$\epsilon$-Capacity of Binary Symmetric Averaged Channels
$\epsilon$-Capacity of Binary Symmetric Averaged Channels
复制标题
$epsilon$-二元对称平均通道的容量
DOI：
10.1109/tit.2006.887087
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发表时间：
2007
影响因子：
2.5
通讯作者：
J. Kieffer
中科院分区：
文献类型：
--
作者：
J. Kieffer
我们认为，通过平均二进制对称信道（BSC）的分量相对于一个加权分布的信道模型。如果在（A，B）中没有信道组件具有容量，并且对于严格包含（A，B）的每个开放区间，该属性失败，则对于该信道模型，非空开放区间（A，B）被称为容量间隙。对于固定的epsi>0，假设希望计算信道的epsi容量，其是信道可以经由每个实现块错误概率lesepsi的信道码序列编码的最大渐近速率。在1963年，Parthasarathy提供了一个epsi容量的公式，它对所有但至多可数个epsi值都有效。当该公式失效时，存在唯一的电容间隙（A，B），使得epsi电容位于[A，B]中，但人们不知道精确的位置。通过编码定理和匡威，我们建立了一个计算epsi容量的公式，该公式作为相关容量间隙（A，B）的端点A，B的函数;该公式在容量间隙足够窄时成立
We consider the channel model obtained by averaging binary symmetric channel (BSC) components with respect to a weighting distribution. A nonempty open interval (A, B) is called a capacity gap for this channel model if no channel component has capacity in (A, B) and this property fails for every open interval strictly containing (A, B). For a fixed epsi>0, suppose one wishes to compute the epsi-capacity of the channel, which is the maximum asymptotic rate at which the channel can be encoded via a sequence of channel codes each achieving block error probability lesepsi. In 1963, Parthasarathy provided a formula for epsi-capacity which is valid for all but at most countably many values of epsi. When the formula fails, there exists a unique capacity gap (A, B) such that the epsi-capacity lies in [A, B], but one does not know precisely where. Via a coding theorem and converse, we establish a formula for computing epsi-capacity as a function of the endpoints A, B of the associated capacity gap (A, B); the formula holds whenever the capacity gap is sufficiently narrow in width