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Improved Bounds on the Finite Length Scaling of Polar Codes

机译:极坐标代码的有限长度缩放的改进边界

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摘要

Improved upper bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is obtained. The main result is that the blocklength required to communicate reliably scales at most as , where is the code rate and is the symmetric capacity of the channel . The results are then extended to polar lossy source coding at rate of a source with symmetric distortion-rate function . The blocklength required scales at most as , where is the maximal allowed gap between the actual average (or typical) distortion and .
机译:得出了在低于给定错误概率的情况下,使用极性码在二进制输入通道上进行通信所需的块长度的改进上限。为此,获得了对非偏振通道数量的改进的限制。主要结果是,可靠通信所需的块长度最多可扩展为,其中,是码率,是信道的对称容量。然后将结果扩展到具有对称失真率函数的源的速率的极有损源编码。所需的块长最大缩放为,其中是实际平均(或典型)失真与之间的最大允许间隙。

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