Computer Science – Information Theory
Scientific paper
2010-01-25
IEEE Trans. Inform. Theory, vol. 57, no. 10, pp. 6650-6672, 2011
Computer Science
Information Theory
Submitted to the IEEE Transactions on Information Theory
Scientific paper
10.1109/TIT.2011.2162179
Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit $-1.59 \tr{dB}$. It is shown that the $\Eb/N_0$ required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.
Agrell Erik
Alvarado Alex
No associations
LandOfFree
On the BICM Capacity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the BICM Capacity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the BICM Capacity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-643074