带记忆的信道极化
天体物理仪器与方法
2025-06-26 v2 机器学习
摘要
本文考察了在具有记忆的信道下极化码的信道极化行为。通过引入仆人信道模型，首先我们表明，尽管存在记忆效应，极化子信道仍会收敆至极端信道。更重要的是，我们明确量化了忽略记忆效应所实现的互信息与在充分极化后实际获得的信道容量之间的差距。证明即使在没有信道噪声先验知识的情况下，信道容量仍可实现。 Furthermore, we demonstrate that the polarization rate is slower than that in the binary-input memoryless channel (BMC) case, provided that the channel transition function satisfies certain conditions. In particular, the Bhattacharyya parameter is asymptotically upper-bounded and lower-bounded by a polynomial function and an exponential function with respect to the block length, respectively.
引用
@article{arxiv.2411.16556,
title = {Anomaly Detection and Radio-frequency Interference Classification with Unsupervised Learning in Narrowband Radio Technosignature Searches},
author = {Ben Jacobson-Bell and Steve Croft and Carmen Choza and Alex Andersson and Daniel Bautista and Vishal Gajjar and Matthew Lebofsky and David H. E. MacMahon and Caleb Painter and Andrew P. V. Siemion},
journal= {arXiv preprint arXiv:2411.16556},
year = {2025}
}
备注
21 pages, 14 figures