Signal Shaping for BICM at Low SNR
Artikel i vetenskaplig tidskrift, 2013

The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.

Binary labeling

bit-interleaved coded modulation (BICM)


interleaved coded modulation

trellis codes

wide-band regime

spectral efficiency

generalizedmutual information (GMI)



Erik Agrell

Signaler och system, Kommunikationssystem, informationsteori och antenner, Kommunikationssystem

Alex Alvarado

University of Cambridge

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 59 2396-2410 6374254


Elektroteknik och elektronik