Multi-Device Task-Oriented Communication via Maximal Coding Rate Reduction

In task-oriented communications, most existing work designed the physical-layer communication modules and learning based codecs with distinct objectives: learning is targeted at accurate execution of specific tasks, while communication aims at optimizing conventional communication metrics, such as throughput maximization, delay minimization, or bit error rate minimization. The inconsistency between the design objectives may hinder the exploitation of the full benefits of task-oriented communications. In this paper, we consider a task-oriented multi-device edge inference system over a multiple-input multiple-output (MIMO) multiple-access channel, where the learning (i.e., feature encoding and classification) and communication (i.e., precoding) modules are designed with the same goal of inference accuracy maximization. Instead of end-to-end learning which involves both the task dataset and wireless channel during training, we advocate a separate design of learning and communication to achieve the consistent goal. Specifically, we leverage the maximal coding rate reduction (MCR2) objective as a surrogate to represent the inference accuracy, which allows us to explicitly formulate the precoding optimization problem. We cast valuable insights into this formulation and develop a block coordinate descent (BCD) algorithm for efficient problem-solving. Moreover, the MCR2 objective also serves the loss function for feature encoding and guides the classification design. Simulation results on synthetic features explain the mechanism of MCR2 precoding at different SNRs. We also validate on the CIFAR-10 and ModelNet10 datasets that the proposed design achieves a better latency-accuracy tradeoff compared to various baselines. As such, our work paves the way for further exploration into the synergistic alignment of learning and communication objectives in task-oriented communication systems.