Abstract
The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this method, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.
| Original language | English |
|---|---|
| Pages (from-to) | 1355-1358 |
| Number of pages | 4 |
| Journal | Physical Review Letters |
| Volume | 84 |
| Issue number | 6 |
| Publication status | Published - 7 Feb 2000 |
Bibliographical note
Copyright of the American Physical SocietyKeywords
- Gallager's error-correcting code
- statistical physics
- transmitted codeword
- matrices
- Shannon's channel capacity
- decoding aspects
- TAP approach