| Presentation | 2005/12/8 High-Rate LDPC Codes Derived from Finite Geometries Norifumi KAMIYA, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Low-Density Parity-Check (LDPC) codes have attracted a great deal of attention because of their outstanding error-performance and reasonable decoding complexity. The error-performance of LDPC codes can be characterized in terms of threshold and error-floor. It is known that the threshold performance of an LDPC code strongly depends on the degree distribution of the parity-check matrix and that density evolution provides a powerful tool for finding good degree distributions. LDPC codes with good threshold performance can be obtained by choosing degree distributions appropriately. For high coding rates and moderate code lengths, however, LDPC codes designed in this way tend to suffer from a high error-floor. LDPC codes with good error-performance are difficult to construct for high coding rates and moderate code lengths while several applications require the use of such codes. In this talk, we will present construction methods which allow to construct high-rate moderate length LDPC codes with good error-performance. The methods are based on such combinatorial designs as affine and projective geometries. After giving a brief review of finite geometry codes, we will present several classes of high-rate quasi-cyclic (QC) LDPC codes derived from finite affine planes. One class of these consists of duals of one-generator QC codes. For codes contained in this class, we will present the exact minimum-distance and the lower bound on the multiplicity of the minimum-weight codewords. It is shown that the lower bound on the multiplicity provides an accurate indication of the bit error performance at high signal-to-noise ratios. We also discuss a class consisting of codes from circulant permutation matrices and present a formula for the dimension of these codes. It is shown that each of these codes can be identified as a code constructed from an MDS codes in a similar manner to the RS-based LDPC codes. Experimental results show that a number of high-rate QC-LDPC codes with excellent performance are contained in these classes. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | LDPC codes / Quasi-Cyclic Codes / Error-floor / Finite-Geometries / Affine Planes |
| Paper # | MR2005-34 |
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| Committee | MR |
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| Conference Date | 2005/12/8(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
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| Vice Chair | |
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| Assistant | |
| Paper Information | |
| Registration To | Magnetic Recording (MR) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | High-Rate LDPC Codes Derived from Finite Geometries |
| Sub Title (in English) | |
| Keyword(1) | LDPC codes |
| Keyword(2) | Quasi-Cyclic Codes |
| Keyword(3) | Error-floor |
| Keyword(4) | Finite-Geometries |
| Keyword(5) | Affine Planes |
| 1st Author's Name | Norifumi KAMIYA |
| 1st Author's Affiliation | Internet Systems Research Laboratories, NEC Corporation() |
| Date | 2005/12/8 |
| Paper # | MR2005-34 |
| Volume (vol) | vol.105 |
| Number (no) | 473 |
| Page | pp.pp.- |
| #Pages | 13 |
| Date of Issue | |