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Achievable Information Rates for Probabilistic Amplitude Shaping: An Alternative Approach via Random Sign-Coding
Yunus Can Gültekin1, Alex Alvarado1, Frans M J Willems1
1Information and Communication Theory Lab, Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
Probabilistic amplitude shaping (PAS) combines constellation shaping and channel coding for efficient communication. This study offers new proofs for PAS achieving channel capacity using weak typicality and constructive random sign-coding arguments.
Area of Science:
- Communications Engineering
- Information Theory
Background:
- Probabilistic amplitude shaping (PAS) integrates constellation shaping and channel coding.
- PAS is a key strategy in wireless and optical communications.
- Previous studies investigated achievable information rates (AIRs) using Gallager's error exponent approach.
Purpose of the Study:
- To revisit and provide alternative proofs for the capacity-achieving property of PAS.
- To derive AIRs for PAS using weak typicality.
- To develop constructive proofs based on random sign-coding arguments.
Main Methods:
- Utilizing weak typicality for deriving AIRs.
- Employing constructive random sign-coding arguments, where some input signs are randomized and others are determined.
- Considering both symbol-metric and bit-metric decoding schemes.
Main Results:
- The study provides alternative, constructive proofs for PAS achieving the capacity of the additive white Gaussian noise channel.
- New derivations of AIRs for PAS are presented using weak typicality.
- The constructive approach offers insights into the practical implementation of PAS.
Conclusions:
- PAS is confirmed to be a capacity-achieving modulation strategy.
- The developed constructive proofs enhance the understanding of PAS's performance.
- The findings are relevant for advancing high-performance communication systems.
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