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We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ- MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information- theoretic quantities. 

In this paper we consider the information-theoretic characterization of performance limits of a broad class of multiterminal communication problems with general continuousvalued sources and channels. In particular, we consider point-topoint source coding and channel coding with side information, distributed source coding with distortion constraints and function reconstruction problems (two-help-one). We develop an approach that uses fine quantization of the source and the channel variables followed by random coding with unstructured as well as structured (linear) code ensembles. This approach leads to lattice-like codes for general sources and channels.