[Paper Review] On Channel Output Feedback in Deterministic Interference Channels

Achaleshwar Sahai, Vaneet Aggarwal+2 more|ArXiv.org|May 14, 2009

Wireless Communication Security Techniques11 references3 citations

TL;DR

This paper investigates the impact of channel output feedback on sum capacity in symmetric deterministic interference channels. It demonstrates that a single feedback link from one receiver to its transmitter achieves the same sum capacity as four feedback links, and that half-duplex feedback with symmetric time-sharing does not improve sum capacity in strong interference regimes, challenging assumptions about feedback gains in practical systems.

ABSTRACT

In this paper, we study the effect of channel output feedback on the sum capacity in a two-user symmetric deterministic interference channel. We find that having a single feedback link from one of the receivers to its own transmitter results in the same sum capacity as having a total of 4 feedback links from both the receivers to both the transmitters. Hence, from the sum capacity point of view, the three additional feedback links are not helpful. We also consider a half-duplex feedback model where the forward and the feedback resources are symmetric and timeshared. Surprisingly, we find that there is no gain in sum-capacity with feedback in a half-duplex feedback model when interference links have more capacity than direct links.

Motivation & Objective

• To analyze the effect of channel output feedback on sum capacity in symmetric deterministic interference channels.
• To evaluate whether additional feedback links beyond one provide capacity gains in symmetric interference channels.
• To investigate the performance of a half-duplex feedback model where forward and feedback channels share time resources equally.
• To determine whether feedback can enhance sum capacity in strong interference regimes under practical time-division constraints.
• To compare the sum capacity gains across one, four, and half-duplex feedback models in symmetric deterministic interference channels.

Proposed method

• The authors model a two-user symmetric deterministic interference channel with direct link capacity $ n $ and cross-link capacity $ m $, using bit-level signal models with shift matrices and XOR operations.
• For one-sided feedback, the transmitter uses past received signals to decode and re-encode interference-affected bits, enabling cooperation that doubles the rate of the non-feedback user.
• In the four-feedback-link model, both transmitters receive feedback from both receivers, but the sum capacity remains unchanged compared to one feedback link due to rate-sharing trade-offs.
• A half-duplex feedback model is introduced where forward and feedback transmissions share time resources equally, with identical link capacities, modeling practical TDD systems.
• The sum capacity is derived using asymptotic analysis over $ T $ time slots, with feedback occurring in $ T-1 $ slots, and the achievable rate is bounded using limits as $ T \to \infty $.
• The analysis uses $ l_{\text{max}} = \max(n-m, m) $ and $ l_{\text{min}} = \min(n-m, m) $ to characterize decodable bit levels and derive rate expressions.

Experimental results

Research questions

• RQ1 Does a single feedback link from one receiver to its transmitter achieve the same sum capacity as multiple feedback links in a symmetric deterministic interference channel?
• RQ2 Can additional feedback links (beyond one) improve sum capacity in a deterministic interference channel with full feedback from both receivers?
• RQ3 Does feedback provide a sum capacity gain in a half-duplex feedback model where forward and feedback channels are time-shared symmetrically?
• RQ4 How does the sum capacity scale in the presence of strong interference (i.e., $ m \gg n $) under half-duplex feedback constraints?
• RQ5 What is the fundamental limit of sum capacity when feedback is constrained by time-sharing and equal-capacity feedback links?

Key findings

• A single feedback link from one receiver to its transmitter achieves the same sum capacity as four feedback links, indicating that additional feedback links do not improve sum capacity.
• The sum capacity under one feedback link is $ 2n - m $, which matches the upper bound derived for the symmetric feedback model, confirming optimality.
• In the half-duplex feedback model with symmetric time-sharing and equal-capacity forward and feedback links, feedback does not increase sum capacity in the strong interference regime ($ m/n \geq 2 $).
• For $ m/n \leq 2/3 $, the achievable sum rate approaches $ 2n - m $, matching the upper bound, showing that one feedback link is sufficient to achieve the optimal sum capacity.
• When $ m/n \geq 2 $, the sum capacity is $ m $, achieved by routing $ m-n $ bits via the interference path, demonstrating that feedback can exploit interference links for rate gain only under specific conditions.
• The result implies that in practical half-duplex systems with symmetric feedback, interference links with higher capacity do not enhance sum capacity due to resource sharing bottlenecks.