具有因果观测的二元干扰信道的无干扰容量

中文摘要 AI 辅助

我们确定了具有接收端控制观测的两用户二元干扰信道的容量区域，并证明因果端口选择可以达到无干扰极限。物理-观测双轴表述将观测核作为受显式因果和资源约束的设计变量。对于两个等概率、初始未知的块状态，匹配的逆命题和编码构造给出了固定端口、开环和因果策略下每信道使用分别为1、$4/3$和2比特的精确和容量。这些结果在平均和最大消息错误下，对于低于$1/2$的每个固定联合错误阈值均成立，其中错误在块状态上取平均。每个接收端每时隙进行一次观测，并且最多切换一次端口；发射端不接收反馈，接收端不合作。因此，因果观测使最优固定端口和容量翻倍，并超过最优开环和容量50%。对于保留概率为$p$的独立擦除，精确因果区域为$[0,p]^2$。一个有限块长界联合考虑了状态识别导频和编码冗余。我们还针对固定码优化观测策略：一个精确的有限时域解将消息错误从10.76%降低到7.52%，一个二阶近似界控制了对连续观测方向的优化。线性阵列设计和编码实验考察了相应的训练、可靠性和控制成本。容量结果确定了一种观测设计消除整个干扰惩罚的设置，其增益通过逆命题和可达构造得以确立。

英文摘要

We determine the capacity region of a two-user binary interference channel with receiver-controlled observation and prove that causal port selection attains the interference-free limit. The physical--observation dual-axis formulation makes the observation kernel a design variable subject to explicit causal and resource constraints. For two equiprobable, initially unknown block states, matching converses and coding constructions give exact sum capacities of 1, $4/3$, and 2 bits per channel use for fixed-port, open-loop, and causal policies, respectively. These results hold for every fixed joint error threshold below $1/2$, under both average and maximal message error, with error averaged over the block state. Every receiver makes one observation per slot and switches ports at most once; the transmitters receive no feedback and the receivers do not cooperate. Causal observation thus doubles the optimal fixed-port sum capacity and exceeds the optimal open-loop sum capacity by 50\%. With independent erasures of retention probability $p$, the exact causal region is $[0,p]^2$. A finite-blocklength bound accounts jointly for state-identification pilots and coding redundancy. We also optimize observation policies for fixed codes: an exact finite-horizon solution reduces message error from 10.76\% to 7.52\%, and a second-order approximation bound controls optimization over continuous observation directions. Linear-array designs and coding experiments examine the corresponding training, reliability, and control costs. The capacity result identifies a setting in which observation design removes the entire interference penalty, with the gain established by a converse as well as an achievable construction.

发表机构

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

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