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arXiv 1601.06101cs.ITcs.CCcs.FLmath.ITquant-ph
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记忆效应可以使通信信道的传输能力不可计算

Memory effects can make the transmission capability of a communication channel uncomputable

David Elkouss, David Pérez-García

摘要:

大多数通信信道都受到噪声的影响。信息论的目标之一是在信息的传输中增加冗余,使信息可靠地传输,并且通过信道传输的信息量尽可能大。可靠传输的最大速率称为容量。如果信道不保留其过去的记忆,则容量由简单的优化问题给出,并且可以有效地计算。具有记忆的通道的情况不太清楚。在这里,我们表明,通道与内存的容量不能计算精度1/5。我们的结果保持,即使我们考虑一个最简单的家庭这样的渠道-信息稳定的有限状态机渠道-,限制输入和输出的通道分别为4和1位,并允许6位的内存。

英文摘要:

Most communication channels are subjected to noise. One of the goals of Information Theory is to add redundancy in the transmission of information so that the information is transmitted reliably and the amount of information transmitted through the channel is as large as possible. The maximum rate at which reliable transmission is possible is called the capacity. If the channel does not keep memory of its past, the capacity is given by a simple optimization problem and can be efficiently computed. The situation of channels with memory is less clear. Here we show that for channels with memory the capacity cannot be computed to within precision 1/5. Our result holds even if we consider one of the simplest families of such channels -information-stable finite state machine channels-, restrict the input and output of the channel to 4 and 1 bit respectively and allow 6 bits of memory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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