Rank-order coding, a form of temporal coding, has emerged as a promising
scheme to explain the rapid ability of the mammalian brain. Owing to its speed
as well as efficiency, rank-order coding is increasingly gaining interest in
diverse research areas beyond neuroscience. However, much uncertainty still
exists about the performance of rank-order coding under noise. Herein we show
what information rates are fundamentally possible and what trade-offs are at
stake. An unexpected finding in this paper is the emergence of a special class
of errors that, in a regime, increase with less noise.

通过研究发现，基于排名编码的一种时间编码形式是解释哺乳动物大脑快速能力的一种有前途的方案。然而，在噪声环境下，对于排名编码的性能仍存在不确定性。本文揭示了基本可能的信息速率和可能存在的权衡，并发现在某种情况下会出现一类特殊错误，其数量与噪声减少而增加。

噪声神经通信中的内在权衡：基于排序编码

An Inherent Trade-Off in Noisy Neural Communication with Rank-Order  Coding

This paper represents an extended version of an earlier note [10]. The
concept of weighted entropy takes into account values of different outcomes,
i.e., makes entropy context-dependent, through the weight function. We analyse
analogs of the Fisher information inequality and entropy power inequality for
the weighted entropy and discuss connections with weighted Lieb's splitting
inequality. The concepts of rates of the weighted entropy and information are
also discussed.

这篇论文扩展了之前的笔记，阐述了加权熵的概念及其与 Fisher 信息不等式、熵能不等式和 Lieb 分裂不等式的关系，并讨论了关于加权熵和信息速率的概念。

加权熵：基本不等式

Weighted entropy: basic inequalities

In this paper we introduce a fundamental principle for optimal communication
over general memoryless channels in the presence of noiseless feedback, termed
posterior matching. Using this principle, we devise a (simple, sequential)
generic feedback transmission scheme suitable for a large class of memoryless
channels and input distributions, achieving any rate below the corresponding
mutual information. This provides a unified framework for optimal feedback
communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath
scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that
the Horstein scheme indeed attains the BSC capacity, settling a longstanding
conjecture. We further provide closed form expressions for the error
probability of the scheme over a range of rates, and derive the achievable
rates in a mismatch setting where the scheme is designed according to the wrong
channel model. Several illustrative examples of the posterior matching scheme
for specific channels are given, and the corresponding error probability
expressions are evaluated. The proof techniques employed utilize novel
relations between information rates and contraction properties of iterated
function systems.

本文提出了一种基本原则，即后验匹配，用于通讯过程中的反馈传输方案，在一定条件下，在广泛类别的无记忆信道和输入分布情况下，实现相对应的互信息以下的任何传输速率，该方案提供了一种优化反馈通讯的统一框架，并证明了 Horstein 方案确实实现了 BSC 容量，同时提供了反馈方案的错误概率表达式和可实现的速率范围。