Title: Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers,
Abstract: We propose two coded schemes for the distributed computing problem of
multiplying a matrix by a set of vectors. The first scheme is based on
partitioning the matrix into submatrices and applying maximum distance
separable (MDS) codes to each submatrix. For this scheme, we prove that up to a
given number of partitions the communication load and the computational delay
(not including the encoding and decoding delay) are identical to those of the
scheme recently proposed by Li et al., based on a single, long MDS code.
However, due to the use of shorter MDS codes, our scheme yields a significantly
lower overall computational delay when the delay incurred by encoding and
decoding is also considered. We further propose a second coded scheme based on
Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes
may reduce the delay over the partitioned scheme at the expense of an increased
communication load. We also consider distributed computing under a deadline and
show numerically that the proposed schemes outperform other schemes in the
literature, with the LT code-based scheme yielding the best performance for the
scenarios considered.