Johannes Georg Klotz

Antenna selection criteria for interference alignment

Antenna selection is a powerful method in order to reduce the complexity of transmission and reception in a multi-antenna system. Interestingly, this method has been considered mostly for point-to-point communication. In this paper, we investigate the impact of different antenna selection criteria on the performance of wireless networks using interference alignment, a transmit strategy which has attracted a lot of interest, in order to improve the performance of wireless interference networks significantly. The selection criteria we consider for antenna selection are based on the properties of the channel such as signal-to-leakage-noise ratio, chordal distance, eigenvalues of the effective channel matrices and receiver side SNR. In order to avoid the exhaustive search needed to obtain the optimal solution we introduce three greedy low complexity selection algorithms. These algorithms perform reasonably well, however there remains a gap to the exhaustive search.

Canalizing Boolean Functions Maximize Mutual Information

Information processing in biologically motivated Boolean networks is of interest in recent information theoretic research. One measure to quantify this ability is the well-known mutual information. Using Fourier analysis, we show that canalizing functions maximize mutual information between a single input variable and the outcome of a function with fixed expectation. A similar result can be obtained for the mutual information between a set of input variables and the output. Further, if the expectation of the function is not fixed, we obtain that the mutual information is maximized by a function only dependent on this single variable, i.e., the dictatorship function. We prove our findings for Boolean functions with uniformly distributed as well as product distributed input variables.

Properties of Boolean networks and methods for their tests

Transcriptional regulation networks are often modeled as Boolean networks. We discuss certain properties of Boolean functions (BFs), which are considered as important in such networks, namely, membership to the classes of unate or canalizing functions. Of further interest is the average sensitivity (AS) of functions. In this article, we discuss several algorithms to test the properties of interest. To test canalizing properties of functions, we apply spectral techniques, which can also be used to characterize the AS of functions as well as the influences of variables in unate BFs. Further, we provide and review upper and lower bounds on the AS of unate BFs based on the spectral representation. Finally, we apply these methods to a transcriptional regulation network of Escherichia coli, which controls central parts of the E. coli metabolism. We find that all functions are unate. Also the analysis of the AS of the network reveals an exceptional robustness against transient fluctuations of the binary variables.a

Adaptive coding and modulation in MIMO OFDMA systems

Adaptive coding and modulation are well known techniques for enhancing the performance of systems transmitting over quasi-static fading channels. Especially their application in OFDM based systems promises gains in spectral efficiency. In former work we presented an efficient method for the joint optimization of code rate and modulation formats if rate-compatible punctured codewords are mapped onto sub-symbols with heterogeneous channel quality and modulation formats. In this paper, we demonstrate the application of our scheme to MIMO techniques. More specifically, we investigate non-orthogonal spatial multiplexing schemes in bit-interleaved coded OFDM systems. The techniques are evaluated within the context of the OFDMA/TDMA system designed within the EU FP6 Integrated Project WINNER.

Model-based analysis of an adaptive evolution experiment with Escherichia coli in a pyruvate limited continuous culture with glycerol

Bacterial strains that were genetically blocked in important metabolic pathways and grown under selective conditions underwent a process of adaptive evolution: certain pathways may have been deregulated and therefore allowed for the circumvention of the given block. A block of endogenous pyruvate synthesis from glycerol was realized by a knockout of pyruvate kinase and phosphoenolpyruvate carboxylase in E. coli. The resulting mutant strain was able to grow on a medium containing glycerol and lactate, which served as an exogenous pyruvate source. Heterologous expression of a pyruvate carboxylase gene from Corynebacterium glutamicum was used for anaplerosis of the TCA cycle. Selective conditions were controlled in a continuous culture with limited lactate feed and an excess of glycerol feed. After 200–300 generations pyruvate-prototrophic mutants were isolated. The genomic analysis of an evolved strain revealed that the genotypic basis for the regained pyruvate-prototrophy was not obvious. A constraint-based model of the metabolism was employed to compute all possible detours around the given metabolic block by solving a hierarchy of linear programming problems. The regulatory network was expected to be responsible for the adaptation process. Hence, a Boolean model of the transcription factor network was connected to the metabolic model. Our model analysis only showed a marginal impact of transcriptional control on the biomass yield on substrate which is a key variable in the selection process. In our experiment, microarray analysis confirmed that transcriptional control probably played a minor role in the deregulation of the alternative pathways for the circumvention of the block.

Required Transmit Power Applying Tomlinson-Harashima-Precoding in Scalar and MIMO Broadcast Systems

Tomlinson-Harashima-precoding can be used as dirty-paper-coding method for transmissions over a broadcast channel. However, applying it to the individual user messages the final transmit power may vary from the sum of single user powers. This paper investigates the required transmit power for Tomlinson-Harashima-precoding in two user broadcast systems. Additionally, upper and lower bounds on the required power are derived. First our considerations are done in scalar channels. Then we extend the results to MIMO systems. In order to judge the performance of THP applied as broadcast technique we finally determine the achievable user rates.

Bounds on the average sensitivity of nested canalizing functions.

Nested canalizing Boolean functions (NCF) play an important role in biologically motivated regulatory networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on the network dynamics. It is well known that the average sensitivity plays a central role for the stability of (random) Boolean networks. Here we provide a tight upper bound on the average sensitivity of NCFs as a function of the number of relevant input variables. As conjectured in literature this bound is smaller than . This shows that a large number of functions appearing in biological networks belong to a class that has low average sensitivity, which is even close to a tight lower bound.

Computing preimages of Boolean networks

In this paper we present an algorithm based on the sum-product algorithm that finds elements in the preimage of a feed-forward Boolean networks given an output of the network. Our probabilistic method runs in linear time with respect to the number of nodes in the network. We evaluate our algorithm for randomly constructed Boolean networks and a regulatory network of Escherichia coli and found that it gives a valid solution in most cases.

The performance of QPSK in low-SNR interference channels

We investigate the low-SNR sum rate performance of QPSK for symmetric interference channels. The QPSK performance is described by the minimum energy per bit and the wideband slope pertaining to the sum capacity. Comparing this with the minimum energy per bit and wideband slope of corresponding interference channels using optimal inputs, we find that QPSK achieves optimal performance in all of the cases where exact sum capacities are known. We also show that a simplified Han-Kobayashi scheme is suboptimal in the low-SNR regime when the input alphabet is the whole set of complex numbers.

The wideband slope region of BPSK and QPSK for broadcast channels in the low-power regime

We consider a multi-user scenario, where the users are operating at a low SNR level. The low SNR level entails that the energy per bit of each user is close to the minimum that allows for reliable transmission. In existing work of the last years, the wideband slope was introduced, which describes the behavior of capacity as SNR tends to zero and which thus is an adequate quality criterion for channels with low SNR. It has already been shown that in single-user channels, QPSK achieves the optimum slope reached by Gaussian alphabets, while BPSK only achieves half the slope. In this paper, we extend this result to two-user broadcast channels and show that the users achieve the optimum slope region if they use QPSK. As in the single-user case, each users slope attainable with QPSK is halved when using BPSK instead. Furthermore, we show that the suboptimality of the TDMA slope region, which was already shown for multi-user channels with Gaussian inputs, persists.