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Simultaneous Information and Energy Transmission with Short Packets and Finite Constellations

Sadaf ul Zuhra, Samir M. Perlaza, H. Vincent Poor, Mikael Skoglund

TL;DR

A novel method for constructing a family of codes that can satisfy a target information rate, energy rate, DEP and EOP is proposed and achievability results identify the set of tuples of information rate, energy rate, DEP and EOP that can be simultaneously achieved by the constructed family of codes.

Abstract

This paper characterizes the trade-offs between information and energy transmission over an additive white Gaussian noise channel in the finite block-length regime with finite channel input symbols. These trade-offs are characterized in the form of inequalities involving the information transmission rate, energy transmission rate, decoding error probability (DEP) and energy outage probability (EOP) for a given finite block-length code. The first set of results identify the set of necessary conditions that a given code must satisfy for simultaneous information and energy transmission. Following this, a novel method for constructing a family of codes that can satisfy a target information rate, energy rate, DEP and EOP is proposed. Finally, the achievability results identify the set of tuples of information rate, energy rate, DEP and EOP that can be simultaneously achieved by the constructed family of codes.

Simultaneous Information and Energy Transmission with Short Packets and Finite Constellations

TL;DR

A novel method for constructing a family of codes that can satisfy a target information rate, energy rate, DEP and EOP is proposed and achievability results identify the set of tuples of information rate, energy rate, DEP and EOP that can be simultaneously achieved by the constructed family of codes.

Abstract

This paper characterizes the trade-offs between information and energy transmission over an additive white Gaussian noise channel in the finite block-length regime with finite channel input symbols. These trade-offs are characterized in the form of inequalities involving the information transmission rate, energy transmission rate, decoding error probability (DEP) and energy outage probability (EOP) for a given finite block-length code. The first set of results identify the set of necessary conditions that a given code must satisfy for simultaneous information and energy transmission. Following this, a novel method for constructing a family of codes that can satisfy a target information rate, energy rate, DEP and EOP is proposed. Finally, the achievability results identify the set of tuples of information rate, energy rate, DEP and EOP that can be simultaneously achieved by the constructed family of codes.
Paper Structure (26 sections, 17 theorems, 24 equations, 4 figures, 1 table)

This paper contains 26 sections, 17 theorems, 24 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. State of the art
  3. Contributions
  4. Notation
  5. System Model
  6. Information and Energy Transmission
  7. Encoding and decoding
  8. Energy Harvesting
  9. Necessary Conditions
  10. DEP
  11. Energy Transmission Rate and EOP
  12. Information Transmission Rate
  13. Code Construction for SIET
  14. Constellation Design
  15. Codeword Design
  16. ...and 11 more sections

Key Result

Theorem 3.1

If a given constant composition $(n,M,\mathcal{X})$-code, $\mathscr{C}$, with $\mathcal{X}$ in EqCIsymbols, is an $(n,M,\mathcal{X},\epsilon,B,\delta)$-code for the random transformation in EqYXdistribution, then the following conditions simultaneously hold: where, the information rate $R(\mathscr{C})$ is defined in EqRbound; the function $Q$ is defined in DefQfunc; for all $\ell \in \lbrace 1,

Figures (4)

  • Figure 1: A comparison of the information-energy region defined by the necessary conditions (Theorem \ref{['TheoremImpossibility']}) versus the achievable information-energy region (Theorem \ref{['TheoremAchievableRegion']}) for constant composition codes in the family ${\sf C} \left(C,\boldsymbol{A},\boldsymbol{L},\boldsymbol{\alpha},\boldsymbol{p},\boldsymbol{r} \right)$.
  • Figure 2: Bounds on the information transmission rate $R$ in \ref{['EqRbound']} as a function of the harvested energy $e$ in \ref{['Eq33']}.
  • Figure 3: A comparison of the bounds on the information rate from the necessary conditions in \ref{['EqRbound']} (Necessary 1) and \ref{['EqCorRUpperBoundRelax']} (Necessary 2) for finite block-length SIET with the finite block-length converse in polyanskiy2010channel as a function of the block-length $n$.
  • Figure 4: Graphical representation of the symbols in layer $c$ defined in \ref{['EqLayerCircle']}

Theorems & Definitions (40)

  • Definition 2.1: $(n,M,\mathcal{X})$-code
  • Definition 2.2: $(n,M,\mathcal{X},\epsilon,B,\delta)$-code
  • Definition 3.1: Constant Composition Codes
  • Theorem 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Theorem 3.4
  • ...and 30 more