Collaborative Decoding of Polynomial Codes for Distributed Computation

Abstract: We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes return erroneous values. For an additive random Gaussian error model, we show that for all $t < N-K$, errors can be corrected with probability 1. Further, numerical results show that in the presence of additive errors, when $L$ Reed-Solomon codes are collaboratively decoded, the numerical stability in recovering the error locator polynomial improves with increasing $L$.