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Switched Feedback for the Multiple-Access Channel

Oliver Kosut, Michael Langberg, Michelle Effros

TL;DR

This work studies a two-user MAC with switched feedback, where at each time slot the channel output is either observed by the transmitters (feedback) or by the receiver (feedforward), modeled via a time-varying function $p(t)$. It derives simple inner and outer bounds on the capacity region, and identifies a channel class with tight bounds under a constant $p$ by showing rate limits of the form $R_1 \le \min\{H(X_1|X_2),\; p I(X_1,X_2;Y)\}$ and $R_2 \le \min\{H(X_2|X_1),\; p I(X_1,X_2;Y)\}$. For known switching patterns, the sum-capacity is characterized by a variational integral involving the two-way channel capacity and mutual information terms, and in the deterministic case with $p(t)\in\{0,1\}$ the switched-feedback region collapses to the known-switching-pattern region $\mathcal{C}_{\text{KSP}}$, with an optimal strategy that front-loads feedback. Overall, the results quantify the trade-off between cooperation via feedback and direct forward transmission, providing guidance for networks with intermittent or half-duplex feedback and highlighting connections to two-way channels and conferencing MACs.

Abstract

A mechanism called switched feedback is introduced; under switched feedback, each channel output goes forward to the receiver(s) or back to the transmitter(s) but never both. By studying the capacity of the Multiple-Access Channel (MAC) with switched feedback, this work investigates the benefits of feedback, seeking to maximize that benefit under reliable and unreliable feedback scenarios. The study is used to explore the tradeoffs between cooperation and transmission in the context of communication systems. Results include upper and lower bounds on the capacity region of the MAC with switched feedback.

Switched Feedback for the Multiple-Access Channel

TL;DR

This work studies a two-user MAC with switched feedback, where at each time slot the channel output is either observed by the transmitters (feedback) or by the receiver (feedforward), modeled via a time-varying function . It derives simple inner and outer bounds on the capacity region, and identifies a channel class with tight bounds under a constant by showing rate limits of the form and . For known switching patterns, the sum-capacity is characterized by a variational integral involving the two-way channel capacity and mutual information terms, and in the deterministic case with the switched-feedback region collapses to the known-switching-pattern region , with an optimal strategy that front-loads feedback. Overall, the results quantify the trade-off between cooperation via feedback and direct forward transmission, providing guidance for networks with intermittent or half-duplex feedback and highlighting connections to two-way channels and conferencing MACs.

Abstract

A mechanism called switched feedback is introduced; under switched feedback, each channel output goes forward to the receiver(s) or back to the transmitter(s) but never both. By studying the capacity of the Multiple-Access Channel (MAC) with switched feedback, this work investigates the benefits of feedback, seeking to maximize that benefit under reliable and unreliable feedback scenarios. The study is used to explore the tradeoffs between cooperation and transmission in the context of communication systems. Results include upper and lower bounds on the capacity region of the MAC with switched feedback.
Paper Structure (10 sections, 8 theorems, 70 equations, 1 figure)

This paper contains 10 sections, 8 theorems, 70 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Simple Bounds
  4. The Capacity Region of a Class of Channels
  5. Known Switching Pattern
  6. Deterministic switching pattern
  7. Conclusions
  8. Probability of Error Analysis for the Proof of Theorem \ref{['thm:gen_adder']}
  9. Proof of Lemma \ref{['lemma:achievability']}
  10. Proof of Lemma \ref{['lemma:converse']}

Key Result

Proposition 1

For any $(R_1,R_2)\in\mathcal{C}$,

Figures (1)

  • Figure 1: The switched feedback model for the multiple-access channel. In this example, the feedforward probability $p$ is fixed over time.

Theorems & Definitions (10)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Example 1
  • Example 2
  • Theorem 2
  • Lemma 1
  • Lemma 2
  • Proposition 3
  • Corollary 1