Latency Analysis of Coded Computation Schemes over Wireless Networks

Large-scale distributed computing systems face two major bottlenecks that limit their scalability: straggler delay caused by the variability of computation times at different worker nodes and communication bottlenecks caused by shuffling data across many nodes in the network. Recently, it has been shown that codes can provide significant gains in overcoming these bottlenecks. In particular, optimal coding schemes for minimizing latency in distributed computation of linear functions and mitigating the effect of stragglers was proposed for a wired network, where the workers can simultaneously transmit messages to a master node without interference. In this paper, we focus on the problem of coded computation over a wireless master-worker setup with straggling workers, where only one worker can transmit the result of its local computation back to the master at a time. We consider 3 asymptotic regimes (determined by how the communication and computation times are scaled with the number of workers) and precisely characterize the total run-time of the distributed algorithm and optimum coding strategy in each regime. In particular, for the regime of practical interest where the computation and communication times of the distributed computing algorithm are comparable, we show that the total run-time approaches a simple lower bound that decouples computation and communication, and demonstrate that coded schemes are $\Theta(\log(n))$ times faster than uncoded schemes

Bounding the Optimal Length of Pliable Index Coding via a Hypergraph-based Approach

In pliable index coding (PICOD), a number of clients are connected via a noise-free broadcast channel to a server which has a list of messages. Each client has a unique subset of messages at the server as side-information and requests for any one message not in the side-information. A PICOD scheme of length $\ell$ is a set of $\ell$ encoded transmissions broadcast from the server such that all clients are satisfied. Finding the optimal (minimum) length of PICOD and designing PICOD schemes that have small length are the fundamental questions in PICOD. In this paper, we use a hypergraph-based approach to derive new achievability and converse results for PICOD. We present an algorithm which gives an achievable scheme for PICOD with length at most $\Delta(\mathcal{H})$, where $\Delta(\mathcal{H})$ is the maximum degree of any vertex in a hypergraph that represents the PICOD problem. We also give a lower bound for the optimal PICOD length using a new structural parameter associated with the PICOD hypergraph called the nesting number. We extend some of our results to the PICOD problem where each client demands $t$ messages, rather than just one. Finally, we identify a class of problems for which our converse is tight, and also characterize the optimal PICOD lengths of problems with $\Delta(\mathcal{H})\in\{1,2,3\}$.Comment: Accepted at the IEEE Information Theory Workshop, 202