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The Complexity of Iterated Multiplication

N. Immerman, S. Landau
1995 Information and Computation  
For a monoid G, the iterated multiplication problem is the computation of the product of n elements from G.  ...  By re ning known completeness arguments, we s h o w t h a t a s G varies over a natural series of important groups and monoids, the iterated multiplication problems are complete for most natural, low-level  ...  Thanks to two a n o n ymous referees who saved us embarrassment b y p o i n ting out some gaps in the logic of an earlier version of this paper.  ... 
doi:10.1006/inco.1995.1007 fatcat:3p2mpm7qbjfvtf4kogc3x2t67e

The complexity of iterated multiplication

N. Immerman, S. Landau
[1989] Proceedings. Structure in Complexity Theory Fourth Annual Conference  
For a monoid G, the iterated multiplication problem is the computation of the product of n elements from G.  ...  By re ning known completeness arguments, we s h o w t h a t a s G varies over a natural series of important groups and monoids, the iterated multiplication problems are complete for most natural, low-level  ...  Thanks to two a n o n ymous referees who saved us embarrassment b y p o i n ting out some gaps in the logic of an earlier version of this paper.  ... 
doi:10.1109/sct.1989.41816 dblp:conf/coco/ImmermanL89 fatcat:tkboeoojmfhkpccsapbyzgg2be

Algorithm to Compute Cubes of 1st &quotN" Natural Numbers using Single Multiplication per Iteration

Rajat Tandon, Rajika Tandon
2014 International Journal of Computer Applications  
overall computational complexity per iteration is of the order of O  ...  So, keeping the number of iterations same in both, in the traditional approach, the overall computational complexity per iteration is expressed in the order of O(n 2 ) while in the current approach the  ...  The complexity of the multiplication "(6*a)" is of the order of O(3n) because 3 bits are used to represent the number "6".  ... 
doi:10.5120/17761-8872 fatcat:a3o6iz5op5gonaxkjtracdncxa

Computationally Efficient Channel Estimation in 5G Massive Multiple-Input Multiple-output Systems

Imran Khan, Mohammad Zafar, Majid Ashraf, Sunghwan Kim
2018 Electronics  
an enormous amount of computations, which result in high computational complexity and make them impractical to implement.  ...  Simulation results showed that the proposed algorithm had better channel estimation performance, which improved the signal detection by 31.68% while the complexity was reduced by 45.72%, compared with  ...  Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/electronics7120382 fatcat:ilfmpl6obfa4hio3gqy3kjk4cq

An Improved Jacobi-Based Detector for Massive MIMO Systems

Xiaoqing Zhao, Zhengquan Li, Song Xing, Yang Liu, Qiong Wu, Baolong Li
2019 Information  
Massive multiple-input-multiple-output (MIMO) is one of the key technologies in the fifth generation (5G) cellular communication systems.  ...  As the result, the fast convergence and the low computationally complexity of the proposed Jacobi-based algorithm are obtained and proved.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/info10050165 fatcat:n4jw2hmznbeedjj64tt3agc2y4

Low-complexity near-optimal signal detection for uplink large-scale MIMO systems [article]

Xinyu Gao, Linglong Dai, Yongkui Ma, Zhaocheng Wang
2015 arXiv   pre-print
The complexity can be reduced from O(K3) to O(K2), where K is the number of users. We also provide the convergence proof of the proposed algorithm.  ...  Minimum mean square error (MMSE) signal detection algorithm is near- optimal for uplink multi-user large-scale multiple input multiple output (MIMO) systems, but involves matrix inversion with high complexity  ...  Computational Complexity: The complexity in terms of required number of multiplications is analyzed for comparison.  ... 
arXiv:1507.04443v1 fatcat:q5t2vj3a7rdyxh3gv4eyx7oyuq

High-convergence-speed low-computation-complexity SVD algorithm for MIMO-OFDM systems

Cheng-Zhou Zhan, Kai-Yuan Jheng, Yen-Lian Chen, Ting-Jhun Jheng, An-Yeu Wu
2009 2009 International Symposium on VLSI Design, Automation and Test  
The proposed SVD algorithm has the following features: (1) low total computational complexity, (2) fast convergence speed, (3) the ability of reconfigurable to different numbers of transmitter and receiver  ...  Multiple-input multiple-output (MIMO) wireless communication systems with orthogonal frequency-division multiplexing (OFDM) achieve high spectral efficiency high channel capacity, and many MIMO-OFDM systems  ...  It means the iterative multiplication of getting the last right singular vector, ‫ܞ‬ ே ,is unneeded, and it reduces the total computational complexity.  ... 
doi:10.1109/vdat.2009.5158128 fatcat:gn2vo2h7rvg2davkw7ebvfd4ie

A Robust Hybrid Iterative Linear Detector for Massive MIMO Uplink Systems

Mahmoud A. Albreem, Mohammed H. Alsharif, Sunghwan Kim
2020 Symmetry  
In such iterative methods, the performance, complexity, and convergence rate are highly dependent on the initial vector.  ...  A large-scale multiple-input multiple-output (MIMO), or massive MIMO (mMIMO), technology has a major impact to secure high data rate, high spectral efficiency, and quality of service (QoS).  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym12020306 fatcat:l4n6iqffbzbujlmvv7spokhdii

Analysis and design of power-efficient coding schemes with parallel concatenated convolutional codes

S. Huettinger, J. Huber
2006 IEEE Transactions on Communications  
In the low signal-to-noise ratio regime, the performance of concatenated coding schemes is limited by the convergence properties of the iterative decoder.  ...  In this paper, we extend the method of extrinsic information transfer charts, that is limited to the case of a concatenation of two component codes, to the case of multiple turbo codes.  ...  The complexity of the iterative algorithm then is given by the sum over all , which is the number of states visited within each full iteration, multiplied by the number of iterations . IV.  ... 
doi:10.1109/tcomm.2006.876847 fatcat:gdohk2rytzhwxflqhu2iim7ahm

MapReduce for Parallel Reinforcement Learning [chapter]

Yuxi Li, Dale Schuurmans
2012 Lecture Notes in Computer Science  
We give time and space complexity analysis of the proposed algorithms. This study demonstrates how parallelization opens new avenues for solving large scale reinforcement learning problems.  ...  We investigate the parallelization of reinforcement learning algorithms using MapReduce, a popular parallel computing framework.  ...  We give time and space complexity analysis of the proposed algorithms.  ... 
doi:10.1007/978-3-642-29946-9_30 fatcat:jyoovu2waffuzd5v3bxqyjdffm

Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks

Mahmoud A. Albreem, Mohammed H. Alsharif, Sunghwan Kim
2020 Symmetry  
Numerical Results show that utilization of S achieves the target performance within few iterations, and, hence, the computational complexity is reduced.  ...  Most of the existing iterative linear detectors are using a diagonal matrix ( D ) in initialization because the equalization matrix is almost diagonal.  ...  Complexity Analysis Complexity is highly affected by the number of multiplications, divisions, and number of iterations.  ... 
doi:10.3390/sym12010071 fatcat:gz6tv4djjzdixhvtijnnlillyi

Iterative Signal Processing in Communications

Christian Schlegel, Peter Hoeher, Owe Axelsson, Lance Pérez
2010 Journal of Electrical and Computer Engineering  
in fact the same order complexity as that of an iterative matrix solver.  ...  It is precisely this complexity which is avoided by the use of an iterative algorithm.  ... 
doi:10.1155/2010/862392 fatcat:j55huaeasffqpjsygtjn7ge4xq

Channel estimation for MIMO-OFDM systems based on data nulling superimposed pilots

Emad Farouk, Michael Ibrahim, Mona Z. Saleh, Salwa Elramly
2017 2017 21st Conference of Open Innovations Association (FRUCT)  
The simulation results of the proposed algorithm show improvement in the estimation accuracy, bit error rate (BER) and computational complexity compared to that of the conventional superimposed pilot technique  ...  receiver complexity.  ...  COMPLEXITY ANALYSIS In this section, we analyze the computational complexity of the proposed DNSP scheme in terms of the required number of real multiplications and real additions for channel estimation  ... 
doi:10.23919/fruct.2017.8250172 dblp:conf/fruct/FaroukISE17 fatcat:crlhaxf3xzc6hea24blqhiolge

Adaptive Iterative Layered Space-Frequency Equalization For Single-Carreir Mimo Systems

Xu Zhu
2005 Zenodo  
Publication in the conference proceedings of EUSIPCO, Antalya, Turkey, 2005  ...  COMPLEXITY ANALYSIS The signal processing complexity of AILSFE in terms of the number of complex multiplications, is shown in Table I for the first iteration and Table II for each of the remaining  ...  In the decision-directed mode, the channel estimates are updated iteration by iteration instead of block by block (detection of each blocks consist of multiple iterations), to increase the convergence  ... 
doi:10.5281/zenodo.39306 fatcat:c6hdb5oumfec3dch5rqlwbouei

Simplified Parallel Interference Cancelation for Underdetermined MIMO Systems

Chen Qian, Jingxian Wu, Yahong Rosa Zheng, Zhaocheng Wang
2014 IEEE Transactions on Vehicular Technology  
In the first iteration, the candidate sequences used for PIC are selected by exploring the statistical properties of the received signals.  ...  A low complexity detection scheme is proposed in this paper for under-determined multiple-input multiple-output (UD-MIMO) wireless communication system that employs N transmit antennas and M < N receive  ...  Substituting (36) into (28) leads to an estimate of the number of complex multiplications of the proposed algorithm in the first iteration.  ... 
doi:10.1109/tvt.2014.2298232 fatcat:qiblxd6kbfd7fculre6uwww6uu
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