On the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles

On the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles

Random bipartite graphs, random lifts of bipartite protographs, and random cyclic lifts of bipartite protographs are used to represent random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes, respectively. In this paper, we study the distribution of cycles of different length in all these three categories of graphs....

on the girth of tanner (3,7) quasi-cyclic ldpc codes

‎s‎. ‎kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (qc) low-density parity-check (ldpc)‎ ‎codes‎, ‎i.e‎. ‎tanner $(3,5)$ of length $5p$‎, ‎where $p$ is a prime of‎ ‎the form $15m+1$‎. ‎in this paper‎, ‎by extension this method to‎ ‎tanner $(3,7)$ codes of length $7p$‎, ‎where $p$ is a prime of the‎ ‎form $21m‎+ ‎1$‎, ‎the girth values of tanner $(3,7...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH

One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the p...

On LDPC Code Based Massive Random-Access Scheme for the Gaussian Multiple Access Channel

This paper deals with the problem of massive random access for Gaussian multiple access channel (MAC). We continue to investigate the coding scheme for Gaussian MAC proposed by A. Vem et al in 2017. The proposed scheme consists of four parts: (i) the data transmission is partitioned into time slots; (ii) the data, transmitted in each slot, is split into two parts, the first one set an interleav...