Factored LT and Factored Raptor Codes for Large-Scale Distributed Matrix Multiplication

We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These are adaptations Luby Transform (LT) codes and Raptor to termed Factored LT (FLT) codes (FRT) . show that all nodes Tanner graph a randomly sampled code have tree-like neighborhood with high probability. This ensures density evolution analysis gives reasonable estimate average recovery threshold FLT codes. The proposed is asymptotically optimal when output degree distribution Soliton. Empirically, we FRT an excellent while number worker moderately large. In addition, using Azuma–Hoeffding inequality, derive concentration results chosen close ensemble average. better thresholds compared Product they expected numerical stability Polynomial codes, can also be decoded low-complexity decoding algorithm. Finally, matched practically important case sparse matrix-matrix as many previous schemes.