Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors
Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors
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DOI：
10.1109/tit.2016.2616117
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发表时间：
2016-12-01
影响因子：
2.5
通讯作者：
Urbanke, Rudiger L.
中科院分区：
文献类型：
--
作者：
Mondelli, Marco;Hassani, S. Hamed;Urbanke, Rudiger L.
考虑在二进制无记忆对称信道W上传输块长度N和速率R的极性码，并令P-e为连续消除解码下的块错误概率。在本文中，我们开发了新的界限来表征参数 R、N、P-e 和通道 W 的质量之间的关系，通道 W 的质量通过其容量 /(W) 及其 Bhattacharyya 参数 Z(W) 进行量化。在之前的工作中，研究了两种主要制度。在误差指数体系中，通道W和速率R<I(W)是固定的，并且证明误差概率Pe大致为2(-根N)。在缩放指数方法中，信道W和错误概率P-e是固定的，并且证明容量/(W)R的差距缩放为N-1/mu。这里，mu 被称为缩放指数，该缩放指数取决于通道 W。二进制擦除通道 (BEC) 的启发式计算给出 mu = 3.627，并且结果表明，对于任何通道 W，3.579
Consider the transmission of a polar code of block length N and rate R over a binary memoryless symmetric channel W and let P-e be the block error probability under successive cancellation decoding. In this paper, we develop new bounds that characterize the relationship of the parameters R, N, P-e, and the quality of the channel W quantified by its capacity /(W) and its Bhattacharyya parameter Z(W). In previous work, two main regimes were studied. In the error exponent regime, the channel W and the rate R < I(W) are fixed, and it was proved that the error probability Pe scales roughly as 2(-root N). In the scaling exponent approach, the channel W and the error probability P-e are fixed and it was proved that the gap to capacity /(W) R scales as N-1/mu. Here, mu is called scaling exponent and this scaling exponent depends on the channel W. A heuristic computation for the binary erasure channel (BEC) gives mu = 3.627 and it was shown that, for any channel W, 3.579