Achievable Rates for Probabilistic Shaping
Information Theory
2018-05-23 v5 math.IT
Abstract
For a layered probabilistic shaping (PS) scheme with a general decoding metric, an achievable rate is derived using Gallager's error exponent approach and the concept of achievable code rates is introduced. Several instances for specific decoding metrics are discussed, including bit-metric decoding, interleaved coded modulation, and hard-decision decoding. It is shown that important previously known achievable rates can also be achieved by layered PS. A practical instance of layered PS is the recently proposed probabilistic amplitude shaping (PAS).
Cite
@article{arxiv.1707.01134,
title = {Achievable Rates for Probabilistic Shaping},
author = {Georg Böcherer},
journal= {arXiv preprint arXiv:1707.01134},
year = {2018}
}
Comments
Compared to v4, a simpler proof of Proposition 1 (achievable encoding rate) is given and an interpretation of the uncertainty as a cross-entropy is added