Encoding (memory)

Mathematical analysis

Programming language

Combinatorics

Physics

Computer science

Diagonal

Quantum mechanics

Mathematics

Block (permutation group theory)

Decoding methods

Block matrix

Algorithm

Separable space

Scheme (mathematics)

Theoretical computer science

Artificial intelligence

Block code

Eigenvalues and eigenvectors

Set (abstract data type)

Geometry

Code (set theory)

IEEE Transactions on Communications

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 propo...

Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers