  Large-scale machine learning and data mining methods routinely distribute
computations across multiple agents to parallelize processing. The time
required for the computations at the agents is affected by the availability of
local resources giving rise to the "straggler problem". As a remedy to this
problem, linear coding of the matrix sub-blocks can be used, i.e., the
Parameter Server (PS) utilizes a channel code to encode the matrix sub-blocks
and distributes these matrices to the workers for multiplication. In this
paper, we employ Unequal Error Protection (UEP) codes to obtain an
approximation of the matrix product in the distributed computation setting in
the presence of stragglers. The resiliency level of each sub-block is chosen
according to its norm, as blocks with larger norms have higher effects on the
result of the matrix multiplication. In particular, we consider two approaches
in distributing the matrix computation: (i) a row-times-column paradigm, and
(ii) a column-times-row paradigm. For both paradigms, we characterize the
performance of the proposed approach from a theoretical perspective by bounding
the expected reconstruction error for matrices with uncorrelated entries. We
also apply the proposed coding strategy to the computation of the
back-propagation step in the training of a Deep Neural Network (DNN) for an
image classification task in the evaluation of the gradient during
back-propagation. Our numerical experiments show that it is indeed possible to
obtain significant improvements in the overall time required to achieve the DNN
training convergence by producing matrix product approximations using UEP
codes.
