Improved Capacity Upper Bounds for the Deletion Channel using a Parallelized Blahut-Arimoto Algorithm

TL;DR

This paper introduces a GPU-accelerated version of the Blahut-Arimoto algorithm to compute tighter upper bounds on the capacity of the binary deletion channel, especially for high deletion probabilities.

Contribution

The authors develop a parallelized implementation of the Blahut-Arimoto algorithm that improves capacity bounds for the binary deletion channel.

Findings

Capacity of the deletion channel is at most 0.3578(1-d) for d ≥ 0.64.

GPU parallelization significantly speeds up the computation.

New upper bounds are tighter than previous estimates.

Abstract

We present an optimized implementation of the Blahut-Arimoto algorithm via GPU parallelization, which we use to obtain improved upper bounds on the capacity of the binary deletion channel. In particular, our results imply that the capacity of the binary deletion channel with deletion probability $d$ is at most $0.3578(1-d)$ for all $d\geq 0.64$.