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Bounds for the capacity error function for unidirectional channels with noiseless feedback
Theoretical Computer Science ( IF 1.1 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.tcs.2020.11.049
Christian Deppe , Vladimir Lebedev , Georg Maringer

In digital systems such as fiber optical communications, the ratio between probability of errors of type 10 and 01 can be large. Practically, one can assume that only one type of error can occur. These errors are called asymmetric. Unidirectional errors differ from asymmetric type of errors; here both 10 and 01 type of errors are possible, but in any submitted codeword all the errors are of the same type. This can be generalized for the q-ary case.

We consider q-ary unidirectional channels with feedback where the errors have magnitude one and give bounds for the capacity error function. It turns out that the bounds depend on the parity of the alphabet size q. Furthermore, we show that for feedback, the capacity error function for the binary asymmetric channel is different from the symmetric channel. This is in contrast to the behavior of the function without feedback.



中文翻译:

具有无噪声反馈的单向通道的容量误差函数的界限

在诸如光纤通信之类的数字系统中,类型错误概率之间的比率 1个001个可以很大。实际上,可以假设只有一种错误会发生。这些错误称为不对称。单向错误不同于非对称错误;这两个1个001个错误类型是可能的,但是在任何提交的代码字中,所有错误都是同一类型。对于q元情况,可以将其概括。

我们考虑带有反馈的q元单向信道,其中误差的大小为1,并给出了容量误差函数的界限。事实证明,范围取决于字母大小q的奇偶性。此外,我们表明,对于反馈,二进制非对称信道的容量误差函数不同于对称信道。这与没有反馈的功能的行为形成对比。

更新日期:2021-01-16
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