Distributed Linearly Separable Computation

This paper formulates a distributed computation problem, where master asks ${\mathsf N}$ workers to compute linearly separable function. The task function can be expressed as K}_{\mathrm{ c}}$ linear combinations of K}$ messages, each message is one dataset. Our objective find the optimal tradeoff between cost (number uncoded datasets assigned worker) and communication symbols must download), such that from answers any N}_{\mathrm{ r}}$ out recover with high probability, coefficients are uniformly i.i.d. over some large enough finite field. formulated problem seen generalized version existing problems, gradient coding transform. In this paper, we consider specific case minimum, propose novel achievability schemes converse bounds for cost. Achievability coincide system parameters; when they do not match, prove achievable computing scheme under constraint widely used ‘cyclic assignment’ on datasets. results also show K}= {\mathsf , same proposed by Tandon et al. which recovers combination our let additional r}}-1$ independent messages probability.