In this paper, we put forward the model of zero-error distributed function compression system of two binary memoryless sources X and Y, where there are two encoders En1 and En2 and one decoder De, connected by two channels (En1, De) and (En2, De) with the capacity constraints C1 and C2, respectively. The encoder En1 can observe X or (X,Y) and the encoder En2 can observe Y or (X,Y) according to the two switches s1 and s2 open or closed (corresponding to taking values 0 or 1). The decoder De is required to compress the binary arithmetic sum f(X,Y)=X+Y with zero error by using the system multiple times. We use (s1s2;C1,C2;f) to denote the model in which it is assumed that C1 \geq C2 by symmetry. The compression capacity for the model is defined as the maximum average number of times that the function f can be compressed with zero error for one use of the system, which measures the efficiency of using the system. We fully characterize the compression capacities for all the four cases of the model (s1s2;C1,C2;f) for s1s2= 00,01,10,11. Here, the characterization of the compression capacity for the case (01;C1,C2;f) with C1>C2 is highly nontrivial, where a novel graph coloring approach is developed. Furthermore, we apply the compression capacity for (01;C1,C2;f) to an open problem in network function computation that whether the best known upper bound of Guang et al. on computing capacity is in general tight.

翻译：本文提出了一种二元无记忆信源X和Y的无错分布式函数压缩系统模型，该系统包含两个编码器En1和En2以及一个解码器De，分别通过容量受限信道(En1, De)和(En2, De)连接，信道容量分别为C1和C2。根据两个开关s1和s2的断开或闭合（对应取值为0或1），编码器En1可观测X或(X,Y)，编码器En2可观测Y或(X,Y)。解码器De需多次使用系统，以无错方式压缩二元算术和函数f(X,Y)=X+Y。我们用(s1s2;C1,C2;f)表示该模型，并基于对称性假设C1 ≥ C2。该模型的压缩容量定义为系统单次使用时可无错压缩函数f的最大平均次数，用于度量系统使用效率。我们完整刻画了模型(s1s2;C1,C2;f)在所有四种情况（s1s2=00,01,10,11）下的压缩容量。其中，当C1>C2时情况(01;C1,C2;f)的压缩容量表征高度非平凡，为此我们提出了一种新颖的图着色方法。此外，我们将(01;C1,C2;f)的压缩容量应用于网络函数计算中的一个开放问题——Guang等人关于计算容量的最优已知上界是否普遍紧致。