相关论文: Double Cylinder Cycle codes of Arbitrary Girth

In this paper, the concept of the {\it broken diagonal pair} in the chess-like square board is used to define some well-structured block designs whose incidence matrices can be considered as the parity-check matrices of some high rate cycle…

We present a general approach to designing capacity-approaching high-girth low-density parity-check (LDPC) codes that are friendly to hardware implementation. Our methodology starts by defining a new class of "hierarchical" quasi-cyclic…

This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an…

Quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of LDPC codes with a simple construction facilitating hardware implementation while achieving excellent performance. In this paper, we introduce an algorithm that…

For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to making short cycles. Also, the existing high-rate quasi-cyclic…

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…

An algorithm for constructing parity-check matrices of non-binary 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…

In the literatures, it is well-known that Fossorier code has the girth among LDPC codes. In this paper, we introduce a new class of low-density parity-check (LDPC) codes, with higher girth than other previous constructed codes. Especially…

We propose a low-complexity method to find quasi-cyclic low-density parity-check block codes with girth 10 or 12 and shorter length than those designed through classical approaches. The method is extended to time-invariant spatially coupled…

An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check codes achieving high girth is presented. The construction allows flexibility in the choice of design parameters like rate, average…

A method to construct girth-12 (3,L) quasi-cyclic low-density parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes…

A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N>=2) non-overlapping…

We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of ones of the parity-check matrix of the codes presented is typically higher than the…

Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication.…

Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant…

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2^m), where m>0 cyclic low-density parity-check codes. The construction method produces the dual code idempotent…

We study a class of quasi-cyclic LDPC codes. We provide precise conditions guaranteeing high girth in their Tanner graph. Experimentally, the codes we propose perform no worse than random LDPC codes with their same parameters, which is a…

A class of doubly-generalized low-density parity-check (D-GLDPC) codes, where single parity-check (SPC) codes are used as variable nodes (VNs), is investigated. An expression for the growth rate of the weight distribution of any D-GLDPC…

Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived -- one based on nonprimitive narrow-sense BCH codes and the other directly…

This paper introduces a class of structured lowdensity parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some…