PDL Abstract

Rateless Sum-Recovery Codes For Distributed Non-Linear Computations

Information Theory Workshop (ITW), November 6-9, 2022. Mumbai, India.

Ankur Mallick,Gauri Joshi

Carnegie Mellon University

We address the problem of slowdown caused by straggling nodes in distributed non-linear computations. Many common non-linear computations can be written as a sum of inexpensive non-linear functions (for e.g. Taylor series). Based on this observation, we propose a new class of rateless codes called rateless sum-recovery codes whose aim is to recover the sum of source symbols, without necessarily recovering individual symbols. Source symbols correspond to individual inexpensive functions and each encoded symbol is the sum of a subset of source symbols. Encoded symbols are computed in a distributed fashion and for a computation that can be written as a sum of m inexpensive functions, successful sum-recovery is possible with high probability as long as slightly more than m encoded symbols are received. Our code is rateless, systematic and has sparse parities. Moreover, encoded symbols are constructed by sampling without replacement at individual nodes, thereby making decoding superfluous if the encoded symbols from any node cover all source symbols. We validate our claims through a range of simulations and also discuss open questions for future works.