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arXiv 1209.2820cs.ITmath.IT
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单调信道容量的条件

Conditions for a Monotonic Channel Capacity

Erik Agrell

摘要:

受光通信中的结果的启发,其中如果发射功率充分增加,则性能会显著降低,信道容量被表征为各种无记忆矢量信道。证明了对于所有静态点对点信道,信道容量是功率的非减函数。因此,对于这样的信道,在具有一定功率的所有输入分布上最大化互信息等同于在具有上限功率的较大输入分布集合上最大化它。对于干扰信道,如光波分复用系统,主信道容量总是不随功率而减小,如果所有的干扰用户与主用户以相同的分布进行发送。此外,如果干扰信道中的所有输入分布被联合优化,则可实现的和速率容量再次是非递减的。结果推广到信道容量作为一个广泛的一类成本的函数,而不仅仅是功率。

英文摘要:

Motivated by results in optical communications, where the performance can degrade dramatically if the transmit power is sufficiently increased, the channel capacity is characterized for various kinds of memoryless vector channels. It is proved that for all static point-to-point channels, the channel capacity is a nondecreasing function of power. As a consequence, maximizing the mutual information over all input distributions with a certain power is for such channels equivalent to maximizing it over the larger set of input distributions with upperbounded power. For interference channels such as optical wavelength-division multiplexing systems, the primary channel capacity is always nondecreasing with power if all interferers transmit with identical distributions as the primary user. Also, if all input distributions in an interference channel are optimized jointly, then the achievable sum-rate capacity is again nondecreasing. The results generalizes to the channel capacity as a function of a wide class of costs, not only power.

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