Title :
Signal Shaping for BICM at Low SNR
Author :
Agrell, Erik ; Alvarado, Alex
Author_Institution :
Dept. of Signals & Syst., Chalmers Univ. of Technol., Goteborg, Sweden
Abstract :
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 - 1.59 dB 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.
Keywords :
fading channels; information theory; interleaved codes; modulation coding; probability; ήxed input alphabet; Shannon limit; binary labeling; bit-interleaved coded modulation system; fading channel; generalized mutual information; geometrical shaping; hypercube; input distribution; low signal-to-noise ratio; low-SNR BICM-GMI; numerical results; probabilistic shaping; signal shaping; zero-mean linear projection; Labeling; Mutual information; Probabilistic logic; Signal to noise ratio; Transforms; Vectors; Wideband; Binary labeling; Hadamard transform; Shannon limit (SL); bit-interleaved coded modulation (BICM); generalized mutual information (GMI); probabilistic shaping; wideband regime;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2012.2231900
