How quickly can we approach channel capacity?
How quickly can we approach channel capacity?
复制标题
我们能多快达到渠道容量？
DOI：
10.1109/acssc.2004.1399310
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Richard Baraniuk
中科院分区：
文献类型：
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作者：
D. Baron;M. Khojastepour;Richard Baraniuk
代码设计的最新进展使得了解通信系统达到其极限的速度变得至关重要。为了解决信道容量 C 的这个问题，我们将非渐近容量 C/sub NA/(n, /spl epsi/) 定义为在使用长度为 n 的码字时实现码字错误概率 /spl epsi/ 的码本的最大速率。我们证明对于二元对称通道，C/sub NA/(n,/spl epsi/)=C-K(/spl epsi/)//spl radic/n+o(1//spl radic/n)，其中 K(/spl epsi/) 可以以封闭形式获得。我们还描述了高斯通道的类似结果。这些结果可能会导致实际通信系统中更有效的资源使用。
Recent progress in code design has made it crucial to understand how quickly communication systems can approach their limits. To address this issue for the channel capacity C, we define the nonasymptotic capacity C/sub NA/(n, /spl epsi/) as the maximal rate of codebooks that achieve a probability /spl epsi/ of codeword error while using codewords of length n. We prove for the binary symmetric channel that C/sub NA/(n,/spl epsi/)=C-K(/spl epsi/)//spl radic/n+o(1//spl radic/n), where K(/spl epsi/) is available in closed form. We also describe similar results for the Gaussian channel. These results may lead to more efficient resource usage in practical communication systems.