A probability-theoretic problem under information constraints for the concept of optimal control over a noisy-memoryless channel is considered. For our Observer-Controller block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we propose a Blahut-Arimoto-type algorithm $-$ which is, to the best of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for $ \mathop {{\rm min}} _{\mathscr {P}(i), i \in \lbrace \mathscr {Y}, \hat{\mathscr {S}}, \mathscr {X},{\mathscr {S}},\hat{\mathscr {X}}\rbrace } {\rm \; } \phi _1 \mathscr {I}(\mathscr {Y};\hat{\mathscr {S}}|\mathscr {X,S})-\phi _2 \mathscr {I}(\mathscr {Y};\hat{\mathscr {X}}|\mathscr {X,S})$. This problem is an $NP-$hard and non-convex multi-objective optimisation (MOO) one, were the objective functions are respectively the distortion function $dim (Null (\mathscr {I}(\hat{\mathscr {S}};{\mathscr {S}})) \rightarrow \infty$ and the memoryless-channel capacity $dim (Null (\mathscr {I}(\mathscr {X};\hat{\mathscr {X}})) \rightarrow 0$. Our novel algorithm applies an Alternating optimisation method. Subsequently, a robust version of the algorithm is discussed with regard to the perturbed PMFs $-$ parameter uncertainties in general. The aforementioned robustness is actualised by exploiting the simultaneous-perturbation-stochastic-approximation (SPSA). The principles of detectability-and-stabilisability as well as synchronisability are explored, in addition to providing the simulations - by which the efficiency of our work is shown. We also calculate the total complexity of our proposed algorithms respectively as $\mathscr {O} (\mathscr {T}\mathscr {K}\mathscr {M}_0(\mathscr {K} \log \mathscr {K}))$ and $\mathscr {O} (\mathscr {T}\mathscr {K}\mathscr {M}_0(\mathscr {K} \log \mathscr {K}+0.33 \mathscr {K}))$. Our methodology is generic which can be applied to other fields of studies which are optimisation-driven.

中文翻译：

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\textit{Blahut-Arimoto} 类型算法的新奇：对嘈杂通信通道的优化控制

考虑在信息约束下的概率论问题，用于优化控制噪声无记忆信道的概念。对于我们的观察者-控制器 块，即有损联合源信道编码（JSCC）方案，在提供相关数学表达式后，我们提出了一个 布拉胡特-有本-类型算法 $-$据我们所知，这是第一次。该算法有效地找到了所需的概率质量函数 (PMF)$ \mathop {{\rm min}} _{\mathscr {P}(i), i \in \lbrace \mathscr {Y}, \hat{\mathscr {S}}, \mathscr {X},{\ mathscr {S}},\hat{\mathscr {X}}\rbrace } {\rm \; } \phi _1 \mathscr {I}(\mathscr {Y};\hat{\mathscr {S}}|\mathscr {X,S})-\phi _2 \mathscr {I}(\mathscr {Y}; \hat{\mathscr {X}}|\mathscr {X,S})$. 这个问题是一个$NP-$硬和非凸多目标优化（MOO）之一，目标函数分别是失真函数 $dim (Null (\mathscr {I}(\hat{\mathscr {S}};{\mathscr {S}})) \rightarrow \infty$ 和无记忆信道容量 $dim (Null (\mathscr {I}(\mathscr {X};\hat{\mathscr {X}})) \rightarrow 0$. 我们的新算法应用了一个交替优化方法。随后，关于扰动的 PMF 讨论了算法的鲁棒版本$-$参数不确定性一般。上述鲁棒性是通过利用同时扰动随机近似(SPSA)。的原则可探测性和稳定性除了提供模拟之外，还探索了同步性 - 通过模拟显示了我们的工作效率。我们还分别计算了我们提出的算法的总复杂度为$\mathscr {O} (\mathscr {T}\mathscr {K}\mathscr {M}_0(\mathscr {K} \log \mathscr {K}))$ 和 $\mathscr {O} (\mathscr {T}\mathscr {K}\mathscr {M}_0(\mathscr {K} \log \mathscr {K}+0.33 \mathscr {K}))$. 我们的方法是通用的，可以应用于其他优化驱动的研究领域。