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Hardware Implementation of a Fixed-Point Decoder for Low-Density Lattice Codes.

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Capacity-Achieving Input Distributions of Additive Vector Gaussian Noise Channels: Even-Moment Constraints and

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Entropy (Basel, Switzerland)
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We studied capacity-achieving inputs for Gaussian noise channels. The input distribution

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Area of Science:

  • Information Theory
  • Probability Theory
  • Stochastic Processes

Background:

  • Vector-valued Gaussian noise channels are fundamental in communication systems.
  • Understanding input distributions is crucial for maximizing channel capacity.
  • Radial even-moment constraints are often imposed on inputs.

Purpose of the Study:

  • To characterize the support of capacity-achieving input distributions for vector-valued Gaussian noise channels.
  • To analyze the impact of input domain restrictions (unrestricted vs. compact subset) on the input support.
  • To determine the geometric and measure-theoretic properties of these capacity-achieving supports.

Main Methods:

  • Mathematical analysis of probability distributions.
  • Geometric measure theory concepts, including submanifolds and Lebesgue measure.
  • Investigation of radial even-moment constraints on input distributions.

Main Results:

  • The support of the capacity-achieving input is a countable union of submanifolds with dimension n-1 or less.
  • When the input is restricted to a compact subset, this union becomes finite.
  • The support is shown to have Lebesgue measure 0 and be nowhere dense in Rn.

Conclusions:

  • The structure of capacity-achieving inputs is highly constrained, lying on low-dimensional manifolds.
  • Input restrictions significantly simplify the structure of the support.
  • These findings have implications for designing efficient communication schemes under specific constraints.