## A Bit-Level-Based Approach to Coded Multicarrier Transmission

Dissertation, published online, 2009.

Band 28, Erlanger Berichte aus Informations- und Kommunikationstechnik, Herausgeber: A. Kaup, W. Koch, J. Huber. Shaker Verlag, Aachen, 2010.

Presentation slides here

### Abstract

In this thesis bit-interleaved coded multicarrier transmission at high spectral efficiency is studied from a bit-level perspective. The analysis is based on an equivalent representation of the cascade of bit mapping and channel by a set of parallel binary-input channels, the so-called bit levels. This alternative representation was initially introduced in the context of bit-interleaved coded modulation and multilevel codes. By use of the chain rule of information theory, this model also allows for an intuitive and plausible approach to bit-interleaved coded multicarrier transmission. For the sake of low complexity and low latency, the system implementations considered in this thesis are restricted to non-iterative variants of BICM. Terminated convolutional codes in combination with a simple Viterbi decoder are employed for the coding scheme. Furthermore, the use of square QAM signal constellations is assumed to achieve the required high spectral efficiencies. Our considerations are mainly founded on variables initially defined for the description of the equivalent channel model. In particular, we utilize the bit-level capacity and the parallel-decoding capacity in order to evaluate the multicarrier system and its individual building blocks.

The investigations are first limited to a single carrier of the multicarrier system and start with the introduction and a thorough analysis of the equivalent channel model. The latter's characteristics, especially the parallel-decoding capacity, strongly depend on the employed bit mapping. We assess several binary labeling rules with regard to this quantity and provide optimal solutions. The presented results disprove (respectively specify) a conjecture alleged by Caire et al. which has gone unchallenged since its publication in 1998. Subsequently, the study of the equivalent channel model is extended to the bit error ratio of uncoded transmission. The bit error ratio is traced back and related to the individual level-dependent bit error ratios. Exploiting a numerically established relation between bit-level capacity and level-dependent bit error ratio, the findings on bit mappings optimal in terms of the parallel-decoding capacity can be transferred to the bit error ratio and vice versa. These results show a significant relation between maximum parallel-decoding capacity and minimum bit error ratio which in the following is exploited for the optimization of (uncoded) multicarrier transmission. The connection between these two quantities allows for a novel, slightly different approach to the issue of rate allocation over parallel subchannels. Motivated by the equivalent channel model, we provide new, very efficient rate allocation algorithms applicable for both, coded and uncoded transmission. The related problem of distributing the transmit power over the individual carriers is also analyzed with regard to the quantities bit-level capacity and parallel-decoding capacity. Several strategies known in the literature are classified in these terms.

The remainder of the thesis focuses on aspects of coded transmission. First, the bit-metric computation performed at the receiver is looked at from the bit-level perspective. The impact of a commonly employed simplified metric computation on the results of transmission with large signal constellations and the level-dependent average reliability of the bit metrics are of particular interest in this context. The insights obtained on the bit-metric reliability represent the foundation of the studies performed in the last part of this thesis, where the design of the bit interleavers is analyzed. Using the bit-level capacity as a figure of merit for the average reliability of the bit metrics, the Viterbi decoder used at the receiver and its sliding processing-window characteristics are studied. The latter immediately entails an optimization objective for the bit-interleaver design. The two general solutions to this problem presented in this thesis mainly differ in the availability of channel state information at the transmitter side. Adaptive bit interleaving utilizing channel knowledge for the arrangement of the bit metrics yields significant gains over global random bit interleaving. Intralevel bit interleaving just exploiting the knowledge of the bit level indices also outperforms conventional interleaver designs. Finally, the combination of bit-interleaved coded multicarrier modulation and rate and power loading is discussed. For larger signal constellations in particular the rate adaptation is shown to be not necessarily rewarding if not even counterproductive. Power loading may lead to small gains, though.