An Improved Upper Bound on the Capacity of the Primitive Diamond Relay Channel

2026-10-08

AI Summary

This study addresses the looseness of existing capacity upper bounds for the diamond relay channel, which hinders precise characterization of its fundamental limits. By leveraging the Csiszár–Körner–Marton identity and Gallager-type identification techniques, this work derives a tighter capacity upper bound. To evaluate the improvement, an inner bound is constructed via a time-sharing strategy combining decode-and-forward and compress-and-forward relaying. The proposed upper bound strictly improves upon the cut-set bound and existing results for discrete memoryless channels, while coinciding with the strongest known upper bound in Gaussian settings. By quantifying the resulting performance gains, this research establishes a new theoretical benchmark for the capacity analysis of diamond relay channels.

Abstract

We study the capacity of the primitive diamond relay channel and derive an improved upper bound compared with existing upper bounds by employing the Csiszár--Körner--Marton sum identity and Gallager-type identification. For Gaussian primitive diamond relay channels, we show that our proposed bound coincides with the existing strengthened Gaussian upper bound of Wu, Özgür, Peleg, and Shamai. For discrete memoryless channels, our bound can be strictly tighter than both the cut-set bound and the existing upper bound, and we assess the improvement using different channel instances, together with a decode--forward/compress--forward time-sharing inner bound.

Problem

• primitive diamond relay channel
• channel capacity
• upper bound
• Gaussian channels
• discrete memoryless channels

Innovation

• Primitive Diamond Relay Channel
• Channel Capacity Upper Bound
• Csiszár-Körner-Marton Sum Identity
• Gallager-type Identification
• Discrete Memoryless Channels