Complexity Reduction Techniques Research Articles

A novel computational complexity and power reduction technique for H.264 intra prediction

H.264 intra prediction algorithm has a very high computational complexity. This paper proposes a novel technique for reducing the amount of computations performed by H.264 intra prediction algorithm and therefore reducing the power consumption of H.264 intra prediction hardware significantly without any PSNR and bitrate loss. The proposed technique performs a small number of comparisons among neighboring pixels of the current block before the intra prediction process. If the neighboring pixels of the current block are equal, the prediction equations of H.264 intra prediction modes simplify significantly for this block. By exploiting the equality of the neighboring pixels, the proposed technique reduces the amount of computations performed by 4times4 luminance, 16times16 luminance, and 8times8 chrominance prediction modes up to 60%, 28%, and 68% respectively with a small comparison overhead. We also implemented an efficient 4times4 intra prediction hardware including the proposed technique using Verilog HDL. We quantified the impact of the proposed technique on the power consumption of this hardware on a Xilinx Virtex II FPGA using Xilinx XPower, and it reduced the power consumption of this hardware up to 18.6%.

Antenna and User Subset Selection in Downlink Multiuser Orthogonal Space-Division Multiplexing

Block diagonalization (BD) and successive optimization (SO) are two suboptimal but more practical (compared to dirty paper coding (DPC)) orthogonal linear precoding techniques for the downlink of multiuser MIMO systems. Since the numbers of users supported by BD or SO for a given number of transmit antennas are limited, BD or SO should be combined with scheduling so that a subset of users is selected at a given time slot while meeting the dimensionality requirements of these techniques. On the other hand, receive antenna selection (RAS) is a promising hardware complexity reduction technique. In this paper, we consider user scheduling in conjunction with receive antenna selection. Since exhaustive search is computationally prohibitive, we propose simplified and suboptimal user scheduling algorithms for both BD and SO. For BD, we propose capacity and Frobenius-norm based suboptimal algorithms with the objective of sum rate maximization. Starting from an empty set, each step of proposed algorithms adds the best user from the set of users not selected yet until the desired number of users have been selected. Proposed receive antenna selection works in conjunction with user scheduling to further enhance the sum rate of BD. For SO, a Frobenius-norm based low complexity algorithm is proposed, which maximizes the ratio of the squared Frobenius norm of the equivalent channel (projected to the joint null space of the previously selected users) to the sum of the squared Frobenius norms of the previously selected users' preprocessed channels. Simulation results demonstrate that the proposed algorithms achieve sum rates close to exhaustive search algorithms with much reduced complexity. We also show that in addition to reduced hardware complexity at the receiver, antenna selection enhances multiuser diversity gain that is achieved with user scheduling.

Multiframe superresolution of binary images

We describe a new algorithm for superresolving a binary object from multiple undersampled low-resolution (LR) images that are degraded by diffraction-limited optical blur, detector blur, and additive white Gaussian noise. Two-dimensional distributed data detection (2D4) is an iterative algorithm that employs a message-passing technique for estimating the object pixel likelihoods. We present a novel non-training-based complexity-reduction technique that makes the algorithm suitable even for channels with support size as large as 5 x 5 object pixels. We compare the performance and computational complexity of 2D4 with that of iterative backprojection (IBP). In an imaging system with an optical blur spot matched to the object pixel size, 2 x 2 undersampled measurement pixels, and four LR images, the reconstruction error measured in terms of the number of pixel mismatches for 2D4 is 300 times smaller than that for IBP at a signal-to-noise ratio of 38 dB.

A comparative study of single-phase and two-phase approaches for the layout problem with material handling costs

A comparative study of one- and two-phase procedures for material handling cost-based layout problems is presented. A cost function that explicitly accounts for heterogeneous material handling equipment is used as the objective criterion and simulated annealing based search procedures are used to determine layout solutions. Simulated annealing is applied directly in the one-phase procedure and augmented with volume distance based clustering of work centres in the two-phase procedure to reduce computational complexity. The performance of the two approaches are tested on 180 sample problems with 40 work centres that differ in terms of material flow matrix density, work centre space requirements, and variation in the distribution of material flow matrix elements. The results indicate that complexity reduction techniques using surrogate objectives based on volume distance might not always result in layouts that reduce material handling cost.

A maximum a posteriori MIMO detector using recursive metric computations

A complexity reduction technique for soft-output maximum a posteriori probability detection in wireless multiple-input multiple-output (MIMO) channels using rectangular quadrature amplitude modulation (QAM) constellations is derived. In contrast to existing low-complexity detection schemes that reduce the number of candidate tests, we instead focus on lowering the computational burden per candidate. The search over a large number of hypotheses to generate output L-values is facilitated by a doubly recursive mechanism, exploiting differential updates of the distance metrics from candidate to candidate. Moreover, the search over all transmit candidates is simplified using a hierarchical "triangular" (zig-zag) shaped candidate scanning order. The technique is derived conceptually using mathematical terms, and then illustrated by means of a 2 times 2 MIMO system using 64-QAM modulation. Under certain practical assumptions, the new scheme is shown to reduce the overall number of operations per candidate by a factor of about 50-100. While the concept is demonstrated by means of the exhaustive search case, it can be combined with other search-based MIMO detection techniques such as spherical decoding

On LDPC codes over channels with memory

The problem of detection and decoding of low-density parity-check (LDPC) codes transmitted over channels with memory is addressed. A new general method to build a factor graph which takes into account both the code constraints and the channel behavior is proposed and the a posteriori probabilities of the information symbols, necessary to implement maximum a posteriori (MAP) symbol detection, are derived by using the sum-product algorithm. With respect to the case of a LDPC code transmitted on a memoryless channel, the derived factor graphs have additional factor nodes taking into account the channel behavior and not the code constraints. It is shown that the function associated to the generic factor node modeling the channel is related to the basic branch metric used in the Viterbi algorithm when MAP sequence detection is applied or in the BCJR algorithm implementing MAP symbol detection. This fact suggests that all the previously proposed solutions for those algorithms can be systematically extended to LDPC codes and graph-based detection. When the sum-product algorithm works on the derived factor graphs, the most demanding computation is in general that performed at factor nodes modeling the channel. In fact, the complexity of the computation at these factor nodes is in general exponential in a suitably defined channel memory parameter. In these cases, a technique for complexity reduction is illustrated. In some particular cases of practical relevance, the above mentioned complexity becomes linear in the channel memory. This does not happen in the same cases when detection is performed by using the Viterbi algorithm or the BCJR algorithm, suggesting that the use of factor graphs and the sum-product algorithm might be computationally more appealing. As an example of application of the described framework, the cases of noncoherent and flat fading channels are considered

CSDC: a new complexity reduction technique for multiplierless implementation of digital FIR filters

We present a computation reduction technique called computation sharing differential coefficient (CSDC) method, which can be used to obtain low-complexity multiplierless implementation of finite-impulse response (FIR) filters. It is also applicable to digital signal processing tasks involving multiplications with a set of constants. The main component of our proposed CSDC method is to combine the strength of the augmented differential coefficient approach and subexpression sharing. Exploring computation reuse through algorithmic equivalence, the augmented differential coefficient approach greatly expands the design space by employing both differences and sums of filter coefficients. The expanded design space is represented by an undirected and complete graph. The problem of minimizing the adder cost (the number of additions/subtractions) for a given filter is transformed into a problem of searching for an appropriate subexpression set that leads to a minimal adder cost. A heuristic search algorithm based on genetic algorithm is developed to search for low-complexity solutions over the expanded design space in conjunction with exploring subexpression sharing. It is shown that up to 70.1% reduction in the adder cost can be obtained over the conventional multiplierless implementation. Comparison with several existing techniques based on the available data shows that our method yields comparable results for multiplierless FIR filter implementation.

7.1.1 Integrating Views in a Multi‐view Modelling Environment

AbstractThe development of modern technical systems requires the close collaboration of various specialist teams and engineering disciplines in order to reach the expected complex functionality. Even though working with the same system towards the same goal, developers from the different domains use their own specific tools, providing their own specific views of the system to be developed. For the successful integration of the efforts from each of these disciplines, the different views produced need to be appropriately integrated, preventing any inconsistencies and divergences from creeping into the system design.We present an approach to multi‐view modelling which systematically integrates the two generally accepted complexity reduction techniques of hierarchical decomposition and multi‐viewing. While these techniques are common practice in many modern design tools, the approach presented in this paper defines how the inter‐view relationships can be used to tightly interweave the views' hierarchies. This provides a good basis for an information sharing environment enabling model based, multi‐disciplinary development.A small case study is used to exemplify how the proposed method simplifies the process of allocating system functions to a hardware architecture in a truck.

Reduced complexity interleaver growth algorithm for turbo codes

This paper is focused on the problem of significantly reducing the complexity of the recursive interleaver growth algorithm (IGA) with the goal of extending the range of applicability of the algorithm to significantly larger interleavers for a given CPU time and processor. In particular, we present two novel modifications to IGA changing the complexity order of the algorithm from O(N/sub max//sup 4/) to O(N/sub max//sup 2/), present several further minor modifications reducing the CPU time albeit not fundamentally changing the complexity order, and present a mixed mode strategy that combines the results of complexity reduction techniques that do not alter the algorithm outcome itself, with a novel transposition value set cardinality constrained design that does modify the optimization results. The mixed strategy can be used to further extend the range of interleaver sizes by changing the complexity order from O(N/sub max//sup 2/) to O(N/sub max/) (i.e., linear in the interleaver size). Finally, we present optimized variable length interleavers for the Universal Mobile Telecommunications System (UMTS) and Consultative Committee for Space Data Systems (CCSDS) standards outperforming the best interleavers proposed in the literature.

Adaptation of TS Fuzzy Models Without Complexity Expansion: HOSVD-Based Approach

One direction of measured data-set based modeling applies fuzzy logic identification tools and results in a fuzzy rule-base model. A typical problem of fuzzy identification methods is that the complexity of the resulting fuzzy rule-base, namely the number of rules in the rule-base, explodes with the modeling accuracy. As a result, the topic of fuzzy rule-base complexity reduction techniques emerged in the last decade. A common disadvantage of fuzzy rule-base complexity reduction methods is that the resulting complexity minimized fuzzy-rule bases cannot be simply adapted to new information. If we have new information that cannot be described by the fuzzy rules of the complexity minimized fuzzy rule-base, then we have two choices. The first choice is to add new fuzzy rules to the fuzzy rule-base until the new information can be described. The second choice is to modify the new information until it can be described by the fuzzy rule-base without using additional fuzzy rules. This second case has the prominent role if the number of fuzzy rules in the fuzzy rule-base is limited. This paper proposes a method for the second choice. The proposed method minimizes the necessary modification of the new information. This paper focuses attention on a recent complexity reduction method, termed Higher Order Singular Value Decomposition (HOSVD)-based complexity reduction, and Takagi-Sugeno (TS) inference operator-based fuzzy rule-bases. An example is used to provide the validation of the proposed method. In order to demonstrate the effectiveness of the proposed method, a control system of a differential-steered automatic guided vehicle is modeled in the paper.

On Soft-Input Soft-Output Decoding Using “Box and Match” Techniques

The box and match decoding algorithm (BMA) significantly reduces the computational complexity of the ordered statistic decoding algorithm at the expense of increased memory requirements. A soft-input/soft-output version of the BMA is developed. Additional complexity-reduction techniques are also described.

Scalable Variable Complexity Approximate Forward DCT

The discrete cosine transform (DCT) is one of the major components in most of image and video compression systems. The variable complexity algorithm framework has been applied successfully to achieve complexity savings in the computation of the inverse DCT in decoders. These gains can be achieved due to the highly predictable sparseness of the quantized DCT coefficients in natural image/video data. With the increasing demand for instant video messaging and two-way video transmission over mobile communication systems running on general-purpose embedded processors, the encoding complexity needs to be optimized. In this paper, we focus on complexity reduction techniques for the forward DCT, which is one of the more computationally intensive tasks in the encoder. Unlike the inverse DCT, the forward DCT does not operate on sparse input data, but rather generates sparse output data. Thus, complexity reduction must be obtained using different methods from those used for the inverse DCT. In the literature, two major approaches have been applied to speed up the forward DCT computation, namely, frequency selection, in which only a subset of DCT coefficients is computed, and accuracy selection, in which all the DCT coefficients are computed with reduced accuracy. These two approaches can achieve significant computation savings with minor output quality degradation, as long as the coding parameters are such that the quantization error is larger than the error due to the approximate DCT computation. Thus, in order to be useful, these algorithms have to be combined using an efficient mechanism that can select the "right" level of approximation as a function of the characteristics of the input and the target rate, a selection that is often based on heuristic criteria. In this paper, we consider two previously proposed fast, variable complexity, forward DCT algorithms, one based on frequency selection, the other based on accuracy selection. We provide an explicit analysis of the additional distortion that each scheme introduces as a function of the quantization parameter and the variance of the input block. This analysis then allows us to improve the performance of these algorithms by making it possible to select the best approximation level for each block and a target quantization parameter. We also propose a hybrid algorithm that combines both forms of complexity reduction in order to achieve overall better performance over a broader range of operating rates. We show how our techniques lead to scalable implementations where complexity can be reduced if needed, at the cost of small reductions in video quality. Our hybrid algorithm can speed up the DCT and quantization process by close to a factor of 4 as compared to fixed-complexity forward DCT implementations, with only a slight quality degradation in PSNR.

Reliability evaluation for acyclic transmission networks of multi-state elements with delays

Acyclic transmission networks (ATN) consist of a number of positions in which s-independent multi-state elements (ME) capable of receiving and/or sending a signal are allocated. Each network has: a root position where the signal source is located, a number of terminal positions that can only receive a signal, and a number of intermediate positions containing ME that retransmit the received signal to some other positions. The signal propagation is allowed only in direction of the terminal nodes, which avoids cycles in the network. Each ME that is located in a nonterminal node can have different states determined by a set of nodes receiving the signal directly from this ME. The probability of each state is assumed to be known for each ME. The signal retransmission process is associated with delays. The system fails if the signal generated at the first position (source) cannot reach the terminal nodes within a specified time. An algorithm for ATN reliability evaluation is suggested; it is based on an extended universal generating function method that uses a state enumeration approach. A procedure for recurrent derivation of probabilistic distribution of a vector representing delays in ATN is described. A technique for computational complexity reduction is developed.

SVD-based complexity reduction to TS fuzzy models

One of the typical important criteria to be considered in real-time control applications is the computational complexity of the controllers, observers, and models applied. In this paper, a singular value decomposition (SVD)-based complexity reduction technique is proposed for Takagi Sugeno (TS) fuzzy models. The main motivation is that the TS fuzzy model has exponentially growing computational complexity with the improvement of its approximation property through, as usually practiced, increasing the density of antecedent terms. The reduction technique proposed here is capable of defining the contribution of each local linear model included in the TS fuzzy model, which serves to remove the weakly contributing ones as according to a given threshold. Reducing the number of models leads directly to the computational complexity reduction. This work also includes a number of numerical and application examples.

Inference Algorithm Independent SVD Fuzzy Rule Base Complexity Reduction

This paper is motivated by the fact that fuzzy technique is popular engineering tool, however, its use is restricted by its exponential complexity. One of the complexity reduction techniques is the SVD based reduction method which deals with arbitrary shaped fuzzy sets. Despite its advantages it is applicable to rule bases only which are based on product-sum-gravity (PSG) inference algorithm. This paper introduces the extension of the PSG based SVD-reduction method to arbitrary inference based fuzzy algorithms. An example with the control of an automatic guided system is presented to demonstrate the reduction process.

Neural network analysis of follow-up data in primary breast cancer.

This paper reports on the performance of a recently developed neural network environment incorporating likelihood-based optimization and complexity reduction techniques in the analysis of breast cancer follow-up data with the goal of building up a clinical decision support system. The inputs to the neural network include classical factors such as grading, age, tumor size, estrogen and progesterone receptor measurements, as well as tumor biological markers such as PAI-1 and uPA. The network learns the structural relationship between these factors and the follow-up data. Examples of neural models for relapse-free survival are presented, which are based on data from 784 breast cancer patients who received their primary therapy at the Department of Obstetrics and Gynecology, Technische Universität München, Germany. The performance of the neural analysis as quantified by various indicators (likelihood, Kaplan-Meier curves, log-rank tests) was very high. For example, dividing the patients into two equally sized groups based on the neural score (i.e., cutoff = median score) leads to an estimated difference in relapse-free survival of 40% or better (80% vs. 40%) after 10 years in Kaplan-Meier analysis. Evidence for factor interactions as well as for time-varying impacts is presented. The neural network weights included in the models are significant at the 5% level. The use of neural network analysis and scoring in combination with strong tumor biological factors such as uPA and PAI-1 appears to result in a very effective risk group discrimination. Considerable additional comparison of data from different patient series will be required to establish the generalization capability more firmly. Nonetheless, the improvement of risk group discrimination represents an important step toward the use of neural networks for decision support in a clinical framework and in making the most of biological markers.

Efficient complexity reduction technique in trellis decoding algorithm

An efficient reduced search trellis decoding algorithm in which the decoder selects a part of existing paths by using a threshold value of the path metric is proposed. The threshold value at each time stage of the trellis is found by simply investigating the statistics of the path metrics, and does not require any prior knowledge such as the signal-to-noise ratio.

Soft output interference suppression in TDMA wireless communications

We present a novel symbol-by-symbol Bayesian multiuser detector for cochannel interference cancellation in TDMA cellular communications. To begin with, we present the usual composite signal model consisting of the desired signal, interferer, channel parameters and channel noise. Then, we derive the soft output interference cancellation algorithm (SICA) to compute fixed-lag maximum a posteriori (MAP) estimates of the data symbols of the desired user, using a fixed lookahead of D observations. In the process, the interferer symbols are treated as nuisance parameters and averaged out. The complexity of the SICA is exponential in the length of the combined channel at the receiver. Subsequently, we present a simple, yet effective, technique for complexity reduction without significant performance degradation. We apply the algorithm to some typical scenarios, using the IS-136 TDMA standard, to demonstrate its interference suppression capabilities. In this paper, we assume that all relevant channel parameters are known. Hence, our results should be viewed as representing the best possible performance that can be obtained with the SICA in the scenarios considered.

A complexity reduction technique for image vector quantization

A technique for reducing the complexity of spatial-domain image vector quantization (VQ) is proposed. The conventional spatial domain distortion measure is replaced by a transform domain subspace distortion measure. Due to the energy compaction properties of image transforms, the dimensionality of the subspace distortion measure can be reduced drastically without significantly affecting the performance of the new quantizer. A modified LBG algorithm incorporating the new distortion measure is proposed. Unlike conventional transform domain VQ, the codevector dimension is not reduced and a better image quality is guaranteed. The performance and design considerations of a real-time image encoder using the techniques are investigated. Compared with spatial domain a speed up in both codebook design time and search time is obtained for mean residual VQ, and the size of fast RAM is reduced by a factor of four. Degradation of image quality is less than 0.4 dB in PSNR.

Design and hardware architecture of high-order conditional entropy coding for images

High-order conditional entropy coding has not been practical due to its high complexity and lack of hardware to extract the conditioning state efficiently. The authors adopt the recently developed incremental-tree-extension technique to design the conditional tree for high-order conditional entropy coding. In order to make the high-speed conditional entropy coder feasible, they introduce several key innovations in the areas of complexity reduction and hardware architecture. For complexity reduction, they develop two techniques: code table reduction and nonlinear quantization of conditioning pixels. For hardware architecture, they propose a pattern-matching technique for fast conditioning state extraction and a multistage pipelined structure to handle the case of a large number of conditioning pixels. Using the complexity reduction techniques and the hardware structures. the authors demonstrate that it is possible to implement practical high-order conditional entropy codecs using current low-cost very large-scale integration (VLSI) technology.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>