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Robust Joint Message and State Transmission under Arbitrarily Varying Jamming

Yiqi Chen, Holger Boche

TL;DR

This work studies robust joint message and state transmission over arbitrarily varying channels where the state distribution $Q_S$ is fixed but the jammer selects an arbitrary sequence. It develops deterministic coding schemes for both strictly causal and noncausal state observation, under average and maximal error criteria, and derives lower bounds on the capacity-distortion functions $C_a(D)$ and $C_m(D)$, including special cases where capacity is characterized for binary-output channels. The main techniques combine block Markov coding with Wyner–Ziv state descriptions and Gel’fand–Pinsker style coding, with careful attention to nonsymmetrizability of the induced channels to guarantee positive capacity. The results reveal that average-error performance can outperform maximal-error performance, and show how the state-estimation constraint interacts with robust communication, yielding capacity expressions that are relevant for robust ISAC applications in 6G and autonomous systems.

Abstract

Joint message and state transmission under arbitrarily varying jamming is investigated in this paper. The problem is modeled as the transmission over a channel with random states with a fixed distribution and jamming that varies in an unknown manner. We provide lower bounds of the capacity-distortion function of strictly causal and noncausal observations of the states at the encoder under the average error criterion when the jammer is not aware of the transmitted message, as well as the maximal error criterion when the jammer knows the message. Some capacity-achieving cases are also provided. The proposed coding schemes are deterministic, and no randomness is needed to achieve reliable communication and estimation. It turns out that the performance of the system under the average error can strictly outperform the maximal error case, which is in accordance with normal communication over arbitrarily varying channels.

Robust Joint Message and State Transmission under Arbitrarily Varying Jamming

TL;DR

This work studies robust joint message and state transmission over arbitrarily varying channels where the state distribution is fixed but the jammer selects an arbitrary sequence. It develops deterministic coding schemes for both strictly causal and noncausal state observation, under average and maximal error criteria, and derives lower bounds on the capacity-distortion functions and , including special cases where capacity is characterized for binary-output channels. The main techniques combine block Markov coding with Wyner–Ziv state descriptions and Gel’fand–Pinsker style coding, with careful attention to nonsymmetrizability of the induced channels to guarantee positive capacity. The results reveal that average-error performance can outperform maximal-error performance, and show how the state-estimation constraint interacts with robust communication, yielding capacity expressions that are relevant for robust ISAC applications in 6G and autonomous systems.

Abstract

Joint message and state transmission under arbitrarily varying jamming is investigated in this paper. The problem is modeled as the transmission over a channel with random states with a fixed distribution and jamming that varies in an unknown manner. We provide lower bounds of the capacity-distortion function of strictly causal and noncausal observations of the states at the encoder under the average error criterion when the jammer is not aware of the transmitted message, as well as the maximal error criterion when the jammer knows the message. Some capacity-achieving cases are also provided. The proposed coding schemes are deterministic, and no randomness is needed to achieve reliable communication and estimation. It turns out that the performance of the system under the average error can strictly outperform the maximal error case, which is in accordance with normal communication over arbitrarily varying channels.
Paper Structure (27 sections, 18 theorems, 182 equations, 2 figures)

This paper contains 27 sections, 18 theorems, 182 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Models and results
  3. Channel Model
  4. Average Error Criterion
  5. Maximal Error Criterion
  6. Main Results: Average Error Criterion
  7. Main Results: Maximal Error Criterion
  8. binary case
  9. Noncausal Case
  10. Strictly Causal Case
  11. Proof of theorem \ref{['the: achievability of strictly causal']}
  12. Unambiguity Analysis
  13. Error Analysis
  14. Error event $\mathcal{E}_0$
  15. Error event $\mathcal{E}_1$
  16. ...and 12 more sections

Key Result

Lemma 1

If the channel $Q_{Y|XSJ}$ is nonsymmetrizable-$\mathcal{S}|\mathcal{X}$, there exists $\zeta>0$ such that for each pair of channels $T_1:\mathcal{X}\times\mathcal{S}\to\mathcal{J}$ and $T_2:\mathcal{X}\times\mathcal{S}\to\mathcal{J}$,

Figures (2)

  • Figure 1: Joint message and state communication under arbitrarily varying jamming
  • Figure 2: Coding strategies of the jammer with different knowledge: The private correlated randomness (PCR) is available when the correlated randomness is only available at the encoder and decoder.

Theorems & Definitions (36)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4: Symmetrizability
  • Lemma 1
  • proof
  • Theorem 1
  • Definition 5
  • Definition 6
  • Lemma 2
  • ...and 26 more