The Jensen-Shannon divergence is a renown bounded symmetrization of the
unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler
divergence to the average mixture distribution. However the Jensen-Shannon
divergence between Gaussian distributions is not available in closed-form. To
bypass this problem, we present a generalization of the Jensen-Shannon (JS)
divergence using abstract means which yields closed-form expressions when the
mean is chosen according to the parametric family of distributions. More
generally, we define the JS-symmetrizations of any distance using generalized
statistical mixtures derived from abstract means. In particular, we first show
that the geometric mean is well-suited for exponential families, and report two
closed-form formula for (i) the geometric Jensen-Shannon divergence between
probability densities of the same exponential family, and (ii) the geometric
JS-symmetrization of the reverse Kullback-Leibler divergence. As a second
illustrating example, we show that the harmonic mean is well-suited for the
scale Cauchy distributions, and report a closed-form formula for the harmonic
Jensen-Shannon divergence between scale Cauchy distributions. We also define
generalized Jensen-Shannon divergences between matrices (e.g., quantum
Jensen-Shannon divergences) and consider clustering with respect to these novel
Jensen-Shannon divergences.

本文提出了一种使用抽象均值的 Jensen-Shannon（JS）差异的推广来绕过高斯分布之间的 JS 差异无法使用封闭形式表示的问题，并定义了任何距离的 JS 对称化。我们特别分别以几何平均和调和平均为例，推导了封闭形式的公式，其中包括基于相同指数族的概率密度之间的几何 JS 差异以及逆 Kullback-Leibler 差异的几何 JS 对称化，以及在剖面调和分布情况下的调和 JS 差异，同时定义了矩阵之间的 JS 差异，并考虑了在这些新型 JS 差异之下的聚类问题。

关于 Jensen-Shannon 散度的一般化以及基于抽象均值的距离 JS 对称化

On a generalization of the Jensen-Shannon divergence and the  JS-symmetrization of distances relying on abstract means

This paper studies the performance of delay-constrained hybrid automatic
repeat request HARQ protocols. Particularly, we propose a fast HARQ protocol
where, to increase the end-to-end throughput, some HARQ feedback signals and
successive message decodings are omitted. Considering quasi-static channels and
a bursty communication model, we derive closed-form expressions for the message
decoding probabilities as well as the throughput, the expected delay and the
error probability of the HARQ setups. The analysis is based on recent results
on the achievable rates of finite-length codes and shows the effect of the
codeword length on the system performance. Moreover, we evaluate the effect of
various parameters such as imperfect channel estimation and hardware on the
system performance. As demonstrated, the proposed fast HARQ protocol reduces
the packet transmission delay considerably, compared to state-of-the-art HARQ
schemes. For example, with typical message decoding delay profiles and a
maximum of 2,...,5 transmission rounds, the proposed fast HARQ protocol can
improve the expected delay, compared to standard HARQ, by 27, 42, 52 and 60%,
respectively, independently of the code rate/fading model.

本文研究了延迟受限的混合自动重传请求（HARQ）协议的性能。具体而言，我们提出了一种快速 HARQ 协议，其中省略了一些 HARQ 反馈信号以及连续的消息解码，以增加端到端吞吐量。考虑到准静态信道和爆发式通信模型，我们推导出了消息解码概率、吞吐量、预期延迟和 HARQ 设置的误码率的闭式表达式。此外，我们评估了不同参数对系统性能的影响，例如不完美的信道估计和硬件问题。如分析结果所示，相比现有技术，所提出的快速 HARQ 协议显著降低了数据包传输延迟。例如，针对典型的消息解码延迟曲线和最多 2 到 5 个传输回合，与标准 HARQ 相比，所提出的快速 HARQ 协议可以将预期延迟提高 27％、42％、52％和 60％，独立于编码速率 / 衰落模型。