发表机构
Tsinghua University; Princeton University（清华大学; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用二分图唯一刻画确定性广播信道，给出显式闭式容量区域及确定性容量可达编码方案，并支持通过二元线性规划构造最优有限块长编码。
AI 中文摘要
一般广播信道（BC）因作为网络或多用户信息论中的核心问题而备受关注。确定性广播信道（det-BC）中，两个输出符号均为输入符号的函数，它在理解一般广播信道方面起着至关重要的作用。20世纪70年代，Marton和Pinsker分别采用随机编码方法研究了det-BC，并将其容量区域量化为输出符号熵的函数。本文提出了一种纯确定性和组合性的方法处理确定性广播信道，这与Marton和Pinsker的概率性方法形成对比。特别地，我们证明每个det-BC都可以由二分图唯一且完整地表征。基于二分图模型，我们给出了一般det-BC的显式容量区域和一种确定性的容量可达编码方案。具体而言，容量区域边界上的每个点都表示为两部分度序列的显式函数，边界坐标由切线斜率参数化。因此，一个闭式容量区域（此前除Blackwell信道等特殊情况外未知）可以解析确定，无需数值优化输入符号的概率分布。对于由多个孤立子图组成的二分图，在保持最大可达和速率的同时，可能存在一个可共同解码的消息，其可达速率被显式刻画。最后，二分图表述使我们能够通过二元线性规划为det-BC构造最优的有限块长编码。
英文摘要
The general broadcast channel (BC) has attracted considerable attention because it is a central problem in network or multi-user information theory. The deterministic BC (det-BC), in which both output symbols are functions of the input symbol, plays a vital role in understanding general BCs. In the 1970s, Marton and Pinsker investigated the det-BC independently using a random coding approach and hence quantified its capacity region as functions of the entropy of output symbols. In this paper, we present a purely deterministic and combinatorial treatment of the deterministic BC, which is in contrast to Marton and Pinsker's probabilistic treatment. In particular, we show that each det-BC can be uniquely and completely characterized by a bipartite graph. Based on the bipartite graph model, we present the explicit capacity region of the general det-BC and a deterministic capacity-achieving coding scheme. Specifically, each point on the capacity region boundary is expressed as an explicit function of the degree sequences of the two parts, with boundary coordinates parametrized by the tangent slope. As a result, a closed-form capacity region, which was previously unknown except for special cases such as the Blackwell channel, can be analytically determined, without optimizing the probability distribution of input symbols numerically. For a bipartite graph consisting of multiple isolated subgraphs, there can exist a commonly decodable message while preserving the maximum achievable sum rate, and its achievable rate is explicitly characterized. Finally, the bipartite-graph formulation allows us to construct optimal finite-blocklength coding for the det-BC through binary linear programming.
