This paper studies the fundamental limit of semantic communications over the
discrete memoryless channel. We consider the scenario to send a semantic source
consisting of an observation state and its corresponding semantic state, both
of which are recovered at the receiver. To derive the performance limitation,
we adopt the semantic rate-distortion function (SRDF) to study the relationship
among the minimum compression rate, observation distortion, semantic
distortion, and channel capacity. For the case with unknown semantic source
distribution, while only a set of the source samples is available, we propose a
neural-network-based method by leveraging the generative networks to learn the
semantic source distribution. Furthermore, for a special case where the
semantic state is a deterministic function of the observation, we design a
cascade neural network to estimate the SRDF. For the case with perfectly known
semantic source distribution, we propose a general Blahut-Arimoto algorithm to
effectively compute the SRDF. Finally, experimental results validate our
proposed algorithms for the scenarios with ideal Gaussian semantic source and
some practical datasets.

该研究探讨了离散无记忆信道上语义通信的基本限制，采用语义速率失真函数分析最小压缩率、观测失真、语义失真和信道容量之间的关系。对于未知语义源分布的情况，提出了一种基于神经网络的方法来学习语义源分布，同时设计了级联神经网络来估计语义速率失真函数。对于已知完美语义源分布的情况，提出了通用的 Blahut-Arimoto 算法来高效计算语义速率失真函数。最后，通过实验证实了该算法在理想高斯语义源和一些实际数据集的情况下的有效性。

语义通信的基本限制：速率失真的神经估计

Fundamental Limitation of Semantic Communications: Neural Estimation for  Rate-Distortion

The Blahut-Arimoto (BA) algorithm has played a fundamental role in the
numerical computation of rate-distortion (RD) functions. This algorithm
possesses a desirable monotonic convergence property by alternatively
minimizing its Lagrangian with a fixed multiplier. In this paper, we propose a
novel modification of the BA algorithm, letting the multiplier be updated in
each iteration via a one-dimensional root-finding step with respect to a
monotonic univariate function, which can be efficiently implemented by Newton's
method. This allows the multiplier to be updated in a flexible and efficient
manner, overcoming a major drawback of the original BA algorithm wherein the
multiplier is fixed throughout iterations. Consequently, the modified algorithm
is capable of directly computing the RD function for a given target distortion,
without exploring the entire RD curve as in the original BA algorithm. A
theoretical analysis shows that the modified algorithm still converges to the
RD function and the convergence rate is $\Theta(1/n)$, where $n$ denotes the
number of iterations. Numerical experiments demonstrate that the modified
algorithm directly computes the RD function with a given target distortion, and
it significantly accelerates the original BA algorithm.

通过使用一维根查找步骤和牛顿法更新固定乘数的 Blahut-Arimoto 算法的新修改版，可以使算法更加灵活和高效，直接计算给定目标失真下的速率失真函数，并且收敛速度为 O（1/n）。

Blahut 和 Arimoto 主题的变体

Variations on a Theme by Blahut and Arimoto

The optical fiber multiple-input multiple-output (MIMO) channel with
intensity modulation and direct detection (IM/DD) per spatial path is treated.
The spatial dimensions represent the multiple modes employed for transmission
and the cross-talk between them originates in the multiplexers and
demultiplexers, which are polarization dependent and thus timevarying. The
upper bounds from free-space IM/DD MIMO channels are adapted to the fiber case,
and the constellation constrained capacity is constructively estimated using
the Blahut-Arimoto algorithm. An autoencoder is then proposed to optimize a
practical MIMO transmission in terms of pre-coder and detector assuming channel
distribution knowledge at the transmitter. The pre-coders are shown to be
robust to changes in the channel.

本文研究了采用强度调制和直接检测（IM / DD）的光纤多输入多输出（MIMO）信道，并提出一种自编码器优化 MIMO 传输的方法。

衰落少模 MIMO IM / DD 光纤通道的容量和可实现速率

Capacity and Achievable Rates of Fading Few-mode MIMO IM/DD Optical  Fiber Channels

We extend the Blahut-Arimoto algorithm for maximizing Massey's directed
information. The algorithm can be used for estimating the capacity of channels
with delayed feedback, where the feedback is a deterministic function of the
output. In order to do so, we apply the ideas from the regular Blahut-Arimoto
algorithm, i.e., the alternating maximization procedure, onto our new problem.
We provide both upper and lower bound sequences that converge to the optimum
value. Our main insight in this paper is that in order to find the maximum of
the directed information over causal conditioning probability mass function
(PMF), one can use a backward index time maximization combined with the
alternating maximization procedure. We give a detailed description of the
algorithm, its complexity, the memory needed, and several numerical examples.

本文扩展了 Blahut-Arimoto 算法，用于最大化 Massey 的有向信息，提出了一种既适用于分析具有延迟反馈信道的能力的算法，同时也提供了上下边界序列，为了找到有向信息在因果条件概率质量函数下的最大值，我们使用了反向指数时间最大化和替代最大化过程。