一类特殊的改进捕错译码

A Special Kind of Modified Error-Trapping Decoding

捕错译码是传码率满足Ｒ＜１／ｔ的循环码译码最简单的方式，其中ｔ是所能纠错误数的最大值，Ｒ是传码率。这类码传码率低，纠错少。嵩钟雄运用覆盖多项式的概念得出了传码率不满足Ｒ＜１／ｔ的二进制循环码的改进捕错译码方法。本文找到了嵩钟雄译码器的一个子类──一类特殊的改进捕错译码器。作者的译码器同捕错译码器一样易于硬件实现，并且能够用于传码率不满足Ｒ＜１／ｔ的情况。对于纠错码，作者找到了适合于这一译码器的码判别方法，并进一步给出了寻找这类码覆盖单项式的算法。最后指出了覆盖单项式阶数与硬件的简单对应关系。

The error-trapping decoder is the simplest way of decoding cyclic codes satisfying R<1/t,where t is the maximum number of errors to be corrected and R the code rate.These codes have low rates and/or correct only a few errors. Kassami has used the concept of covering polynomials to demonstrate modified error-trapping decoders for several binary cyclic codes not satisfying R <1/t. The author finds out a subset of Kassami's decoders─a special kind of modified error-trapping decoders. The decoder is as easy to be implemented in hardware as an error-trapping decoder,and can be used when R<1/t is not available. For error-correcting codes,we have found the decision method to the codes which is applicable to the decoder, and have given the algorithm of finding covering monomials.Finally,the author points out the simple relation between the order of monomial and the hardware.