• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2554-2580
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• 2018

Lenstra-Lenstra-$Lov{\acute{a}}sz$ (LLL) is an effective receiving algorithm for Multiple-Input-Multiple-Output (MIMO) systems, which is believed can achieve full diversity in MIMO detection of fading channels. However, the LLL algorithm features polynomial complexity and shows poor performance in terms of convergence. The reduction of algorithmic complexity and the acceleration of convergence are key problems in optimizing the LLL algorithm. In this paper, a variant of the LLL algorithm, the Hybrid-Fix-and-Round LLL algorithm, which combines both fix and round measurements in the size reduction procedure, is proposed. By utilizing fix operation, the algorithmic procedure is altered and the size reduction procedure is skipped by the hybrid algorithm with significantly higher probability. As a consequence, the simulation results reveal that the Hybrid-Fix-and-Round-LLL algorithm carries a faster rate of convergence compared to the original LLL algorithm, and its algorithmic complexity is at most one order lower than original LLL algorithm in real field. Comparing to other families of LLL algorithm, Hybrid-Fix-and-Round-LLL algorithm can make a better compromise in performance and algorithmic complexity.

• The Journal of the Acoustical Society of Korea
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• v.17 no.3E
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• pp.53-57
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• 1998

Spectral information at a speech coder should be quantized with sufficient accuracy to keep perceptually transparent output speech. Spectral information at a low bit rate speech coder is usually transformed into corresponding line spectrum pair parameters and is often quantized with a vector quantization algorithm. As the vector quantization algorithm generally has high complexity in the optimal code vector searching routine, the complexity reduction in that routine is investigated using the ordering property of the line spectrum pair. When the proposed complexity reduction algorithm is applied to the well-known split vector quantization algorithm, the 46% complexity reduction is achieved in the distortion measure compu-tation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.173-184
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• 2001

We present an algorithm for the complexity reduction of a general Gaussian mixture model by using a penalized likelihood method. One of our important assumptions is that we begin with an overfitted model in terms of the number of components. So our main goal is to eliminate redundant components in the overfitted model. As shown in the section of simulation results, the algorithm works well with the selected densities.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.3C
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• pp.163-169
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• 2011

Partial transmit sequence (PTS) algorithm is known as one of the most efficient ways to reduce the peak-to-average power ratio (PAPR) in the orthogonal frequency division multiplexing (OFDM) system. The PTS algorithm, however, requires large numbers of computation to implement. Thus there has been a trade-off between performance of PAPR reduction and computational complexity. In this paper, the performance of PAPR reduction and computation complexity of PTS algorithms are analyzed and compared through computer simulations. Subsequently, a new PTS algorithm is proposed which can be a reasonable method to reduce the PAPR of OFDM when both the performance of PAPR reduction and computational complexity are considered simultaneously.

• ETRI Journal
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• v.34 no.4
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• pp.503-510
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• 2012

We analyze the relationship between channel coherence bandwidth and two complexity-reduced lattice reduction aided detection (LRAD) algorithms for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems in correlated fading channels. In both the adaptive LR algorithm and the fixed interval LR algorithm, we exploit the inherent feature of unimodular transformation matrix P that remains the same for the adjacent highly correlated subcarriers. Complexity simulations demonstrate that the adaptive LR algorithm could eliminate up to approximately 90 percent of the multiplications and 95 percent of the divisions of the brute-force LR algorithm with large coherence bandwidth. The results also show that the adaptive algorithm with both optimum and globally suboptimum initial interval settings could significantly reduce the LR complexity, compared with the brute-force LR and fixed interval LR algorithms, while maintaining the system performance.

• Journal of Korea Multimedia Society
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• v.21 no.1
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• pp.18-25
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• 2018

In High Efficiency Video Coding (HEVC), integer motion estimation (IME) requires a large amount of computational complexity because HEVC adopts the high flexible and hierarchical coding structures. In order to reduce the computational complexity of IME, this paper proposes the search range reduction algorithm, which takes advantage of motion vectors similarity between different layers. It needs only a few modification for HEVC reference software. Based on the experimental results, the proposed algorithm reduces the processing time of IME by 28.1% on average, whereas its the $Bj{\emptyset}ntegaard$ delta bitrate (BD-BR) increase is 0.15% which is negligible.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.5
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• pp.88-94
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• 2009

We propose a scheme which reduce the computational complexity of the lattice reduction (LR) aided detector in MIMO system. The performance of the ML detection algorithm is good but the computational complexity grows exponentially with the number of antenna elements and constellation points. LR aided detector shows the same diversity with the ML scheme with relatively less complexity. But the LR scheme still requires many computations since it involves several iterations of size reduction and column vector exchange. We notice that the LR process depends not on the received signal but only on the channel matrix so we can apply LR process offline and store the results in Look-Up Table (LUT). In this paper we propose an algorithm to generate the LUT which require less memory requirement and we evaluate the performance and complexity of the proposed system. We show that the proposed system requires less computational complexity with similar detection performance compared with the conventional LR aided detector.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.05a
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• pp.297-300
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• 2007

Due to its impressive compression performance, the H.264 video coder is highlighted in the video communications industry, such as DMB (Digital Multimedia Broadcasting), PMP (Portable Multimedia Player), etc. The main bottleneck to use the H.264 coder lays in the computational complexity, i.e. five times more complex than the market leading MPEG-4 Simple Profile codec. In this paper, we propose the hierarchical mode decision method for intraframe coding for the reduction of the computation complexity of the encoder. By determining the mode group early, the propose algorithm can skip the computationally demanding computation in the mode decision. The proposed algorithm is composed of three steps: $16{\times}16$ mode decision, $4{\times}4$ mode-group decisions, and final mode decision among the selected mode group. The simulation results show that the proposed algorithm achieves 20% to 50% reduction in the computational complexity compared with the conventional algorithm.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.1
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• pp.10-17
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• 1993

This paper analyzes succinct graph descriptions and its complexity of connectivity problems on context free graph languages under various restrictions. It defines SNLC(Simple Context Free Node Label Controlled) grammar and presents reduction method that solves graph problems without expanding the hierarchical description. It exemplifies the method by giving efficient solutions to connectivity problems on graphs and presents parallel algorithm for reduction and analyzes the complexity. Its results will help application of desing for NETWORK. CAD. VLSI and other engineering problems.