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Relaxed Polar Codes

机译：宽松的极地代码

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摘要

Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of binary-input discrete memoryless channels. Polar encoding and successive cancellation decoding have the complexities of N log N , for code length N. Although, the complexity bound of N log N is asymptotically favorable, we report in this work methods to further reduce the encoding and decoding complexities of polar coding. The crux is to relax the polarization of certain bit-channels without performance degradation. We consider schemes for relaxing the polarization of both very good and very bad bit-channels, in the process of channel polarization. Relaxed polar codes are proved to preserve the capacity achieving property of polar codes. Analytical bounds on the asymptotic and finite-length complexity reduction attainable by relaxed polarization are derived. For binary erasure channels, we show that the computation complexity can be reduced by a factor of six, while preserving the rate and error performance. We also show that relaxed polar codes can be decoded with significantly reduced latency. For additive white Gaussian noise channels with medium code lengths, we show that relaxed polar codes can have lower error probabilities than conventional polar codes, while having reduced encoding and decoding computation complexities.
机译：极码是编码理论中的最新突破，因为它们是具有显式构造的第一个代码家族，可证明实现了二进制输入离散无记忆通道的对称容量。对于代码长度N，极性编码和连续消除解码具有N log N的复杂度。尽管N log N的复杂度边界在渐近上是有利的，但我们在此工作方法中报告了进一步降低极性编码的编码和解码复杂度的方法。关键是要在不降低性能的情况下放松某些位通道的极化。我们考虑在信道极化过程中放松非常好和非常坏的位信道的极化的方案。松弛极性代码被证明可以保持极性代码的容量实现特性。得出了通过松散极化可实现的渐近和有限长度复杂度降低的解析界。对于二进制擦除通道，我们表明可以在保持速率和错误性能的同时将计算复杂度降低六倍。我们还表明，可以用显着减少的延迟来解码轻松的极性代码。对于具有中等码长的加性高斯白噪声信道，我们表明，松弛的极性码比传统的极性码具有更低的错误概率，同时降低了编码和解码的计算复杂度。

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