# On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes

@article{Rosnes2012OnTM, title={On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes}, author={Eirik Rosnes and Marcel Ambroze and Martin Tomlinson}, journal={IEEE Transactions on Information Theory}, year={2012}, volume={60}, pages={5204-5214} }

In this paper, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m q. In the literature, the minimum/stopping distance of these codes (denoted by d(q, m) and h(q, m), respectively) has been thoroughly studied for m 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m = 6, the…

## 24 Citations

### More on the Minimum Distance of Array LDPC Codes

- Computer ScienceIEEE Communications Letters
- 2014

An improved upper bound on the minimum distance of this class of LDPC codes is given.

### Constructions of quasi-cyclic measurement matrices based on array codes

- Computer Science2013 IEEE International Symposium on Information Theory
- 2013

The proposed measurement matrices have perfect quasi-cyclic structures and can make the hardware realization convenient and easy, thus having great potentials in practice and many parity-check matrices of array codes and their submatrices perform better than the corresponding Gaussian random matrices.

### Effect of one redundant parity-check equation on the stopping distance

- Computer Science
- 2019

This paper presents a modified decoding algorithm for array LDPC codes C(m, q) over BEC with the column weight m and row weight q with the aim of correct remaining erasures in the case of an iterative decoding failure.

### Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes with Applications to Stopping Sets

- Computer Science2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

This paper examines a large number of regular and irregular LDPC codes, and demonstrates the efficiency and versatility of the proposed characterization/search technique in finding lower and upper bounds on, and in many cases the exact value of, ${s}_{min}$.

### Structural Analysis of Array-Based Non-Binary LDPC Codes

- Computer ScienceIEEE Transactions on Communications
- 2016

It is shown that there may exist codewords with symbol weight four, six, and seven in array-based NBLDPC codes defined by parity-check matrices with column weight two and that the graphical substructure induced by a weight-7 codeword takes the graphical subgraph induced by the related weight-6codewords as a subgraph.

### Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes With Applications to Stopping Sets

- Computer ScienceIEEE Transactions on Information Theory
- 2019

A characterization for non-elementary trapping sets (NETSs) of low-density parity-check (LDPC) codes based on viewing an NETS as a hierarchy of embedded graphs starting from an ETS corresponds to an efficient search algorithm that under certain conditions is exhaustive.

### From Cages to Trapping Sets and Codewords: A Technique to Derive Tight Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of LDPC Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2019

This paper makes connections between cages and trapping sets, and derives tight upper bounds on the size of the smallest trapping sets for variable-regular LDPC codes with a given variable degree and girth.

### Effect of one redundant parity-check equation on the stopping distance

- Computer ScienceJournal of Applied Mathematics and Computing
- 2018

This paper presents a modified decoding algorithm for array LDPC codes C(m, q) over BEC with the column weight m and row weight q and proposes a technique to correct remaining erasures in the case of an iterative decoding failure.

### Asymptotic Average Number of Different Categories of Trapping Sets, Absorbing Sets and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles

- Computer ScienceArXiv
- 2017

This paper studies the asymptotic average number of different types of trapping sets in random variable-regular and irregular LDPC code ensembles, and demonstrates that, regardless of the type of the TS, the averagenumber of a given structure tends to infinity, to a positive constant, or to zero, if the structure contains no cycle, only one cycle, or more than one cycle.

### Asymptotic Average Multiplicity of Structures Within Different Categories of Trapping Sets, Absorbing Sets, and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles

- Computer ScienceIEEE Transactions on Information Theory
- 2019

The asymptotic results obtained in this work, which are independent of the block length and only depend on the code’s degree distributions, are shown to be accurate even for finite-length codes.

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