Name
Abstract | ||
|---|---|---|
We use the theory of finite classical generalized polygons to derive and study low-density parity-check (LDPC) codes. The Tanner graph of a generalized polygon LDPC code is highly symmetric, inherits the diameter size of the parent generalized polygon, and has minimum (one half) diameter-to-girth ratio. We show formally that when the diameter is four or six or eight, all codewords have even Hamming weight. When the generalized polygon has in addition an equal number of points and lines, we see that the nonregular polygon based code construction has minimum distance that is higher at least by two in comparison with the dual regular polygon code of the same rate and length. A new minimum-distance bound is presented for codes from nonregular polygons of even diameter and equal number of points and lines. Finally, we prove that all codes derived from finite classical generalized quadrangles are quasi-cyclic and we give the explicit size of the circulant blocks in the parity-check matrix. Our simulation studies of several generalized polygon LDPC codes demonstrate powerful bit-error-rate (BER) performance when decoding is carried out via low-complexity variants of belief propagation. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/TIT.2005.856936 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
Hamming codes,cyclic codes,error statistics,graph theory,matrix algebra,parity check codes,BER,Hamming weight,LDPC code,Tanner graph,belief propagation,bit-error-rate,cyclic code,finite classical generalized polygon,finite classical generalized quadrangle,low-density parity-check code,minimum-distance bound,parity-check matrix,sum-product algorithm,Belief propagation,cyclic codes,generalized polygons,low-density parity-check (LDPC) codes,sum–product algorithm | Discrete mathematics,Combinatorics,Polygon,Low-density parity-check code,Regular polygon,Pick's theorem,Generalized polygon,Polygon triangulation,Monotone polygon,Mathematics,Complex polygon | Journal |
Volume | Issue | ISSN |
51 | 11 | 0018-9448 |
Citations | PageRank | References |
19 | 0.91 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Liu, Z. | 1 | 19 | 0.91 |
| Pados, D.A. | 2 | 19 | 0.91 |