Signal Shaping for BICM at Low SNR
Journal article, 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.

wide-band regime

generalizedmutual information (GMI)

spectral efficiency

interleaved coded modulation


bit-interleaved coded modulation (BICM)


Binary labeling

trellis codes


Erik Agrell

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Alex Alvarado

University of Cambridge

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 59 4 2396-2410 6374254

Subject Categories

Electrical Engineering, Electronic Engineering, Information Engineering



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