Bit-Interleaved Coded Modulation in the Wideband Regime

The wideband regime of bit-interleaved coded modulation (BICM) in Gaussian channels is studied. The Taylor expansion of the coded modulation capacity for generic signal constellations at low signal-to-noise ratio (SNR) is derived and used to determine the corresponding expansion for the BICM capacity. Simple formulas for the minimum energy per bit and the wideband slope are given. BICM is found to be suboptimal in the sense that its minimum energy per bit can be larger than the corresponding value for coded modulation schemes. The minimum energy per bit using standard Gray mapping on $M$-PAM or $M^2$ -QAM is given by a simple formula and shown to approach ${-}$ 0.34 dB as $M$ increases. Using the low SNR expansion, a general tradeoff between power and bandwidth in the wideband regime is used to show how a power loss can be traded off against a bandwidth gain.