Reversible Codes
Reversible Codes
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DOI：
10.1016/s0019-9958(64)90438-3
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
J. Massey
中科院分区：
文献类型：
--
作者：
J. Massey
一个代码被定义为可逆的，如果它的码字集在每个码字中的数字的反转下是不变的。这样的代码可以应用于某些数据存储和检索系统。证明了循环码和卷积码是可逆的，当且仅当它们的码生成多项式是自互逆的。可逆码是相当罕见的，因此，但它表明，一个重要的子类的Bose-Chaudhuri码完全由可逆码。开发了一些技术，通过这些技术，任何不可逆循环码都可以转换成具有至少同样多的纠错能力的可逆循环码，但代价是增加了代码冗余度。衍生码的冗余度最多为原码的两倍，并且衍生码可以由为原码构造的解码器解码。类似地，它示出了任何不可逆的卷积码可以被转换成一个可逆的卷积码，至少有尽可能多的纠错能力，但在代码约束长度增加的成本。同样，导出码可以由与原始码基本相同的解码器解码。
A code is defined to be reversible if its code-word set is invariant under a reversal of the digits in each code word. Such codes may have application in certain data storage and retrieval systems. It is shown that cyclic codes and convolutional codes are reversible when and only when their code-generating polynomials are self-reciprocal. Reversible codes are quite rare therefore, but it is shown that an important subclass of the Bose-Chaudhuri codes consists entirely of reversible codes. Techniques are developed by which any nonreversible cyclic code can be converted into a reversible cyclic code with at least as much error-correcting power, but at the cost of increased code redundancy. The redundancy of the derived code is at most twice that of the original code, and the derived code can be decoded by a decoder constructed for the original code. Similarly, it is shown how any nonreversible convolutional code can be converted into a reversible convolutional code with at least as much error-correcting power, but at the cost of increased code constraint length. Again the derived code can be decoded by substantially the same decoder as for the original code.