Two new papers from the group have been accepted for their publication:
|
| The paper «High-SNR asymptotics of mutual information for discrete constellations with applications to BICM» by A. Alvarado, F. Brännström, E. Agrell, and T. Koch has been accepted for publication by the IEEE Transactions on Information Theory. |
|
Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR. |
| The paper «A Rate-Splitting Approach to Fading Multiple-Access Channels with Imperfect Channel-State Information» by A. Pastore, T. Koch, and J.R. Fonollosa has been accepted for presentation at the 2014 International Zurich Seminar on Communications. |
|
As shown by Médard, the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input and by treating the unknown portion of the channel multiplied by the channel input as independent worst-case (Gaussian) noise. Recently, we have demonstrated that this lower bound can be sharpened by a rate-splitting approach: by expressing the channel input as the sum of two independent Gaussian random variables (referred to as layers), say X=X_1+X_2, and by applying Médard’s bounding technique to first lower-bound the capacity of the virtual channel from X_1 to the channel output Y (while treating X_2 as noise), and then lower-bound the capacity of the virtual channel from X_2 to Y (while assuming X_1 to be known), one obtains a lower bound that is strictly larger than Médard’s bound. This rate-splitting approach is reminiscent of an approach used by Rimoldi and Urbanke to achieve points on the capacity region of the Gaussian multiple-access channel (MAC). Here we blend these two rate-splitting approaches to derive a novel inner bound on the capacity region of the memoryless fading MAC with imperfect CSI. Generalizing the above rate-splitting approach to more than two layers, we show that, irrespective of how we assign powers to each layer, the supremum of all rate-splitting bounds is approached as the number of layers tends to infinity, and we derive an integral expression for this supremum. We further derive an expression for the vertices of the best inner bound, maximized over the number of layers and over all power assignments. |
