Achieving the Shannon limit with probabilistically shaped BICM

Author

Agrell, Erik ; Alvarado, Alex

Author_Institution

Dept. of Signals & Syst., Chalmers Univ. of Technol., Göteborg, Sweden

fYear

2012

fDate

1-6 July 2012

Firstpage

2421

Lastpage

2425

Abstract

Probabilistic shaping for bit-interleaved coded modulation (BICM) systems at low signal-to-noise ratio (SNR) is investigated. Using known results for BICM systems with a uniform input distribution, the combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit -1.59 dB are fully characterized. It is found that a BICM system achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube, which is the same condition as for uniform input distributions. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR regime of BICM systems, in addition to what is provided by geometrical shaping.

Keywords

binary codes; modulation coding; probability; BICM; Shannon limit; binary labeling; bit-interleaved coded modulation; geometrical shaping; hypercube; input alphabet; low signal-to-noise ratio; probabilistic shaping; uniform input distribution; zero-mean linear projection; Hypercubes; Interleaved codes; Labeling; Probabilistic logic; Signal to noise ratio; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on

Conference_Location

Cambridge, MA

ISSN

2157-8095

Print_ISBN

978-1-4673-2580-6

Electronic_ISBN

2157-8095

Type

conf

DOI

10.1109/ISIT.2012.6283949

Filename

6283949