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Joint Communication and Channel Discrimination

Han Wu, Hamdi Joudeh

TL;DR

This work analyzes joint communication and channel discrimination (JCAS) for discrete memoryless channels with a binary sensing state and a per-letter input cost. The key result is a complete characterization of the rate-exponent region: there exists an input distribution $P_X$ with cost $\mathbb{E}[b(X)]\le B$ and a tilt parameter $s\in[0,1]$ such that the communication rate and the two channel-discrimination exponents satisfy $R \le I(P_X,P_{Y|X})$, $E_0 \le D(P_s\|P_0|P_X)$, and $E_1 \le D(P_s\|P_1|P_X)$, where $P_s(z|x)$ is the tilted channel between $P_0$ and $P_1$. Achievability is shown using almost constant-composition codes and a constrained channel coding argument, while the converse employs constant-composition subcodes to handle the non-convex input-set constraint. The paper also derives minimax and Neyman-Pearson special cases, linking the rate-exponent region to Chernoff-type and KL-divergence bounds, respectively. The results illuminate the fundamental trade-offs between reliable communication and sensing accuracy in JCAC, and provide a framework for extending to general alphabets and more complex sensing tasks.

Abstract

We consider a basic joint communication and sensing setup comprising a transmitter, a receiver and a sensor. The transmitter sends a codeword to the receiver through a discrete memoryless channel, and the receiver is interested in decoding the transmitted codeword. At the same time, the sensor picks up a noisy version of the transmitted codeword through one of two possible discrete memoryless channels. The sensor knows the codeword and wishes to discriminate between the two possible channels, i.e. to identify the channel that has generated the output given the input. We study the trade-off between communication and sensing in the asymptotic regime, captured in terms of the channel coding rate against the two types of discrimination error exponents. We characterize the optimal trade-off between the rate and the exponents for general discrete memoryless channels with an input cost constraint.

Joint Communication and Channel Discrimination

TL;DR

This work analyzes joint communication and channel discrimination (JCAS) for discrete memoryless channels with a binary sensing state and a per-letter input cost. The key result is a complete characterization of the rate-exponent region: there exists an input distribution with cost and a tilt parameter such that the communication rate and the two channel-discrimination exponents satisfy , , and , where is the tilted channel between and . Achievability is shown using almost constant-composition codes and a constrained channel coding argument, while the converse employs constant-composition subcodes to handle the non-convex input-set constraint. The paper also derives minimax and Neyman-Pearson special cases, linking the rate-exponent region to Chernoff-type and KL-divergence bounds, respectively. The results illuminate the fundamental trade-offs between reliable communication and sensing accuracy in JCAC, and provide a framework for extending to general alphabets and more complex sensing tasks.

Abstract

We consider a basic joint communication and sensing setup comprising a transmitter, a receiver and a sensor. The transmitter sends a codeword to the receiver through a discrete memoryless channel, and the receiver is interested in decoding the transmitted codeword. At the same time, the sensor picks up a noisy version of the transmitted codeword through one of two possible discrete memoryless channels. The sensor knows the codeword and wishes to discriminate between the two possible channels, i.e. to identify the channel that has generated the output given the input. We study the trade-off between communication and sensing in the asymptotic regime, captured in terms of the channel coding rate against the two types of discrimination error exponents. We characterize the optimal trade-off between the rate and the exponents for general discrete memoryless channels with an input cost constraint.
Paper Structure (18 sections, 7 theorems, 92 equations, 1 figure)

This paper contains 18 sections, 7 theorems, 92 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related work
  3. Contribution and comparison
  4. Notation
  5. Problem Setting
  6. Codes and error probabilities
  7. Rate-Exponent region
  8. Main Result
  9. Insights and examples
  10. Channel Discrimination
  11. Proof of Theorem \ref{['theorem:rate_exponent_region']}
  12. Achievability
  13. Converse
  14. Minimax and Neyman-Pearson
  15. Minimax discrimination criterion
  16. ...and 3 more sections

Key Result

Theorem 1

$\mathcal{R}$ is given by the set of all non-negative pairs $(R,E_0, E_1)$ such that for some input distribution $P_X \in \mathcal{P}(\mathcal{X})$ that satisfies $\mathbbmss{E}_{X \sim P_X}[b(X)] \leq B$, and some $s \in [0,1]$.

Figures (1)

  • Figure 1: An illustration of the considered setting. A precise definition of all blocks is given in Section \ref{['sec:problem_setting']}.

Theorems & Definitions (17)

  • Definition 1
  • Theorem 1
  • Example 1
  • Example 2
  • Lemma 1
  • proof
  • Corollary 1
  • proof
  • Lemma 2
  • Definition 2
  • ...and 7 more