was proposed to accelerate the majority logic decoding of difference set low density parity check codes. This is useful as majority logic decoding can be implemented serially with simple hardware but requires a large decoding time. For memory applications, this increases the memory access time. The method detects whether a word has errors in the first iter...

Status of This Memo This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited. Abstract This document describes two Full...

Four different ways of obtaining low-density parity-check codes from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. These bounds are compared with the known eigenvalue-based lower bounds on the minimum distance of expander codes. Furthermore, Tanner’s parity-oriented eigenva...

This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from difference covering arrays. While the original construction by Gallagher was by randomly allocating bits in a sparse parity-check matrix, over the past 20 years researchers have used a variety of more structured approaches to construct these codes, with the more recent constructions of well-structured...

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to com...

The most powerful channel coding schemes, namely those based on turbo codes and low-density parity-check (LDPC) Gallager codes, have in common the principle of iterative decoding. However, the relative coding structures and decoding algorithms are substantially different. This paper presents a 2048-bit, rate-1/2 soft decision decoder for a new class of codes known as Turbo Gallager Codes. These...