Cross Subspace Alignment Codes for Coded Distributed Batch Computation

The goal of coded distributed computation is to efficiently distribute a task, such as matrix multiplication, N-linear computation, or multivariate polynomial evaluation, across S servers through coding scheme, that the response from any R ( called recovery threshold) sufficient for user recover desired computed value. Current state-of-art approaches are based on either exclusively matrix-partitioning (Entangled Polynomial (EP) Codes multiplication), batch processing (Lagrange Coded Computing (LCC) computations evaluations). We present three related classes codes, idea Cross-Subspace Alignment (CSA) which was introduced originally in context secure and private information retrieval. CSA codes characterized by Cauchy-Vandermonde structure facilitates interference alignment along Vandermonde terms, while remain resolvable Cauchy terms. These shown unify, generalize improve upon computing. First we introduce yield LCC special case, outperform general download-limited settings. While (EP codes) multiplication have advantage flexible server latency, (CSA, LCC) significant advantages communication costs well encoding decoding complexity per multiplication. In order combine benefits these approaches, Generalized (GCSA) bridge extremes demonstrate synergistic gains due cross subspace alignment. Finally, N-CSA evaluations. include capable outperforming download-constrained settings upto factor N. Generalizations X-secure data B-byzantine also provided.