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In this paper the problem of maximizing the multi-user capacity of Gaussian multiple-input multiple-output (MIMO) broadcast channels (BC) under total power constraint is considered. Although dirty-paper coding (DPC) is capacity achieving for this channel, employing dirty-paper coding is a computationally complex non-convex problem. To deal with this problem, many algorithms use iterative procedures to find the optimal solution. However, when the number of active users is large, these algorithms introduce a high order of complexity and suffer from memory drawback. Best Group (BG) selection is a method to address this problem. We propose a new BG selection algorithm that when is used jointly with the iterative dirty paper coding algorithm, provides acceptable results. The main feature of the proposed algorithm is that it is more efficient in a sense of computationally complexity than the similar algorithms. In addition as our simulation results show the proposed algorithm not only is much faster than similar algorithms, but also, it has very negligible reduction in the BC capacity.

A novel self-adaption strategy for the parameter epsiv in epsiv-MOEA is proposed in this paper based on the analyses of the relationship between the value of epsiv and the maximum number of non-dominated solutions. Then this novel strategy is applied in epsiv-MOEA and tested on 10 common benchmark functions. The experimental results demonstrate that even if without the good initial value for the parameter s, epsiv-MOEA with this self-adaption strategy (named Algorithm 1) is able to approximately obtain the expected number of non-dominated solutions, which are very close to and uniformly distributed on the Pareto-optimal front. Furthermore, the genetic drift phenomenon in Algorithm 1 is discussed Two cases of genetic drift are pointed out, and one case can be fixed up by a simple approach proposed in this paper.

This paper deals with the design of coding schemes for lossy transmission of a source over a broadcast channel when there is correlated side information at the receivers. Using ideas from Slepian-Wolf coding over broadcast channels and dirty paper coding, new schemes are presented and their rate-distortion performance is derived. For the binary Hamming and quadratic Gaussian scenarios, when the source and the channel bandwidths are equal, it is shown that these schemes are sometimes optimal and that they can outperform both separate source and channel coding, and uncoded transmission.

A kind of method for small-shaped space target recognition was proposed in this paper based on feature extraction with wavelet decomposition and formative support vector machine (FSVM) with sequential minimal optimization (SMO) algorithm. Firstly, the significance and characteristics of space target recognition were discussed and a two-stage recognition strategy was designed. And then aiming at the characteristics of small-shaped space target recognition, a new method was implemented based on feature extraction with wavelet decomposition and FSVM with SMO algorithm. Simulation results show the good performance of the algorithm proposed in this paper: the correct rate is more than 97% within 1360 simulation samples of ten classes of small shaped space targets; meanwhile the algorithm is characterized with high speed of near real time in both implementation of training and testing.

Wyner-Ziv coding (WZC) is a compression technique which uses decoder side-information to help reconstruction. The vector WZC is a key element to solve the vector Gaussian CEO problem for sensor networks. Compared with the scalar CEO problem, in the vector CEO problem sensor node array is used by each agent and a vector source is to be estimated. In this paper, we present a nested-lattice based vector WZC structure, which is a generalization of the scalar WZC proposed by Zamir et al. The key is to explore the duality between the WZC problem and the dirty paper coding (DPC) problem. This coding structure is shown to be able to achieve the Berger-Tung sum rate, which is the best known compression rate for the CEO problem.

In the previous works, performance of different transmission algorithms in multi-antenna multi-user MIMO broadcast channel were investigated. The result showed that Eigenmode Dirty Paper Coding (EM-DPC) algorithm was superior to the others. Nevertheless, the problem of EM-DPC is that the precoding algorithm significantly increases Peak-to- Average Power Ratio (PAPR). In this paper, to face with the PAPR problem, we propose a new algorithm called Eigenmode Tomlinson-Harashima Precoding (EM-THP), by introduction of modulo operations at both the transmitter and the receiver. It is found from numerical analyses that the proposed method can approximately achieve the throughput performance of the ideal EM-DPC while limiting the PAPR to a lower level.

The paper analyzes a downlink system where a 2-antenna base station is sending independent signals to two 2-antenna mobile users simultaneously in the same physical (time and frequency) channel. To multiplex the signals in the spatial domain, we consider the use of orthogonal space-division multiplexing (OSDM), broadly known as generalized zero-forcing (GZF), that allows the users to be completely separated before decoding. The paper's main contribution is that we derive the optimal array processing solutions for both the sum-rate maximization problem, subject to a fixed transmit power constraint, and the sum-power minimization problem, subject to a fixed rate constraint. The capacity and signal-to-noise ratio (SNR) regions for the OSDM system are also derived, and results for dirty-paper coding (DPC) and time-division systems are provided for comparison.

Multiple watermarking is concerned with embedding several messages into the same host signal, with different robustness and transparency requirements. This paper proposes two implementable scalar schemes for multiple user "dirty paper coding". The first - straightforward - approach consists of an independent superposition of two scalar dirty paper coding schemes. The second consists in the joint design of a scalar dirty paper coding. This joint approach is based on the ideal dirty paper coding scheme for broadcast channels with noncausal side information known to the transmitter. For this purpose, the "scalar Costa scheme" that has been originally conceived for one user is extended to two users. Performance evaluations, including bit error rates and capacity region curves are provided for both methods, illustrating the improvements brought by a joint design.

Multiple user information embedding is concerned with embedding several messages into the same host signal. While emphasizing the tight relationship with conventional multiple user information theory, this paper presents several implementable "dirty paper coding" (DPC) based schemes for multiple user information embedding. These are obtained by exploring strong connections with the well-known Gaussian multiple access channel (MAC) with state information at the encoders. Two practical schemes are compared. The first -rather intuitive- consists in a straightforward superimposition of DPC schemes. The second consists in a joint design of these dirty paper coding schemes, based on the ideal DPC-based coding for the equivalent MAC channel. These results extend to the multiple user case the practical implementations (QIM and SCS) that have been originally conceived for one user. Then, we extend the results to a more general coding based on lattice (vector) codebooks, showing that the gap to full performances can be bridged up by using finite dimensional lattice codebooks, at the cost of an increased computational complexity. The improvements brought by a joint design are illustrated by bit error rates curves and achievable rates region

The sum rate capacity of the multi-antenna Gaussian broadcast channel has recently been computed. However, the search for computationally efficient practical schemes that achieve it is still in progress. When the channel state information is fully available at the transmitter, the dirty paper coding (DPC) technique is known to achieve the maximal throughput, but is computationally infeasible. In this paper, we analyze the asymptotic behavior of one of its alternatives - the recently suggested so-called vector perturbation technique. We show that for a square channel, where the number of users is large and equal to the number of transmit antennas, its sum rate approaches that of the DPC technique. More precisely, we show that at both low and high signal-to-noise ratio (SNR), the scheme under consideration is asymptotically optimal. Furthermore, we obtain similar results in the case where the number of users is much larger than the number of transmit antennas.

In this paper, we study the limited feedback model for partial CSI at the basestation (BS) for multiple antenna broadcast channels: the BS has the knowledge of quantized CSI of each user. We first give a practical limited feedback scheme designed for multiple antenna broadcast channels. Then, we study the sum rate performance of zero-forcing dirty paper coding under the proposed limited feedback scheme. An upper bound is also derived to get some insight about the impact of the use of limited feedback. Interestingly, we find that the systems experience a ceiling effect on the sum rate for a fixed feedback rate.

The sum-capacity of a multi-antenna broadcast Gaussian channel is known to be achieved by Dirty Paper Coding techniques, or, asymptotically in the number of users n, by beamforming methods, that require full channel state information at the base station. Based on the opportunistic beamforming principle, it has been recently shown that the optimal scaling law of the sum-rate with respect to n, for fixed signal to noise ratio and number of transmitting antennas M, (i.e., M log log n) can be achieved by employing a feedback of only one real and one integer number per user. Moreover, it was proved that a linear scaling with respect of M can be guaranteed only if M scales no faster than log n. In this paper, the optimal scaling law of the sum-rate with respect to n is proved to be achievable with only one bit of feedback per user. The proof builds on opportunistic beamforming and binary quantization of the signal to noise plus interference ratio. Moreover, the linear scaling of the sum-rate with M is demonstrated to hold for M growing no faster than log n even with such a reduced feedback. Finally, the results above are extended to the MIMO case, where each user is equipped with multiple antennas.

The paper provides a proof of the converse for the capacity region of the Gaussian MIMO broadcast channel under total average transmit power constraint. The proof uses several ideas from earlier works on the problem including the recent converse proof by Weingarten, Steinberg and Shamai. First the duality between Gaussian multiple access and broadcast channels is employed to show that every point on the boundary of the dirty paper coding region can be represented as the optimal solution to a convex optimization problem. Using the optimality conditions for this convex problem, a degraded broadcast channel is constructed for each point. It is then shown that the capacity region for this degraded broadcast channel contains the capacity region of the original channel. Moreover, the same point lies on the boundary of the dirty paper coding region for this degraded channel. Finally, the standard entropy power inequality is used to show that this point lies on the boundary of the capacity region of the degraded channel as well and consequently it is on the boundary of the capacity region of the original channel.

In this paper, the multiple access channel (MAC) with channel state is analyzed in a scenario where a) the channel state is known non-causally to the transmitters and b) there is perfect causal feedback from the receiver to the transmitters. An achievable region and an outer bound are found for a discrete memoryless MAC that extend existing results, bringing together ideas from the two separate domains of MAC with state and MAC with feedback. Although this achievable region does not match the outer bound in general, non-trivial conditions are found where they meet. In the case of Gaussian MAC, a specialized achievable region is found by using a combination of dirty paper coding and a generalization of the Schalkwijk-Kailath (1966), Ozarow (1984) and Merhav-Weissman (2005) schemes, and this region is found to be capacity achieving. Specifically, it is shown that additive Gaussian interference that is known non-causally to the transmitter causes no loss in capacity for the Gaussian MAC with feedback

This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n + M log P/M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n rarr infin. When the channel exhibits some spatial correlation with a covariance matrix R (non-singular with tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n + M log P/M + log det(R) + o(1). We further show that the sum-rate of various beamforming schemes achieves M log log n + M log P/M + M log c + o(1) where c les 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in M. Sharif et al. (2005) and more generally, for random beamforming with preceding in which beams are pre-multiplied by a fixed matrix. Simulation results are presented at the end of the paper.

For multiple antenna broadcast channels, perfect channel state information (CSI) at the basestation plays a critical role in achieving the sum rate advantage provided by the multiple antennas. For practical system implementation, the CSI is usually estimated from training sequences. In this paper, we study the effect of channel estimation error on the sum rate capacity of multiple antenna broadcast channels. A lower bound is derived based on the sum rate performance of the zero forcing dirty paper coding scheme under CSI estimation error. A cooperative upper bound is established from the capacity upper bound of a single user multiple-input multiple-output (MIMO) channel given the same channel imperfectness. We further analyze the asymptotic sum rate loss caused by channel estimation error. If we assume that the variance of the channel estimation error is fixed, imperfect CSI results in a sum rate ceiling for high SNR. For systems with orthogonal training sequences and minimum mean square error (MMSE) channel estimator, the asymptotic sum rate loss is about N bit per channel use where N is the number of transmit antennas. I. INTRODUCTION Techniques employing multiple antennas are important for wireless communication systems because they provide the possibility of a significant increase in system spectrum effi- ciency. In the last decade, lots of works have been done on point-to-point, i.e., single user, multiple-input multiple-output (MIMO) systems. Larger rate gains, however, are available when MIMO multi-user systems are considered. Recently, the sum rate capacity of the multiple antenna broadcast channel, which models the downlink in a MIMO cellular network, was solved (1), (2), (3), (4). These works show that perfect channel state information (CSI) at the basestation is critical for the system to achieve the sum rate advantage. With perfect CSI

This paper derives scaling laws of the sum rate throughput for MIMO Gaussian broadcast channels using time-sharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Assuming a fixed total average transmit power, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nTV for DPC and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and TV are fixed, the sum rate of time-sharing to the strongest user scales like min(M,N) log log n. It is also shown that if M grows as logn, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of time-sharing scales like N log log n.

Multiuser multiple-input multiple-output (MU-MIMO) systems can achieve higher data rates compared to single user (SU-MIMO) by exploiting multi-user diversity. The capacity bound for MU-MIMO systems is given by the MIMO broadcast channel (BC) capacity. Dirty paper coding (DPC) is a well known non-linear algorithm to achieve this bound. Zero forcing DPC (ZF-DPC) is a sub-optimal way to achieve DPC by triagularizing the channel. In our previous work, we had proposed an enhancement of ZF-DPC by introducing additional receiver which was shown to improve the achievable rates over linear schemes such as block diagonalization. In practise Block Diagonalization is implemented by the receiver feeding back quantized information about the channel and the transmitter figuring out the precoders subsequently. To establish a comparison of ZF-DPC to Block Diagonalization for such practical feedback, we first derive the framework for operating ZF-DPC with quantized feedback. Next we compare the performance of ZF-DPC over Block Diagonalization with quantized feedback and demonstrate that the former still performs better.

This paper presents classification of the quality of agarwood oils from Malaysia using Z-score technique. Six agarwood oil samples named as MU, MUS, MN, MNS, R5 and HD are analyzed by GC-MS to examine their chemical profiles. The extraction showed that at least forty three volatile compounds are found. The Z-score technique is proposed to identify the significant chemical compounds of the agarwood oils. It is found that six chemical compounds are recognized. They are β-agarofuran, α-agarofuran, 10-epi-□-eudesmol, α-eudesmol, dihydrocollumellarin and □-eudesmol. These volatile compounds have different abundances pattern responsible to the different qualities of agarwood oil such as high and low. The Z-score applied in this study give a promising result in discriminating agarwood oil to high and low quality. It is important and useful in solving the grading agarwood oil system which is currently done manually.

We consider the minimization of the energy per bit (or, equivalently, the maximization of the energy efficiency) in multiple-input multiple-output (MIMO) broadcast channels with rate balancing constraints for fairness between users, and we propose a framework to find the globally optimal energy-efficient solution, which relies on dirty paper coding (DPC). The main idea is to introduce a continuous, differentiable, and concave optimal rate function, which transforms the problem into a convex-concave fractional program in one scalar variable. This not only allows an efficient solution, but also an intuitive interpretation of the method as well as the possibility to extend the method to related problems. In numerical simulations, we compare the energy efficiency with and without fairness constraints.

Fuzzy Inference System was designed to select the combination of feedstock that would provide over 55% methane yield in an anaerobic biogas digester at the same time maintaining neutral pH in it. This area was left untouched by fuzzy system experts in spite of the great importance it holds in determining the retention time of feedstock inside the digester which directly influences digester design dimensions. An FIS based on ‘Mamdani style’ was designed with six Fuzzy ‘If-then’ rules to act on two input variables of Feed stocks-C/N Ratio and Methane Yield that the feed stocks produced on anaerobic decomposition. The output was defuzzified using ‘centroid method’ to classify the Feedstock as ‘Select’ or ‘Reject’. Feedstock 1 with a C/N ratio of 16.5 and a methane yield of 65% was rejected with a membership of only 0.28 on the output selection scale. Feedstock 2 with a C/N of 25.8 and a methane yield of 70 % met 66 % of the selected feedstock criteria framed while Feedstock 3 proved the most suitable feedstock material featuring at 0.73 on the Feedstock selection membership scale with a C/N of 30.8 and 85% methane yield. The FIS model designed was evaluated for all combinations of C/N Ratio and methane yield. Feedstock belonging to [20–37.5] C/N range yielding at least 55% methane yield fell among the selected category of feedstock. Highest (6–7) membership range of selected feedstock was occupied by feed stocks between 25 to 35 C/N range yielding around 57.2% to 100% methane.

In this paper, a new approach is presented for the control large-scale spatially distributed systems. These systems are encountered in several applications such as automated vehicles in a platoon, micro electro mechanical systems and paper machine processes. In order to obtain tractable algorithms, existing methods for the control of large-scale systems assume that they are spatially invariant, which usually means that the systems considered have infinite spatial extent. This paper shows how to achieve spatial invariance for systems that are finite in space, thus making the tractable linear matrix inequality-based algorithms for the control of spatially invariant systems available for practical application.

An extended car-following model is proposed in this paper based on the idea of the dynamical cooperation between nearest-neighbor vehicles. The stability condition of the new model is derived by using the linear stability theory. By using the reductive perturbation method and nonlinear analysis, the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic density waves in the unstable region. And the corresponding kink-antikink solution is used to describe the traffic congestions. It is found that the dynamical collaboration between two consecutive vehicles can further stabilize traffic flow and suppress traffic jams effectively, which is verified by direct numerical simulations.

A dynamic recognition factor is proposed in this paper based on the concept of approximate entropy. We transform the DNA sequence into time sequence by graphical representation, and identify the similarity of DNA sequence by calculating the dynamic recognition factor between different DNA sequences. This method has been proofed available for the five DNA sequences.

This paper based on the rough set attribute reduction algorithm analysis and exposition. From theory of algorithms, algorithm performance and other aspects, the author undertook an analysis, classification, research and summary. On the attribute reduction algorithm based on rough set for the future research work is prospected and discuss.

In this short paper we give an affirmative answer to the problem left open in \cite{IEEE how to: GDCK}, that is, for any residuated lattice $L$, if prime filters and prime filters of the second kind coincide, then $L$ must be an MTL-algebra.

Since subjectivity of opinions can be more effectively manipulated in the framework of fuzzy set theory, it is promising way to aggregate experts' judgments using fuzzy set theory. In this short paper, a simple method to aggregate experts' opinions is proposed. In our method, the multiplication operation on fuzzy numbers based on graded mean integration representation is used to simple the aggregation procedure. In addition, since the confidence indices for experts are obtained as crisp number, the final weight of each expert can be calculated without setting the degree of optimism, which also contributes the less complexity of the proposed method. An example in nuclear power plant is used to illustrate the efficiency of the proposed method.

The performance of a multiuser MIMO broadcast system depends highly on how the users being served are selected from the pool of users requesting service. Though dirty paper coding can obtain the optimal capacity of multiuser MIMO Broadcast systems, the computational complexity is high. We examine this problem in the context of systems using Zero Forcing Beamforming (ZFBF) which have low complexity and reasonable throughput. The channels of the selected users may not be orthogonal to each other resulting in harmful interference and reduction in the performance of the system. This work identifies and thoroughly investigates the main factors affecting the performance and proposes some mitigating schemes to fully exploit multiuser diversity. In particular, we develop improved user selection schemes designed to maximize the sum rate that offer a range of complexity to performance tradeoff. Simulation results show that the selection schemes developed compare favorably with existing techniques.

In this paper, straw and rice bran is the object of the molding process. It analyzes the impact of straw and rice bran mixture ratio and temperature on the main indicators of forming fuel. Based on the LS-SVM, multi-objective optimization function and the model of the straw and rice bran mixed-compression molding process have been established. Also the model and molding process has been tested and optimization with the experimental data. The results show that the model prediction and experimental values of the average maximum relative error is 1.59%, with good simulation results. Meanwhile, when the proportion of rice straw is 55.9% and the molding temperature is about 129.07°C, the optimal value is very close to the experimental maximum value and the maximum relative error is 2.86%.

A new construction of frequency hopping (FH) sequences, designated as cubic prime sequences, is presented in this paper based on the multiplication of extension Galois field GF(P3) with P an odd prime. Cubic prime sequences provide more sequences, longer period and more families compared with prime sequences, with ideal Hamming auto-correlation properties and maximum Hamming cross-correlation value four. And after partition, FH sequences in the same group show ideal Hamming cross correlation properties.

Compared with capacity-achieving dirty paper coding [1], block diagonalization (BD) algorithm [2] is known as a suboptimal but more practical beamforming scheme for multiuser MIMO downlink systems with multiantenna users. However BD suffers from two major drawbacks: the dimensionality constraint on antennas arrangement and the difficulty in handling spatially correlated users. User selection capable of selecting some most sum-rate-contributive users is a promising measure to alleviating this situation.

The operation of the multiple input multiple output (MIMO) Gaussian broadcast channel (BC) with K transmit antennas and K over r users with r receive antennas each is analyzed when channel state information (CSI) is obtained at the transmitter from the ith user via finite-rate feedback link of capacity B i bits. It is proved that if B i is scaled at the rate of α i r(K - r) log 2 P, where P is the transmit power and α ∈ [0, 1], then using dirty paper coding (DPC), the multiplexing gain of α i r can be achieved for user i. This result on the feedback scaling rate rests on an elegant achievability scheme, the construction of which brings to light several new insights on the manner in which DPC achieves the complete multiplexing gain in the perfect-CSIT case.

A heterogeneous multiple-input-multiple-output (MIMO) broadcast (BC) system is considered, with some of the users having target-rate requirements while other users are working with best-effort data rates. We assume the use of dirty paper coding, and we exploit the duality between the capacity regions of the multiple access and broadcast channels in order to optimally and jointly optimize the rates, powers and decoding order. We use the concept of stream achievable rate region (rather than user achievable rate region) and show that the best-effort users can achieve higher rates when the data streams of any user are not restricted to be decoded consecutively and when timesharing between different decoding orders is allowed. It is shown that the problem can be formulated as a convex optimization problem. We also propose an algorithm to obtain the time-sharing factors and decoding orders (corner points) required to achieve the optimal solution.

RST invarian watermarking scheme is proposed in this paper based on the SIFT feature points and improved pseudo-Zernike moment. Firstly, feature points are detected using SIFT, and some suitable points are selected to form localized feature regions which are scaled to a standard sized. After computing these regions by the improved pseudo-Zernike moments of these regions , the digital watermark are embedded into the host image by quantizing some low-lever moments. Experimental results show this scheme is robust against the rotation, shearing, JPEG compression, noise and filtering attack.

The cognitive radio MIMO Gaussian broadcast channels model is proposed, and the capacity is also studied under both the cognitive users' transmit power constraint and a set of interference power constraints at the licensed receivers. A duality technique and dirty paper coding (DPC) are used to simplify channel model where multiple antennas are available for both licensed and cognitive users in a spectrum sharing environment. Subgradient iterative power allocation (SIPA) algorithm is also used to solve the parameters of constraint in order to obtain the optimal values. Our analysis and simulation results show that the proposed channel model can be suitable for multiple cognitive users and a few of licensed users with multiple antennas.

This work introduces an information-theoretic lower bound on the number of fundamental cycles for bipartite graphs of low-density parity-check (LDPC) code ensembles. This information-theoretic bound is expressed in terms of the achievable gap to capacity when the transmission of the code ensemble takes place over a memoryless binary-input output-symmetric (MBIOS) channel. The bound shows quantitatively the necessity of cycles in bipartite graphs which represent good LDPC code ensembles. More explicitly, it shows that the number of fundamental cycles should grow at least like log 1/e where e designates the gap in rate to capacity, hence, it is unbounded as the gap to capacity vanishes. For the derivation of this bound, a new information-theoretic lower bound on the average right degree, which also behaves like log 1/e, is derived. The interested reader is referred to the full paper version [9].

We study a rate-limited version of the well known problem of coding for channels with random parameters which was studied by Gelfand and Pinsker [1]. In particular, we consider a state-dependent channel when the transmitter is supplied with the state information at a rate R e . We obtain a new upper bound on the capacity, C(R e ), for this channel. We explicitly evaluate this upper bound for the rate-limited dirty paper coding (DPC) problem and show that it strictly improves upon the DPC capacity for certain values of R e .

We consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems. If the state space matrices of these systems satisfy a certain structural property, then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant. This procedure is basically a multiobjective optimization under linear matrix inequality constraints, with system norms as performance indices. The explicit expressions for computing these controllers are given for both H infin or H 2 performance, and both for static state feedback and dynamic output feedback (in discrete time). At the end of the paper, two application examples illustrate the effectiveness of the approach.

We present a high SNR analysis of the rate region geometry when linear filtering is applied in the MIMO broadcast channel and time sharing is not considered. In particular, the set of weakly Pareto optimal points of the asymptotic rate region is derived. While all different permutations of user sorting have to be investigated for the complete rate region when nonlinear dirty paper coding is applied, we show that the analogon to different sorting orders is the number of active streams per user when linear filtering is applied. Furthermore, we reveal that only a small fraction of weakly Pareto optimal points is in charge of maximizing an asymptotic weighted sum rate and points belonging to that fraction are all obtained when every user applies full multiplexing. In contrast, switching off some data streams may be optimal when it comes to balancing or maximizing a user's rate while keeping the other users' rates constant. Many of the derived results are not only applicable to systems with enough antennas at the base station, but also to configurations with too few degrees of freedom, which so far have never been discussed in any asymptotic analysis before.

To avoid the complexity of nearly optimum implementations for dirty paper coding (DPC) linear zero-forcing approaches are often preferred. Finding the optimum user allocation, transmit and receive filters for maximizing sum rate in the multiple-input multiple-output (MIMO) broadcast channel constitutes a non-convex combinatorial optimization problem. Here we present an efficient linear zero-forcing algorithm for this problem, which is derived from maximizing a lower bound for the sum rate. It successively allocates data streams to users and in contrast to state of the art approaches thereby also determines the corresponding receive filters. Compared to existing approaches drastic complexity reductions can be achieved even with slight performance gains.

Multiuser trellis shaping for space-time trellis codes (STTC) is proposed to realize dirty paper coding (DPC) in downlink multiuser channel, which is sometimes referred to as vector Gaussian broadcast channel. Our proposal considers not only the current transmit signal, but also the entire sequence of the signal for multiple users to achieve the higher capacity. In our proposal, the STTC is transmitted to each user and preceding is used to pre-subtract the interference among the users. An increase in transmit power due to the preceding is reduced by trellis shaping that adds trellis codewords to the information sequence for each user. The shaping code and the STTC are separated in order to systematically design both codes in our system. Simulation results indicate that the shaping gain of more than 3 dB is achieved by applying the different shaping codes for each user, and that frame error rate of the proposed scheme shows better performance than that of the conventional Tomlinson-Harashima precoding.

We give graph-theoretic formalization of origami, the art of paper folding. Starting from the abstract origami system, we model origami construction as are write sequence of abstract origami's. To reason about the entire origami construction for the computational purposes, we define a labeled hypergraph for origami and give the abstraction of origami fold as a set of algebraic graph rewrite rules. We give detailed description of the fold operation in terms of graph rewriting. The graph-theoretic formalism enables us to reason in two separate domains of discourse, i.e. pure combinatoric domain and geometrical domain R2.

Modern coding applications, including dirty paper coding and information hiding, hinge critically on a classical 'general decoding problem,' known to be NP hard. Various attempts to find good solutions at reasonable complexity can be traced throughout the decades, most recently with attempts to achieve the rate-distortion bound in code word quantization. Here we take a step back to examine two computationally simple procedures in this direction: gradient decoding and a simple yet surprisingly effective variant on belief propagation that we dub truthiness propagation.