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The Listsize Capacity of the Gaussian Channel with Decoder Assistance.

Amos Lapidoth¹, Yiming Yan¹

¹Signal and Information Processing Laboratory, ETH Zurich, 8092 Zurich, Switzerland.

Entropy (Basel, Switzerland)

|January 21, 2022

Summary

A helper can improve information transmission over a Gaussian channel by providing a limited description of the noise sequence. This enhances the listsize capacity, particularly when the helper offers fine-grained noise information.

Keywords:

Gaussian channel bit pipe cutoff rate decoder assistance helper listsize capacity

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Area of Science:

Information Theory
Digital Communications

Background:

The Gaussian channel is a fundamental model in information theory.
Listsize capacity quantifies the number of messages a decoder can distinguish.

Purpose of the Study:

To compute the listsize capacity of a Gaussian channel with a helper.
To analyze the impact of rate-limited helper information on channel capacity.

Main Methods:

The study involves theoretical analysis of information transmission over a Gaussian channel.
A helper provides a rate-limited description of the channel-noise sequence to the decoder.
Capacity is calculated as the sum of the cutoff rate and the rate of help.

Main Results:

The listsize capacity with a helper equals the sum of the cutoff rate and the rate of help.
Zero-rate help increases listsize capacity to the cutoff rate.
This is achieved through quantization of the noise sequence's normalized squared Euclidean norm.

Conclusions:

Helper-assisted communication can significantly enhance channel capacity.
The effectiveness of the helper depends on the quality of information provided about the noise sequence.