關于糾刪碼的研究與進展

Research and development on erasure codes

摘要: 該文簡述了幾類糾刪碼的糾刪原理,系統(tǒng)地綜合分析了各類糾刪碼的優(yōu)缺點及其相互區(qū)別與聯系,證明了若選取MDS(Maximal Distance Separable)碼作為糾刪碼,只要接收者接收到源數據個數的數據,就能恢復原來的源數據。分析結果表明:復損碼以及旋風(Tornado)碼不僅能以線性時間可編碼和可成功地譯碼,而且能以任意接近刪除信道容量的速率進行傳輸,最后指出了目前復損碼的研究中需要解決的一些問題,這些分析和結論為進一步研究糾刪碼提供了理論基礎和新的思路。
- 糾刪碼; 范德蒙碼; 柯西碼; 復損碼; 旋風碼; 二元刪除信道
Abstract: This paper describes the principles of a few types of erasure codes, and analyzes their merits, drawbacks and relationships systematically. It is shown that if MDS codes are chosen as erasure codes, a receiver can reconstruct the original source data once it receives any portion of the encoding data equal to the length of message. The analysis shows that loss-resilient codes and Tornado codes can not only be both encoded and decoded successfully in linear time, but also can come arbitrarily close to the channel capacity. Finally, some problems on loss-resilient codes which remain to be solved are presented. These analyses and conclusions provide theoretical base and new ideas for further studying erasure codes.