Collaborative Decoding of Polynomial Codes for Distributed Computation
2019 IEEE INFORMATION THEORY WORKSHOP (ITW)(2019)
摘要
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 $L$.
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关键词
collaborative decoding,Polynomial codes,distributed matrix multiplication,Generalized Reed-Solomon codes,fault-tolerant setup,additive random Gaussian error model,decoding complexity
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