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Energy-limited Joint Source--Channel Coding via Analog Pulse Position Modulation

Omri Lev, Anatoly Khina

TL;DR

A joint source–channel coding scheme using analog pulse position modulation (PPM) is constructed and it is shown that this scheme outperforms existing techniques since its quadratic distortion attains both the exponential and polynomial decay orders of Burnashev's outer bound.

Abstract

We study the problem of transmitting a source sample with minimum distortion over an infinite-bandwidth additive white Gaussian noise channel under an energy constraint. To that end, we construct a joint source--channel coding scheme using analog pulse position modulation (PPM) and bound its quadratic distortion. We show that this scheme outperforms existing techniques since its quadratic distortion attains both the exponential and polynomial decay orders of Burnashev's outer bound. We supplement our theoretical results with numerical simulations and comparisons to existing schemes.

Energy-limited Joint Source--Channel Coding via Analog Pulse Position Modulation

TL;DR

A joint source–channel coding scheme using analog pulse position modulation (PPM) is constructed and it is shown that this scheme outperforms existing techniques since its quadratic distortion attains both the exponential and polynomial decay orders of Burnashev's outer bound.

Abstract

We study the problem of transmitting a source sample with minimum distortion over an infinite-bandwidth additive white Gaussian noise channel under an energy constraint. To that end, we construct a joint source--channel coding scheme using analog pulse position modulation (PPM) and bound its quadratic distortion. We show that this scheme outperforms existing techniques since its quadratic distortion attains both the exponential and polynomial decay orders of Burnashev's outer bound. We supplement our theoretical results with numerical simulations and comparisons to existing schemes.

Paper Structure

This paper contains 10 sections, 4 theorems, 59 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Problem Statement
  4. Main Results
  5. Upper Bound on the Distortion for a Uniform Source
  6. Upper Bound on the Distortion for a Gaussian Source
  7. Simulations
  8. Discussion and Future Research
  9. Upper Bound on the Small-Error Distortion in Prop. \ref{['prop:UpperBound_GaussianPrior']}
  10. Upper Bound on the Large-Error Distortion in Prop. \ref{['prop:UpperBound_GaussianPrior']}

Key Result

Proposition 1

The distortion of the MAP estimator eq:AnalogPPM:Receiver_MaxCorr of a scalar source that is uniformly distributed over a unit interval, transmitted using analog PPM with a rectangular pulse is bounded from above by where are upper bounds on the "small-error" distortion (when the error is less than or equal to $1/\beta$), "large-error" distortion, and the probability of a large error, respective

Figures (3)

  • Figure 1: The optimized empirical SDR and the lower bound on the SDR of Prop. \ref{['prop:UpperBound_UniformPrior']} of analog PPM for a uniform source.
  • Figure 2: The optimized empirical SDR and the lower bound on the SDR of Prop. \ref{['prop:UpperBound_GaussianPrior']} of analog PPM for a standard Gaussian source .
  • Figure 3: The empirical distortion, the upper bound of Prop. \ref{['prop:UpperBound_GaussianPrior']} and the asymptotic bound of \ref{['eq:UpperBounf_UniformPrior_Explicit2']} of analog PPM for a standard Gaussian source. $\beta = 3.68$ was used in the simulations.

Theorems & Definitions (7)

  • Proposition 1
  • Theorem 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 2
  • Theorem 2