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Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from…

Information Theory · Computer Science 2017-01-03 Hassan Khodaiemehr , Dariush Kiani

This paper consists of three parts. The first part presents a large class of new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose parity-check matrices are constructed based on cyclic subgroups of finite fields.…

Information Theory · Computer Science 2015-03-14 Li Zhang , Shu Lin , Khaled Abdel-Ghaffar , Zhi Ding , Bo Zhou

In this paper, a new method is given for counting cycles in the Tanner graph of a (Type-I) quasi-cyclic (QC) low-density parity-check (LDPC) code which the complexity mainly is dependent on the base matrix, independent from the CPM-size of…

Information Theory · Computer Science 2023-10-20 Mohammad Gholami , Zahra Gholami

The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…

Quantum Physics · Physics 2026-03-06 Andrey Boris Khesin , Jonathan Z. Lu

We consider the problem of constructing $(3,L)$ quasi-cyclic low-density parity-check (LDPC) codes from complete protographs. A complete protograph is a small bipartite graph with two disjoint vertex sets such that every vertex in the…

Information Theory · Computer Science 2016-11-17 Sudarsan V. S. Ranganathan , Dariush Divsalar , Richard D. Wesel

Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly influenced by short-cycle structure and other harmful…

Information Theory · Computer Science 2026-05-05 Anthony Gómez-Fonseca , Gretchen L. Matthews , Kirsten D. Morris , Tefjol Pllaha

This paper gives necessary and sufficient conditions for the Tanner graph of a quasi-cyclic (QC) low-density parity-check (LDPC) code based on the all-one protograph to have girth 6, 8, 10, and 12, respectively, in the case of parity-check…

Information Theory · Computer Science 2021-06-03 Anthony Gómez-Fonseca , Roxana Smarandache , David G. M. Mitchell

In the given paper we present a novel approach for constructing a QC-LDPC code of smaller length by lifting a given QC-LDPC code. The proposed method can be considered as a generalization of floor lifting. Also we prove several…

Information Theory · Computer Science 2017-02-07 Nikita Polyanskii , Vasiliy Usatyuk , Ilya Vorobyev

We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate that the QC structure of the code…

Information Theory · Computer Science 2019-06-18 Bashirreza Karimi , Amir. H Banihashemi

Quantum error correction (QEC) is critical for practical realization of fault-tolerant quantum computing, and recently proposed families of quantum low-density parity-check (QLDPC) code are prime candidates for advanced QEC hardware…

Information Theory · Computer Science 2025-03-11 Nithin Raveendran , David Declercq , Bane Vasić

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…

Information Theory · Computer Science 2016-11-25 Mehdi samadieh , Mohammad Gholami

To obtain a better cycle-structure is still a challenge for the low-density parity-check (LDPC) code design. This paper formulates two metrics firstly so that the progressive edge-growth (PEG) algorithm and the approximate cycle extrinsic…

Information Theory · Computer Science 2019-04-16 Xuan He , Liang Zhou , Junyi Du

Due to their capacity approaching performance low-density parity-check (LDPC) codes gained a lot of attention in the last years. The parity-check matrix of the codes can be associated with a bipartite graph, called Tanner graph. To decrease…

Information Theory · Computer Science 2025-07-02 Elisa Junghans , Julia Lieb

Low decoding latency and complexity are two important requirements of channel codes used in many applications, like machine-to-machine communications. In this paper, we show how these requirements can be fulfilled by using some special…

Information Theory · Computer Science 2018-09-14 Massimo Battaglioni , Alireza Tasdighi , Marco Baldi , Mohammad H. Tadayon , Franco Chiaraluce

Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of…

Quantum Physics · Physics 2016-11-18 Salah A. Aly

We study square-base Calderbank--Shor--Steane (CSS) hypergraph-product codes as a finite-length class for regular high-girth quantum low-density parity-check (LDPC) design. For base matrices of small column weight, we give checkable…

Quantum Physics · Physics 2026-05-01 Koki Okada , Kenta Kasai

This paper presents a unifying framework to construct low-density parity-check (LDPC) codes with associated Tanner graphs of desired girth. Towards this goal, we highlight the role that a certain square matrix that appears in the product of…

Information Theory · Computer Science 2021-08-04 Roxana Smarandache , David G. M. Mitchell

Joint encryption-encoding schemes have been released to fulfill both reliability and security desires in a single step. Using Low Density Parity Check (LDPC) codes in joint encryption-encoding schemes, as an alternative to classical linear…

Information Theory · Computer Science 2019-02-22 Hossein Khayami , Taraneh Eghlidos , Mohammad Reza Aref

We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM…

Quantum Physics · Physics 2026-05-26 Eren Guttentag , Anthony Gómez-Fonseca

One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in…

Discrete Mathematics · Computer Science 2016-11-18 Olgica Milenkovic , Navin Kashyap , David Leyba