信息论(英语:information theory)是运用概率论与数理统计的方法研究信息、信息熵、通信系统、数据传输、密码学、数据压缩等问题的应用数学学科。 信息论将信息的传递作为一种统计现象来考虑,给出了估算通信信道容量的方法。信息传输和信息压缩是信息论研究中的两大领域。这两个方面又由信道编码定理、信源-信道隔离定理相互联系。

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本教程关注信息理论在统计学中的应用。被称为信息散度或Kullback-Leibler距离或相对熵的信息度量起着关键作用。涵盖的主题包括大偏差、假设检验、指数族的最大似然估计、列联表的分析以及具有“信息几何”背景的迭代算法。同时,还介绍了通用编码的理论,以及由通用编码理论驱动的最小描述长度原理的统计推理。

https://www.nowpublishers.com/article/Details/CIT-004

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This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $\epsilon$-variable-length resolvability. We derive the general formula of the $\epsilon$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint the value of the average variational distance is smaller than or equal to some constant. Our result clarifies a dual relationship between the general formula of $\epsilon$-variable-length resolvability and that of $\epsilon$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

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We consider an energy harvesting transmitter equipped with two batteries having finite storage capacities, communicating over an additive white Gaussian channel. The work is motivated by an observation that many practical batteries, when repeatedly charged after being partially discharged, suffer from degradation in the usable capacity. The capacity can be recovered by completely discharging the battery before charging it fully again. Hence, in this work, we impose the constraint that a battery must be charged (discharged) only after it is fully discharged (charged). Our goal is to maximize the longterm average throughput with non-causal and causal knowledge of the energy arrivals, which we assume to be Bernoulli. We propose two sub-optimal policies and obtain an upper bound on the performance gap (G) from the optimal long-term average throughput that is achieved with infinite capacity batteries. We find that G remains constant as the amount of energy harvested per arrival increases. Numerically, we also find that G decreases with the battery capacity faster than the inverse of the square root of the battery capacity for a specific energy arrival parameters.

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We consider an energy harvesting transmitter equipped with two batteries having finite storage capacities, communicating over an additive white Gaussian channel. The work is motivated by an observation that many practical batteries, when repeatedly charged after being partially discharged, suffer from degradation in the usable capacity. The capacity can be recovered by completely discharging the battery before charging it fully again. Hence, in this work, we impose the constraint that a battery must be charged (discharged) only after it is fully discharged (charged). Our goal is to maximize the longterm average throughput with non-causal and causal knowledge of the energy arrivals, which we assume to be Bernoulli. We propose two sub-optimal policies and obtain an upper bound on the performance gap (G) from the optimal long-term average throughput that is achieved with infinite capacity batteries. We find that G remains constant as the amount of energy harvested per arrival increases. Numerically, we also find that G decreases with the battery capacity faster than the inverse of the square root of the battery capacity for a specific energy arrival parameters.

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