具有因果观测的混合多址信道的容量

中文摘要 AI 辅助

我们确定了混合二进制多址信道的容量区域，该信道的接收器可以选择每个观测的形成方式。两个端口以保留概率 $\pg>\pb$ 揭示传输符号的模二和；它们的角色由一个在块期间保持固定的未知状态互换。每个信道使用一次观测，无发射机反馈，且切换成本为零，对于低于1的每个固定错误阈值，该区域为 $R_1+R_2\le\pg$，并且强逆成立。对于低于二分之一的错误阈值，最大的开环和速率为 $(\pg+\pb)/2$，而固定端口仅允许 $\pb$。因果接收器通过从擦除标志中学习状态，同时利用每个信道使用进行数据传输，从而获得更大的区域。后验端口规则几乎必然只产生有限次错误选择，且预期错误次数一致有界。精确的随机线性码公式和输出计数逆界量化了有限块的影响。在块长256且 $(\pg,\pb)=(0.9,0.4)$ 的情况下，独立的数值验证支持在百分之一集合失败目标下达到214个消息比特，而同一码集合中最佳开环分配为148比特。由此产生的44.59%的增益是在相同的传输和观测预算下实现的。该分析展示了通过控制观测轴获得的显式容量增益，并将该增益与记录形成后丢失的信息分离开来。

英文摘要

We determine the capacity region of a mixed binary multiple-access channel whose receiver can choose how each observation is formed. Two ports reveal the sum modulo two of the transmitted symbols with retention probabilities $\pg>\pb$; their roles are interchanged by an unknown state that remains fixed during the block. With one observation per channel use, no transmitter feedback, and zero switching cost, the region is $R_1+R_2\le\pg$ for every fixed error threshold below one, and a strong converse holds. For error thresholds below one half, the largest open-loop sum rate is $(\pg+\pb)/2$, whereas a fixed port permits only $\pb$. A causal receiver attains the larger region by learning the state from erasure flags while using every channel use for data. A posterior port rule makes only finitely many incorrect selections almost surely, with a uniformly bounded expected number of mistakes. Exact random linear-code formulas and output-counting converses quantify the finite-block consequences. At blocklength 256 with $(\pg,\pb)=(0.9,0.4)$, independent numerical validation supports 214 message bits at a one-percent ensemble failure target, compared with 148 bits for the best open-loop allocation in the same code ensemble. The resulting 44.59\% increase is achieved with the same transmission and observation budgets. The analysis exhibits an explicit capacity gain from controlling the observation axis and separates that gain from information lost after a record has already been formed.

发表机构

• Hefei University of Technology（合肥工业大学）

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