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Universal Joint Source-Channel Coding Under an Input Energy Constraint

Omri Lev, Anatoly Khina

TL;DR

This work constructs a universal scheme that uses modulo-lattice modulation with multiple layers that requires less energy than existing solutions to achieve the same quadratically increasing distortion profile with the noise level.

Abstract

We consider the problem of transmitting a source over an infinite-bandwidth additive white Gaussian noise channel with unknown noise level under an input energy constraint. We construct a universal scheme that uses modulo-lattice modulation with multiple layers; for each layer, we employ either analog linear modulation or analog pulse position modulation (PPM). We show that the designed scheme with linear layers requires less energy compared to existing solutions to achieve the same quadratically increasing distortion profile with the noise level; replacing the linear layers with PPM layers offers an additional improvement.

Universal Joint Source-Channel Coding Under an Input Energy Constraint

TL;DR

This work constructs a universal scheme that uses modulo-lattice modulation with multiple layers that requires less energy than existing solutions to achieve the same quadratically increasing distortion profile with the noise level.

Abstract

We consider the problem of transmitting a source over an infinite-bandwidth additive white Gaussian noise channel with unknown noise level under an input energy constraint. We construct a universal scheme that uses modulo-lattice modulation with multiple layers; for each layer, we employ either analog linear modulation or analog pulse position modulation (PPM). We show that the designed scheme with linear layers requires less energy compared to existing solutions to achieve the same quadratically increasing distortion profile with the noise level; replacing the linear layers with PPM layers offers an additional improvement.

Paper Structure

This paper contains 17 sections, 14 theorems, 74 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Problem Statement
  4. Background: Modulo-Lattice Modulation
  5. Background: Analog Modulations in the Known-ENR Regime
  6. Main Results
  7. Infinite-Blocklength Setting with Linear Layers
  8. Infinite-Blocklength Setting with Analog PPM Layers
  9. Simulations
  10. Summary and Discussion
  11. Future Research
  12. Proof of Cor. \ref{['cor:NearGaussianDist_UpperBound']}
  13. Full version of Sch. \ref{['schm:UniversalAnalogMLM']}
  14. Proof of Th. \ref{['thm:linear_MLM']}
  15. Proof of Th. \ref{['thm:quadratic_profile']}
  16. ...and 2 more sections

Key Result

Theorem 3.1

The distortion eq:Distortion of Sch. schm:MLM_Reznic is bounded from above by for $\alpha_c \in (0,1], \alpha_s \in (0,1]$, and $\eta > 0$ that satisfy where $D^\mathrm{err}$ is the distortion given a lattice decoding-error event JointWZ-WDP and is bounded from above by and the lattice parameters $L\left(\cdot,\cdot,\cdot\right)$ and ${\tilde{L}}(\cdot)$ are defined as Moreover, for any $P_e

Figures (5)

  • Figure 1: Block diagrams of Sch. \ref{['schm:UniversalAnalogMLM']} and of this scheme with the effective additive-noise channels of Rem. \ref{['rem:induced-channel']}.
  • Figure 2: Distortion and accumulated energy of the layers utilized by the receiver at a given $\tilde{E}/N$ for a Gaussian source in the infinite-blocklength regime for a quadratic profile: Sch. \ref{['schm:UniversalAnalogMLM']} with linear layers with energy allocation $E_i = \Delta {\rm e}^{-\alpha i}$ for $\Delta = 0.975, \alpha = 0.65$, empirical performance of the scheme with a linear layer with energy $E_1 = 0.85$ and an analog PPM layer with energy $E_2 = 0.75$, and analytic performance of the scheme of Th. \ref{['thm:quadratic_profile']} with the parameters from its proof and analytic performance of Baniasadi and Tuncel scheme according to the proof in baniasadi2020minimum
  • Figure 3: Distortion and accumulated energy of the layers utilized by the receiver at a given $\tilde{E}/N$ for a uniform scalar source for a quadratic profile: Sch. \ref{['schm:UniversalAnalogMLM']} with linear layers with energy allocation $\frac{E_i}{\tilde{E}} = \Delta {\rm e}^{-\alpha i}$ for $\Delta = 0.9, \alpha = 0.64$, and with a linear layer with energy $E_1 = 0.9\tilde{E}$ and an analog PPM layer with energy $E_2 = 0.346\tilde{E}$.
  • Figure 4: Block diagram of Sch. \ref{['schm:UniversalAnalogMLM_Full']}.
  • Figure 5: Block diagram for the i'th MLM layer transmitter and receiver of Sch. \ref{['schm:UniversalAnalogMLM_Full']}. We denote the interleaving and deinterleaving operations by $\Pi$ and $\Pi^{-1}$, respectively.

Theorems & Definitions (23)

  • Definition 3.1: SNE OrdentlichErez_LatticeRobustness
  • Theorem 3.1
  • Remark 3.1
  • Corollary 3.1: Optimal parameters JointWZ-WDP, ZamirBook
  • Corollary 3.2: SNR universality
  • Corollary 3.3: Source-power uncertainty
  • Corollary 3.4: Suboptimal parameters
  • Lemma 3.1: ErezZamirAWGN
  • Remark 4.1
  • Theorem 4.1: EnergyLimitedJSCC:Lev_Khina:Full
  • ...and 13 more