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

2026-04-07

AI Summary

This study addresses the challenge of accurately estimating tight upper bounds on the capacity of the binary erasure channel. To accelerate the computation of these bounds, the work introduces GPU parallelization into the Blahut–Arimoto algorithm for the first time, achieving a significant speedup through an efficient implementation. Leveraging this computational advance, the authors derive a tighter upper bound: for erasure probabilities \( d \geq 0.64 \), the channel capacity is at most \( 0.3578(1 - d) \). By integrating information-theoretic analysis with high-performance computing, this research achieves notable improvements in both computational efficiency and theoretical precision.

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 $d\geq 0.64$.

Problem

• deletion channel
• channel capacity
• upper bounds
• binary deletion channel
• information theory

Innovation

• GPU parallelization
• Blahut-Arimoto algorithm
• deletion channel
• capacity upper bound
• binary deletion channel