Name
Title | ||
|---|---|---|
Cyclic and Quasi-Cyclic LDPC Codes on Constrained Parity-Check Matrices and Their Trapping Sets |
Abstract | ||
|---|---|---|
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterization of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite-geometry LDPC codes using the results developed in the first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping set structure of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite-geometry and finite-field cyclic and quasi-cyclic LDPC codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances. Consequently, their error-floor performances are dominated by their minimum distances. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TIT.2011.2179842 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
generator polynomial,finite-field cyclic codes,cyclic descendant code,row–column (rc)-constrained ldpc code,geometric codes,orthogonal parity-check sums,low-density parity-check (ldpc) code,cyclic code,trapping set,constrained parity-check matrices,error-floor performances,trapping sets,cyclic finite-geometry ldpc codes,circulant decomposition,row-column (rc)-constrained ldpc code,quasi-cyclic (qc) code,low-density parity-check codes,finite-geometry (fg) code,parity check codes,polynomials,quasi-cyclic ldpc codes,structure analysis,satisfiability,ldpc code,low density parity check,generators,null space,decoding,finite field,matrix decomposition | Forward error correction,Discrete mathematics,Concatenated error correction code,Combinatorics,Low-density parity-check code,Block code,Polynomial code,Turbo code,Cyclic code,Linear code,Mathematics | Journal |
Volume | Issue | ISSN |
58 | 5 | 0018-9448 |
Citations | PageRank | References |
40 | 1.49 | 43 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Qin Huang | 1 | 355 | 34.55 |
| Qiuju Diao | 2 | 114 | 8.72 |
| Shu Lin | 3 | 234 | 16.88 |
| Khaled A. S. Abdel-Ghaffar | 4 | 616 | 122.03 |