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In this paper, we put forward the model of zero-error distributed functioncompression system of two binary memoryless sources X and Y, where there aretwo 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. Theencoder 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 takingvalues 0 or 1). The decoder De is required to compress the binary arithmeticsum 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 bysymmetry. The compression capacity for the model is defined as the maximumaverage number of times that the function f can be compressed with zero errorfor 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 themodel (s1s2;C1,C2;f) for s1s2= 00,01,10,11. Here, the characterization of thecompression 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 thecompression capacity for (01;C1,C2;f) to an open problem in network functioncomputation that whether the best known upper bound of Guang et al. oncomputing capacity is in general tight.

Zero-Error Distributed Function Compression for Binary Arithmetic Sum