We consider the problem of shared randomness-assisted multiple access channel (MAC) simulation for product inputs and characterize the one-shot communication cost region via almost-matching inner and outer bounds in terms of the smooth max-information of the channel, featuring auxiliary random variables of bounded size. The achievability relies on a rejection-sampling algorithm to simulate an auxiliary channel between each sender and the decoder, and producing the final output based on the output of these intermediate channels. The converse follows via information-spectrum based arguments. To bound the cardinality of the auxiliary random variables, we employ the perturbation method from [Anantharam et al., IEEE Trans. Inf. Theory (2019)] in the one-shot setting. For the asymptotic setting and vanishing errors, our result expands to a tight single-letter rate characterization and consequently extends a special case of the simulation results of [Kurri et al., IEEE Trans. Inf. Theory (2022)] for fixed, independent and identically distributed (iid) product inputs to universal simulation for any product inputs. We broaden our discussion into the quantum realm by studying feedback simulation of quantum-to-classical (QC) MACs with product measurements [Atif et al., IEEE Trans. Inf. Theory (2022)]. For fixed product inputs and with shared randomness assistance, we give a quasi tight one-shot communication cost region with corresponding single-letter asymptotic iid expansion.

翻译：我们考虑共享随机性辅助的多址信道（MAC）模拟问题，针对乘积输入，通过基于信道平滑最大信息量（包含有界尺寸的辅助随机变量）的几乎匹配的内界和外界，刻画了一次性通信代价区域。可达性依赖于拒绝采样算法来模拟每个发送端与解码端之间的辅助信道，并基于这些中间信道的输出生成最终输出。逆推部分采用基于信息谱的论证。为约束辅助随机变量的基数，我们在一次性设定中运用了[Anantharam等人，《IEEE信息论汇刊》，2019年]中的摄动方法。针对渐近设定与可忽略误差，我们的结果扩展为紧凑的单字母速率刻画，从而将[Kurri等人，《IEEE信息论汇刊》，2022年]中针对固定独立同分布（iid）乘积输入的模拟结果特例推广至任意乘积输入的普适模拟。我们将讨论扩展到量子领域，通过研究符合乘积测量[Atif等人，《IEEE信息论汇刊》，2022年]的量子到经典（QC）多址信道的反馈模拟。对于固定乘积输入并借助共享随机性辅助，我们给出拟紧的一次性通信代价区域，并配套对应单字母渐近iid扩展。