Unified approach for computing sum of sources over CQ-MAC

TL;DR

This paper introduces a new coding scheme for transmitting a bivariate function of two sources over a CQ-MAC, expanding the set of sources that can be reliably communicated by leveraging algebraic and unstructured codes.

Contribution

It develops a fusion of algebraic and unstructured coding techniques and derives new quantum information-theoretic conditions that improve upon existing communication limits.

Findings

New sufficient conditions for source communication over CQ-MAC

Enlarged set of sources capable of reliable transmission

Conditions expressed via single-letter quantum information quantities

Abstract

We consider the task of communicating a generic bivariate function of two classical 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. Inspired by the techniques developed for the analogous classical setting, and employing the technique of simultaneous (joint) decoding developed for the classical-quantum setting, we propose and analyze a coding scheme based on a fusion of algebraic structured and unstructured codes. This coding scheme allows exploiting both the symmetric structure common amongst the sources and the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.