2013 Fiscal Year Final Research Report
Randomness and Structure in Error-Correcting Codes
| Project/Area Number |
23700010
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Fundamental theory of informatics
|
|---|
| Research Institution | Kanazawa University (2012-2013)
(財)九州先端科学技術研究所 (2011) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 誤り訂正符号 / 多項式時間計算 / 加法的通信路 / 誤り訂正能力 |
|---|
| Research Abstract |
We have introduced samplable additive-error channels, and studied the possibilities and limitations of error correction in the channels. "Samplable" means that the errors are efficiently computable, and "additive" means that the errors are added to input codewords without the knowledge of the code or the codewords. If samplable distributions form linear subspaces, we can correct the errors by linear codes. In the situations relativized by oracles, there are samplable errors with low entropy for which no efficient syndrome decoding exists. If samplable distributions are of small-bias, there is a relation between the magnitude of the bias and the information rate on which the errors are correctable.
|
