Robust Hierarchical Broadcasting for AWGN and Flat Rayleigh Fading Channels using Multilevel Codes

| Coded modulation schemes for hierarchical broadcasting employing multilevel coding (MLC) are considered for both, AWGN and at Rayleigh fading channels. Special emphasis is put on good performance in both classes of channels, thus resulting in robust modulation schemes with respect to channel characteristics. Design rules for signal constellations and codes are discussed. INTRODUCTION With the introduction of digital modulation techniques to the broadcast media of television and audio the theoretical description of the broadcast channel, which rst was discussed by Cover [1], has regained considerable interest. The key element is the question of the maximal possible data rates that can be transmitted in a point to multi-point communication environment if the varying receivers exhibit di ering propagation conditions. These di erences can be due to varying receiver qualities because of di ering antennas e.g. or due to the di ering physical channel propagation conditions when transmitting to spacially separated receivers. Whatever the reason for the di ering signal to noise ratio (SNR) at the input of the demodulator is, a hierarchical system o ers the possibility to e ciently transmit data streams decodable at multiple SNRs. One example for a coded modulation scheme capable of performing hierarchical modulation is multilevel coding (MLC) [2] [3] [4]. Another solution, more frequently used up to date, is time-sharing, that is the fragmentation of the available transmission ressources (time, frequency e.g.) into several orthogonal transmission schemes that each have their proper level of protection. In [5] MLC is shown to be far superior to time-sharing in terms of power-bandwidth e ciency. Below, we address the problem of robustness of a MLC-scheme under varying signal propagation conditions. As examples, the additive white Gaussian noise (AWGN) and the at Rayleigh fading channel are chosen. MULTILEVEL CODING The key feature of MLC is the mechanism of splitting the transmission channel into several logical subchannels, with the number of such subchannels depending on the size of the signal constellation of the underlying modulation scheme. Due to the separated subchannels, a multi-stage decoder can be used which asymptotically reaches the performance of an optimal maximum likelihood decoder (MLD) but requires considerable lower decoding complexity [6]. MLC has three major degrees of freedom for its designer. Firstly, the partitioning strategy for the signal constellation. Secondly the choice for the code rates on the individual levels of the MLC-scheme and thirdly, the signal constellation itself with respect to the number of points and their spacing. −10 −5 0 5 10 15 20 25 30 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 10*log(Es/No) [dB] Cap aciti es [b it/sy mbo l] Multilevel Coding for uniform 8−ASK (AWGN)