Capacity upper bounds for deletion-type channels
Capacity upper bounds for deletion-type channels
复制标题
删除型通道的容量上限
DOI：
10.1145/3188745.3188768
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Mahdi Cheraghchi
中科院分区：
文献类型：
--
作者：
Mahdi Cheraghchi
我们基于凸面编程和实际分析的系统方法，以在二进制删除渠道的能力上获得上限，更普遍地使用I.I.D。到Mitzenmacher和Drinea引入的泊松重复通道（IEEE信息理论交易，2006年）。对于任何重复分布（删除和泊松重复通道，与伯诺利和泊松分布的特殊情况相对应）。有界的间隔。随着函数的所需简单性（例如，在我们的结果中，仅具有有效计算的封闭式表达方式，而是具有显式闭合形式的表达）。对于D≥1/2的概率D最多是（1 -d）logϕ，并且假设容量函数为凸，则最多是D <1/2的1 -d log（4/ϕ），其中ϕ =（ 1+√5）/2是黄金比率第一个非平凡的容量在限制案例d→0之外的任何值，这些值是完全显式的，并且在没有计算机的情况下提供了。该通道和删除通道之间的连接，并在某种程度上违反直觉，在分析上比删除通道更简单。对于删除通道的完全理解，我们可能是关键的，我们在删除通道的能力上得出了几个新颖的上限。反过来，我们在明确的基本和标准特殊功能方面绑定了这些功能，它们的最大值可以更有效地发现（有时在分析上，例如，对于d = 1/2）。在此过程中，我们开发了一些潜在的独立兴趣的新技术。新颖的特殊功能可能引起数学分析。
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the classical deletion channel, we give a special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions on Information Theory, 2006). Our framework can be applied to obtain capacity upper bounds for any repetition distribution (the deletion and Poisson-repeat channels corresponding to the special cases of Bernoulli and Poisson distributions). Our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate, real-valued, and often concave function over a bounded interval. The corresponding univariate function is carefully designed according to the underlying distribution of repetitions and the choices vary depending on the desired strength of the upper bounds as well as the desired simplicity of the function (e.g., being only efficiently computable versus having an explicit closed-form expression in terms of elementary, or common special, functions). Among our results, we show that the capacity of the binary deletion channel with deletion probability d is at most (1−d) logϕ for d ≥ 1/2, and, assuming the capacity function is convex, is at most 1−d log(4/ϕ) for d<1/2, where ϕ=(1+√5)/2 is the golden ratio. This is the first nontrivial capacity upper bound for any value of d outside the limiting case d → 0 that is fully explicit and proved without computer assistance. Furthermore, we derive the first set of capacity upper bounds for the Poisson-repeat channel. Our results uncover further striking connections between this channel and the deletion channel, and suggest, somewhat counter-intuitively, that the Poisson-repeat channel is actually analytically simpler than the deletion channel and may be of key importance to a complete understanding of the deletion channel. Finally, we derive several novel upper bounds on the capacity of the deletion channel. All upper bounds are maximums of efficiently computable, and concave, univariate real functions over a bounded domain. In turn, we upper bound these functions in terms of explicit elementary and standard special functions, whose maximums can be found even more efficiently (and sometimes, analytically, for example for d=1/2). Along the way, we develop several new techniques of potentially independent interest. For example, we develop systematic techniques to study channels with mean constraints over the reals. Furthermore, we motivate the study of novel probability distributions over non-negative integers, as well as novel special functions which could be of interest to mathematical analysis.
在遗忘模型和在线模型中针对删除进行编码
影响因子：
2.5
作者：
Guruswami, Venkatesan;Li, Ray
通讯作者：
Li, Ray
改进的离散时间泊松通道的容量上限
DOI：
10.1109/isit.2018.8437514
发表时间：
2018
期刊：
--
影响因子：
--
作者：
Cheraghchi M
通讯作者：
Cheraghchi M