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Joint Identification and Sensing for Discrete Memoryless Channels

Wafa Labidi, Yaning Zhao, Christian Deppe, Holger Boche

TL;DR

This work studies joint identification (ID) and channel-state sensing over a discrete memoryless channel with i.i.d. state. It develops a complete characterization of the ID capacity–distortion function across deterministic and randomized encoders, with and without noiseless feedback, and extends to a joint ID-and-sensing setup where the sender also estimates the state via strictly causal observations. A central finding is that feedback and common randomness enable substantial, even double-exponential, growth in ID capacity under sensing constraints, with precise capacity–distortion expressions such as $C_{ID}^d(D)=\max_{x\in\mathcal{X}_D} H(\mathbb{E}[W_S(\cdot|x,S)])$ and $C_{ID}^r(D)=\max_{P\in\mathcal{P}_D} H(\sum_x P(x) \mathbb{E}[W_S(\cdot|x,S)])$. The results reveal sensing can be treated as an additional resource that enhances ID performance, and they provide constructions, error analyses, and average-distortion considerations, with implications for applications in 6G, control, and molecular communication. The paper also discusses future directions, including Gaussian channels, noisy feedback, and alternative distortion constraints.

Abstract

In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver's goal is simply to verify whether a specific message of interest was sent. Unlike Shannon's transmission codes, which aim for message decoding, ID codes for a Discrete Memoryless Channel (DMC) are far more efficient: their size grows doubly exponentially with the blocklength when randomized encoding is used. This indicates that, when the receiver's objective does not require decoding, the ID paradigm is significantly more efficient than traditional Shannon transmission in terms of both energy consumption and hardware complexity. Further benefits of ID schemes can be realized by leveraging additional resources such as feedback. In this work, we address the problem of joint ID and channel state estimation over a DMC with independent and identically distributed (i.i.d.) state sequences. State estimation functions as the sensing mechanism of the model. Specifically, the sender transmits an ID message over the DMC while simultaneously estimating the channel state through strictly causal observations of the channel output. Importantly, the random channel state is unknown to both the sender and the receiver. For this system model, we present a complete characterization of the ID capacity-distortion function.

Joint Identification and Sensing for Discrete Memoryless Channels

TL;DR

This work studies joint identification (ID) and channel-state sensing over a discrete memoryless channel with i.i.d. state. It develops a complete characterization of the ID capacity–distortion function across deterministic and randomized encoders, with and without noiseless feedback, and extends to a joint ID-and-sensing setup where the sender also estimates the state via strictly causal observations. A central finding is that feedback and common randomness enable substantial, even double-exponential, growth in ID capacity under sensing constraints, with precise capacity–distortion expressions such as and . The results reveal sensing can be treated as an additional resource that enhances ID performance, and they provide constructions, error analyses, and average-distortion considerations, with implications for applications in 6G, control, and molecular communication. The paper also discusses future directions, including Gaussian channels, noisy feedback, and alternative distortion constraints.

Abstract

In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver's goal is simply to verify whether a specific message of interest was sent. Unlike Shannon's transmission codes, which aim for message decoding, ID codes for a Discrete Memoryless Channel (DMC) are far more efficient: their size grows doubly exponentially with the blocklength when randomized encoding is used. This indicates that, when the receiver's objective does not require decoding, the ID paradigm is significantly more efficient than traditional Shannon transmission in terms of both energy consumption and hardware complexity. Further benefits of ID schemes can be realized by leveraging additional resources such as feedback. In this work, we address the problem of joint ID and channel state estimation over a DMC with independent and identically distributed (i.i.d.) state sequences. State estimation functions as the sensing mechanism of the model. Specifically, the sender transmits an ID message over the DMC while simultaneously estimating the channel state through strictly causal observations of the channel output. Importantly, the random channel state is unknown to both the sender and the receiver. For this system model, we present a complete characterization of the ID capacity-distortion function.
Paper Structure (19 sections, 15 theorems, 94 equations, 3 figures)

This paper contains 19 sections, 15 theorems, 94 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Models and Main Results
  3. Proof of the Main Results
  4. Direct Proof of Theorem \ref{['MainTheorem1']}
  5. Converse Proof of Theorem \ref{['MainTheorem1']}
  6. Direct Proof of Theorem \ref{['MainTheorem2']}
  7. Converse Proof of Theorem \ref{['MainTheorem2']}
  8. Direct Proof of Theorem \ref{['theorem:capDist1']}
  9. Coding Scheme
  10. Common Randomness Generation
  11. Error Analysis
  12. Converse Proof of Theorem \ref{['theorem:capDist1']}
  13. Direct Proof of Theorem \ref{['theorem:capDist2']}
  14. Coding Scheme
  15. Common Randomness Generation
  16. ...and 4 more sections

Key Result

Theorem 3

The randomized ID capacity of the channel $W_S$ is given by where $C(W_S)$ denotes the Shannon transmission capacity of $W_S$.

Figures (3)

  • Figure 1: Discrete memoryless channel with random state
  • Figure 2: Discrete memoryless channel with random state and with noiseless feedback
  • Figure 3: State-dependent channel with noiseless feedback

Theorems & Definitions (29)

  • Definition 1
  • Definition 2
  • Theorem 3
  • proof
  • Definition 4
  • Definition 5
  • Definition 6
  • Theorem 7
  • Theorem 8
  • Remark 9
  • ...and 19 more