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Deterministic Identification Codes for Fading Channels

Ilya Vorobyev, Christian Deppe, Holger Boche

TL;DR

This work investigates deterministic identification codes for fading channels as an alternative metric to Shannon capacity in event-triggered communications. It introduces a polynomial-time constructible DI code with energy and distance guarantees, and establishes lower bounds on identification capacity for Gaussian, slow fading, and fast fading channels, with and without CSI. The results show a robust $1/4$ lower bound for fast fading under broad conditions and sharpen the Gaussian upper bound to $1/2$, highlighting a fundamentally different capacity scaling than classic transmission. The findings have practical implications for ultra-reliable, low-latency communications in fading environments, where efficient identification strategies can outperform traditional message transmission under the same constraints.

Abstract

Many communication applications incorporate event-triggered behavior, where the conventional Shannon capacity may not effectively gauge performance. Consequently, we advocate for the concept of identification capacity as a more suitable metric for assessing these systems. We consider deterministic identification codes for the Gaussian AWGN, the slow fading, and the fast fading channels with power constraints. We prove lower bounds on capacities for the slow and the fast fading channels with side information for a wide range of fading distributions. Additionally, we present the code construction with efficient encoding which achieves the lower bound on capacity both for the slow and the fast fading channels. At last, we prove the same lower bound on the capacity of the fast fading channel without side information, i.e., the same lower bound holds even when the receiver does not know the fading coefficients. As a result we show that compared with Shannon's message transmission paradigm we achieved completely different capacity scaling for deterministic identification codes for all relevant fading channels.

Deterministic Identification Codes for Fading Channels

TL;DR

This work investigates deterministic identification codes for fading channels as an alternative metric to Shannon capacity in event-triggered communications. It introduces a polynomial-time constructible DI code with energy and distance guarantees, and establishes lower bounds on identification capacity for Gaussian, slow fading, and fast fading channels, with and without CSI. The results show a robust lower bound for fast fading under broad conditions and sharpen the Gaussian upper bound to , highlighting a fundamentally different capacity scaling than classic transmission. The findings have practical implications for ultra-reliable, low-latency communications in fading environments, where efficient identification strategies can outperform traditional message transmission under the same constraints.

Abstract

Many communication applications incorporate event-triggered behavior, where the conventional Shannon capacity may not effectively gauge performance. Consequently, we advocate for the concept of identification capacity as a more suitable metric for assessing these systems. We consider deterministic identification codes for the Gaussian AWGN, the slow fading, and the fast fading channels with power constraints. We prove lower bounds on capacities for the slow and the fast fading channels with side information for a wide range of fading distributions. Additionally, we present the code construction with efficient encoding which achieves the lower bound on capacity both for the slow and the fast fading channels. At last, we prove the same lower bound on the capacity of the fast fading channel without side information, i.e., the same lower bound holds even when the receiver does not know the fading coefficients. As a result we show that compared with Shannon's message transmission paradigm we achieved completely different capacity scaling for deterministic identification codes for all relevant fading channels.
Paper Structure (21 sections, 14 theorems, 98 equations, 1 figure)

This paper contains 21 sections, 14 theorems, 98 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Our contribution
  3. Outline
  4. Notations and definitions
  5. Gaussian DI Code
  6. Fading Channels with Channel Side Information
  7. Discussion about alternative definitions of the capacity of the slow fading channel
  8. Fast Fading Channel without Side Information
  9. New Results and Discussion
  10. Code Construction
  11. Upper Bound for the Gaussian AWGN channel
  12. Slow Fading Channel with CSI
  13. Fast Fading Channel with CSI
  14. Fast Fading without CSI
  15. Proof of Theorem \ref{['th::construction']}
  16. ...and 6 more sections

Key Result

Theorem 1

For any positive constants $a$, $A$, $B$, $a<1/8$, and any $n>n_0(a)$ there exists a code $\mathcal{U}(n)=\{\mathbf{u}_i\}_{i\in[M]}$, $\mathbf{u}_i\in \mathbb{R}^n$ of size $M\geq 2^{\left(\frac{1}{4}-2a\right)n\log_2n}$ with the following properties. Moreover, such code can be efficiently constructed and encoded, i.e., the time complexity of construction and encoding are polynomial.

Figures (1)

  • Figure 1: Channel model for deterministic identification.

Theorems & Definitions (30)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4: salariseddigh2021deterministic
  • Definition 5
  • Definition 6
  • Theorem 1
  • Theorem 2
  • Remark 1
  • Theorem 3
  • ...and 20 more