没有参数的广义熵如何影响信息优化过程
On how generalised entropies without parameters impact information optimisation processes
摘要：
作为广义统计力学的一个应用，本文研究了一个非广延、非参数熵$H^\pm_D(P)$族的一致广义信息论的可能途径。与其他基于非广延熵与参数依赖性的建议不同，我们的计划是渐近等价的香农制定的，而它不同的区域，其中的状态密度是合理的小，这导致信息分布约束到他们的背景。两个基本概念进行了讨论，以达到这一目的。首先，我们证明了两个有效的编码定理的熵$H^\pm_D(P)$。然后根据这些熵计算了二进制对称信道（BSC）和二进制擦除信道（BEC）的信道容量。我们发现，如数据压缩和信道容量最大化的过程中，可以提高在区域中，有一个低密度的状态，而高密度，我们的结果符合香农的配方。
英文摘要：
As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals based on non-extensive entropies with a parameter dependence, our scheme is asymptotically equivalent to the one formulated by Shannon, while it differs in regions where the density of states is reasonably small, which leads to information distributions constrained to their background. Two basic concepts are discussed to this aim. First, we prove two effective coding theorems for the entropies $H^\pm_D(P)$. Then we calculate the channel capacity of a binary symmetric channel (BSC) and a binary erasure channel (BEC) in terms of these entropies. We found that processes such as data compression and channel capacity maximisation can be improved in regions where there is a low density of states, whereas for high densities our results coincide with Shannon's formulation.
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