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Identification for ISI Gaussian Channels

Mohammad Javad Salariseddigh

Abstract

We establish non-asymptotic lower and upper bounds for the identification capacity of discrete-time Gaussian channels subject to inter-symbol interference (ISI), a canonical model in wireless communication. Our analysis accounts for deterministic encoders under peak power constraint. A principal finding is that, even when the number of ISI taps scales sub-linearly with the codeword length, \(n\), i.e., \(\sim n^κ\) with \(κ\in [0,1/2),\) the number of messages that can be reliably identified grows super-exponentially in \(n\), i.e., \(\sim 2^{(n \log n)R}\), where \(R\) denotes the coding rate.

Identification for ISI Gaussian Channels

Abstract

We establish non-asymptotic lower and upper bounds for the identification capacity of discrete-time Gaussian channels subject to inter-symbol interference (ISI), a canonical model in wireless communication. Our analysis accounts for deterministic encoders under peak power constraint. A principal finding is that, even when the number of ISI taps scales sub-linearly with the codeword length, , i.e., with \(κ\in [0,1/2),\) the number of messages that can be reliably identified grows super-exponentially in , i.e., \(\sim 2^{(n \log n)R}\), where denotes the coding rate.
Paper Structure (14 sections, 4 theorems, 60 equations)

This paper contains 14 sections, 4 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. Notations
  3. Organization
  4. Related Works on Identification Capacity with Deterministic Encoder
  5. System Model and Coding Preliminaries
  6. ISI Gaussian Channel
  7. Identification Coding
  8. Identification Capacity of the ISI Gaussian Channel
  9. Main Results
  10. Achievability
  11. Upper Bound (Converse Proof)
  12. Conclusion
  13. Acknowledgments
  14. Proof of Lemma \ref{['Lem.Converse']}

Key Result

Theorem 1

Consider the ISI Gaussian channel, $\mathcal{G}_{\mathbf{h}},$ with CIR $\mathbf{h}$ fulfilling conditions C1-C2 and assume that the the number of ISI channel taps grows sub-linearly with the codeword length, i.e., $K(n,\kappa) = n^{\kappa},$ where $\kappa \in [0,1/2).$ Then, the identification capa

Theorems & Definitions (10)

  • Definition 1: ISI Gaussian identification code
  • Definition 2: ISI Gaussian identification capacity
  • Theorem 1
  • proof
  • Corollary 1: Identification capacity of standard Gaussian channel
  • proof
  • Lemma 1: minimum distance of the convoluted codebook
  • proof
  • Lemma 2
  • proof