Encoding-Assisted Temporal Direct Mode Decision for B Pictures in H.264/AVC
|
|
- Bernard Warren
- 6 years ago
- Views:
Transcription
1 Ecodig-Assisted Temporal Direct Mode Decisio for B Pictures i H.64/AVC Ya-Neg Fag ad Yiyi Li Hui-Jae Hsieh Departmet of Commuicatio Egieerig Departmet of Iformatio Maagemet Natioal Cetral Uiversity, Taiwa Chie Hsi Uiversity of Sciece ad Techology, Taiwa yili@ce.cu.edu.tw Abstract This paper proposes a ecodig-assisted temporal DIRECT mode decisio algorithm for H.64/AVC iter bipredictive (B) frame video sequeces to improve the codig efficiecy. I the proposed algorithm, we employ motio vectors (s) of co-located block ad its eight eighborig blocks for DIRECT mode decisio. I additio, the weight selectio for bidirectioal predictio is also cosidered. The best ad weight to miimize the sum of absolute predictio error is selected for DIRECT mode decisio. The experimetal results reveal that the proposed algorithm achieves average 0. db PSNR gai or equivaletly average.6% bit-rate reductio, compared to the covetioal DIRECT mode codig that oly uses the of the co-located MB for DIRECT mode decisio. The temporal DIRECT mode decisio suggested i H.64/AVC is simple but ot effective sice i may cases the of co-located MB or block does ot represet the true motio of the curret MB or block [][3]. This could cause severe predictio errors resultig i heavy redudat codig bits. I this paper, we propose a efficiet temporal DIRECT mode decisio algorithm for H.64/AVC B frame video sequeces to improve its codig efficiecy. I the suggested techique, i additio to the of the co-located block we also employ s of its eighborig blocks for DIRECT mode decisio. Keywords: Direct mode decisio, H.64/AVC, Predictio motio vector, Rate-distortio optimizatio (RDO) I. INTRODUCTION The latest H.64/AVC achieves better performace i both PSNR ad visual quality at the same bit rate, compared to prior video codig stadards. This is due to that H.64/AVC features may advaced techiques, such as variable block sizes mode decisio ad multiple referece frames motio estimatio etc., ad also due to the cosideratio of geeralized bi-predictive (B) frame video codig []. Aother importat techique is the uses of Lagragia rate-distortio optimizatio (RDO). I the H.64/AVC ecoder both iter ad itra mode predictios are provided i both predictive (P) ad bipredictive (B) frames. The iter mode predictio provides seve modes for iter-frame motio estimatio, chagig amog 6x6, 6x8, 8x6, 8x8, 8x4, 4x8, ad 4x4. They are performed i each MB to achieve the best codig efficiecy. The itra mode predictio offers I4x4MB predictio mode ad I6x6MB predictio mode. The iter B frame codig ca use backward as well as forward frames for multiple predictios. As a result, high percetage of bits is required to ecode motio iformatio such as predictio mode, motio vector ad referece frame. To alleviate high overhead problem, i additio to iter ad itra modes the SKIP mode ad DIRECT mode are also itroduced i both P ad B frames, respectively. I the SKIP or DIRECT mode codig, the motio iformatio is obtaied directly from previously ecoded MB or blocks ad motio iformatio is ot eeded to trasmit, leadig to great overhead reductio withi the bit stream. Fig. Bidirectioal Predictio i DIRECT mode II. DIRECT MODE DECISION USED IN H.64/AVC I the H.64/AVC ecoder, the iter mode predictio for B frame ca use forward as well as backward referece frames (amely List 0 referece ad List referece) for multiple predictios. The temporal DIRECT mode decisio uses bidirectioal predictios, ad the forward ad backward motio vectors are derived from the motio vector co located used i the co-located block i the sub-sequetial referece frame, i.e., the first List referece frame. As illustrated i Fig., the motio vectors ad for temporal DIRECT mode blocks are calculated as 38
2 ad T = co located ( r0, 0) () L 0 = s T = co located ( u0, 0) () L = v where T ad T are the distaces betwee the curret frame ad the forward/backward referece frames i List 0 referece ad List referece respectively. The bidirectioal predictio for the DIRECT mode is obtaied by averagig associated blocks i these refereces B ( = B( i + r0, j + s0) + B( i u0, j v0) (3) The DIRECT mode decisio allows residual codig of the predictio error betwee the curret block B( ad the predictio block B 0(. There are three types of DIRECT mode used i H.64/AVC based upo the residual iformatio ad the block size: DIRECT 6x6, DIRECT 8x8 ad B SKIP 6x6. The residual iformatio are trasmitted i the bit-stream for both DIRECT 6x6 ad DIRECT 8x8; while o residual iformatio trasmitted for B SKIP 6x6. b b b b b b f f f L Fig. Accurate predictio for DIRECT mode decisio III. ENCODING-ASSISTED DIRECT MODE DECISION FOR B PICTURES The bidirectioal predictio usig (3), takig the of co-located block i the first List referece frame as the estimated, is a simple yet efficiet approach for DIRECT mode decisio. The predictio error however becomes highly critical i occlusio regios or whe the of the co-located block does ot preset the true motio of the curret block. As illustrated i Fig., whe a object is movig from block b 7 i the List 0 referece frame f to block b 3 i the List referece frame f with a costat, a ew object comes ito sight i the ucovered regio ad a existig object goes out of sight i the covered regio i the curret B frame f. Aother object is also covered i block b 3 i the List referece frame f. These areas are referred to as occlusio areas. I additio, the of the co-located block b 5 i the List referece frame f (i.e., iter coded with zero i this case) does ot represet the true of the curret block b 5 i the curret B frame f. As a result, the DIRECT mode decisio proposed i H.64/AVC, usig equal weight ad of the co-located block b 5 i the first List referece frame f, caot produce good predictio for these video occlusios, ad it leads to serious predictio errors. As illustrated i Fig., B L 0( ad B L ( should be respectively used to predict the blocks b 3 ad b7 i the curret B frame for DIRECT mode. I similar, the of the block b 3 i the List referece frame should be used to predict curret block b 5 : B ( = B( i + r3, j + s3) + B( i u3, j v3) (4) where ( r 3, s 3) ad ( u 3, v 3 ) are the s for forward ad backward predictio blocks derived from the of the block b 3 (as deoted as 3 ) i the List referece frame T L 0 = 3 = ( r3, s3) (5) T + T ad T L = 3 = ( u3, v3) (6) To achieve more accurate predictio i DIRECT mode decisio, we propose a geeral bidirectioal predictio for DIRECT mode which is expressed as B ( = w B ( i + r, j + s ) + w B ( i u, j v ) (7) k k k k where w ad w are the weights for forward ad backward predictio blocks respectively i DIRECT mode with w L 0 + w L = ad w, w 0,,} (8) { where w = ( w L 0, w) = (0,) is suitable to appearig objects (i.e., block b 7 i Fig. () while w = ( w L 0, w) = (,0 ) for disappearig objects (i.e., block b 3 ) i occlusio areas of the curret B frame. For o occlusio areas, the weight 39
3 w ( w L, w ) (, ) is the best choice. = 0 = I the proposed DIRECT mode decisio, the estimatios of w = w f, w ) ad v = v x, v ) are accomplished i the ( b ecoder by miimizig (, W ) = arg mi mi ( y k V s W W s j B ( B ( where γ desigates the selected orm, ad γ = is used i the experimet to measure predictio errors betwee the curret block B ( ad the bidirectioal predictio block B ( give i (7). The parameter V s represets the set of all cadidates k i co-located ad its eighborig blocks. The predictio error ca be reduced whe the best or weight is used for DIRECT mode decisio, leadig to less codig bits for the redudat iformatio. Prob. Code_um Codeword Co-located w=(,0) w=(0,) Left-Top Left Left-Bottom Bottom Right-Bottom Right Right-Top Top TABLE I Exp-Golomb code for extra overhead Although the redudat codig bits ca be lowered i DIRECT mode decisio whe the best or weight selected from co-located ad its eighborig blocks is used, the extra overhead that idicates the of which block or weight values used for bidirectioal predictio is required for trasmissio. More eighborig blocks employed for or weight selectio, more heavy extra overhead required for trasmissio i DIRECT mode. The extra overhead degrades the codig performace. To reduce performace degradatio itroduced i the extra overhead, i this paper we oly cosider the weights w = ( w L 0, w) = (0,) ad w = ( w L 0, w) = (,0 ) for co-located block. I additio, we take ito accout the s of the co-located block as well as its eight eighborig blocks for selectio. As a result, we eed to sed extra overhead describig the eleve cases whe the DIRECT mode is fially determied as the best mode through RDO mode decisio. γ (9) To comply with the H.64/AVC ecoder, we employ the Exp-Golomb code as the etropy ecoder to ecode the extra overhead. The extra overhead is iserted after mb_type that describes the best mode for the ecodig block. If the best mode is the DIRECT mode, the extra overhead describig ad weight iformatio is the ecoded usig the Exp-Golomb etropy ecoder, based o the probability distributio of best ad weight. The oe with higher probability is mapped with the shorter codeword, ad vice versa. A itesive experimet was coducted o may video sequeces to ivestigate the average probability distributio of ad weight iformatio. The probability distributio ad associated codewords for extra overhead is documeted i TABLE I. IV. EXPERIMENTAL RESULTS I this sectio, we compare the performace of the proposed temporal DIRECT mode decisio algorithm (deoted as proposed TDMD) with the temporal DIRECT mode decisio method proposed i the H.64/AVC ecoder (deoted as origial TDMD). I the proposed TDMD, the best or weight is selected from the co-located block ad its eight eighborig blocks for DIRECT mode decisio based o the criterio give i (9). The proposed TDMD is oly applied to DIRECT 6x6 ad B SKIP 6x6. To reduce extra overhead, the DIRECT 8x8 mode uses the origial DIRECT mode decisio. QCIF CIF 4CIF Forema Claire Trevor Mobile coastguard Waterfall Stefa ews bus Dacer City Crew Harbour Ice Soccer Code Versio JM. Profile Mai GOP Structure IBPBP... Ecodig Frames 99 Frame Rate 30 N P N B,List0 N B,List N P,List QP QPB=QPP+3 RDO O Etropy Codig CAVLC TABLE II Simulatio coditios We implemet these algorithms ito the JM ecoder JM. to evaluate their performace. The simulatio uses fiftee test sequeces, coverig a wide rage of motio activities ad various formats (QCIF: 76 44, CIF: 35 88, ad 4CIF: ). I the experimetal settig, each sequece has 00 frames i simulatios for sequece coded with IBPBP structure. The frame rate is 30 frames per secod ad the quatizatio parameter for B frames is set as QP QP + 3 []. The B = P 40
4 experimetal settig is summarized i TABLE II. claire sequece are homogeeous ad statioary, ad the bidirectioal predictio usig of the co-located block for DIRECT mode usually gives very good codig efficiecy, compared to its eighborig blocks. As a result, extra overhead for ad weight selectio degrades its codig performace severely. TB k = k T A Fig. 3 biliear iterpolatio for forward/backward s For simplicity the umber of referece frames for motio estimatio is N P =, i.e., with two referece frame buffers. The umbers of referece frame for B frames are N B, List0 = ad N B, List = respectively, while N P, List0 = for P frames. Note that the biliear iterpolatio is employed to procure the desired i the List 0 referece frame whe the referece umber of the List referece P frame is, as illustrated i Fig. 3. The performace is compared based upo Bjotegaard Delta PSNR (BDPSNR) ad Bjotegaard Delta Bit Rate (BDBR) [4] for QP P =0, 4, 8 ad 3. TABLE III displays the BDPNR ad BDBR results, as compared to origial TDMD, that shows both cases with ad without extra overhead. As demostrated, the proposed TDMD achieves average 0. db BDPSNR gai ad 4.% of BDBR bit-rate savig whe the extra overhead is ot cosidered. Whe the extra overhead is take ito accout, the BDPSNR gai lesses from 0. db to 0. db ad the BDBR reductio lesses from 4.% to.6%. The proposed TDMD still outperforms the origial TDMD. As show i TABLE III, the superiority of the proposed algorithm is evidet for fast motio video sequeces such as forema, mobile, bus etc. I these sequeces with high motio activities, the occlusio pheomeo occurs ofte ad the of the co-located block caot usually represet the true motio of the curret ecodig block, leadig serious predictio errors. To obtai further isight, Fig. 4 compares RD performace for various QPs, carried o mobile to show its superiority over origial TDMD algorithm. No matter how, the advatage of the proposed TDMD becomes lost for video sequeces with slow motio activities like claire. This is because that most areas i PSNR (db) Mobole.QCIF QPP0,4,8,3 BDPSNR (db) BDBR (%) No Overhead Overhead No Overhead Overhead Forema Claire QCIF Trevor Mobile coastguard Waterfall Stefa CIF ews bus Dacer City Crew CIF Harbour Ice Soccer Average TABLE III BDPSNR ad BDBR compariso Orig. TDMD Proposed TDMD Bit-Rate (kbps) Fig. 4 Rate distortio curve o mobile V. CONCLUSION I this paper, we suggest a temporal DIRECT mode decisio algorithm for H.64/AVC iter B frame video codig to ehace the codig performace. The proposed algorithm uses s of the co-located block as well as its eight eighborig blocks for DIRECT mode decisio. I additio, the weight selectio is also cosidered for occlusio areas. The experimetal results reveal that average PSNR gai of 0. db, or correspodig to average.6% of bit-rate reductio ca be achieved, compared to the temporal DIRECT mode decisio proposed i H.64/AVC. REFERENCES it R 4
5 [] A. Vectro, C. Christopoulos, ad H. Su, Video trascodig architectures ad techiques: A overview, IEEE Sigal Processig Magazie, vol. 0, pp. 8-9, March 003. [] M. Flierl ad B. Girod, Geeralized B pictures ad the draft H.64/AVC video compressio-stadard, IEEE Tras. Circuits Syst. Video Techol., vol. 3, o. 7, pp , July 003. [3] A. M. Tourapis, F. Wu ad S. L Direct mode codig for bipredictive slices i the H.64 stadard, IEEE Tras. Circuits Syst. Video Techol., vol. 5, o., pp. 9-6, Jauary 005. [4] G. Bjotegaard, Calculatio of average PSNR differece betwee RD curves, ITU-T Q.6/6, Doc. VCEG-M33, April 00. 4
Invariability of Remainder Based Reversible Watermarking
Joural of Network Itelligece c 16 ISSN 21-8105 (Olie) Taiwa Ubiquitous Iformatio Volume 1, Number 1, February 16 Ivariability of Remaider Based Reversible Watermarkig Shao-Wei Weg School of Iformatio Egieerig
More informationRun-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE
Geeral e Image Coder Structure Motio Video (s 1,s 2,t) or (s 1,s 2 ) Natural Image Samplig A form of data compressio; usually lossless, but ca be lossy Redudacy Removal Lossless compressio: predictive
More informationCooperative Communication Fundamentals & Coding Techniques
3 th ICACT Tutorial Cooperative commuicatio fudametals & codig techiques Cooperative Commuicatio Fudametals & Codig Techiques 0..4 Electroics ad Telecommuicatio Research Istitute Kiug Jug 3 th ICACT Tutorial
More informationOPTIMAL PIECEWISE UNIFORM VECTOR QUANTIZATION OF THE MEMORYLESS LAPLACIAN SOURCE
Joural of ELECTRICAL EGIEERIG, VOL. 56, O. 7-8, 2005, 200 204 OPTIMAL PIECEWISE UIFORM VECTOR QUATIZATIO OF THE MEMORYLESS LAPLACIA SOURCE Zora H. Perić Veljo Lj. Staović Alesadra Z. Jovaović Srdja M.
More informationError Resilience Analysis of Multi-Hypothesis Motion Compensated Prediction for Video Coding
1. Research Team Error Resiliece Aalysis of Multi-Hypothesis Motio Compesated Predictio for Video Codig Project Leader: Other Faculty: Post Doc(s): Graduate Studets: Idustrial Parter(s): C.-C. Jay Kuo,
More informationASYMPTOTIC CLOSED-LOOP DESIGN OF ERROR RESILIENT PREDICTIVE COMPRESSION SYSTEMS. Sina Zamani, Tejaswi Nanjundaswamy, Kenneth Rose
ASYMPTOTIC OSED-LOOP DESIGN OF ERROR RESILIENT PREDICTIVE COMPRESSION SYSTEMS Sia Zamai, Tejaswi Najudaswamy, Keeth Rose Departmet of Electrical ad Computer Egieerig, Uiversity of Califoria Sata Barbara,
More informationFundamentals. Relative data redundancy of the set. C.E., NCU, Taiwan Angela Chih-Wei Tang,
Image Compressio Agela Chih-Wei Tag ( 唐之瑋 ) Departmet of Commuicatio Egieerig Natioal Cetral Uiversity JhogLi, Taiwa 2012 Sprig Fudametals Compressio ratio C R / 2, 1 : origial, 2 1 : compressed Relative
More informationFormation of A Supergain Array and Its Application in Radar
Formatio of A Supergai Array ad ts Applicatio i Radar Tra Cao Quye, Do Trug Kie ad Bach Gia Duog. Research Ceter for Electroic ad Telecommuicatios, College of Techology (Coltech, Vietam atioal Uiversity,
More informationModule 5 EMBEDDED WAVELET CODING. Version 2 ECE IIT, Kharagpur
Module 5 EMBEDDED WAVELET CODING Versio ECE IIT, Kharagpur Lesso 4 SPIHT algorithm Versio ECE IIT, Kharagpur Istructioal Objectives At the ed of this lesso, the studets should be able to:. State the limitatios
More informationEntropies & Information Theory
Etropies & Iformatio Theory LECTURE I Nilajaa Datta Uiversity of Cambridge,U.K. For more details: see lecture otes (Lecture 1- Lecture 5) o http://www.qi.damtp.cam.ac.uk/ode/223 Quatum Iformatio Theory
More informationInformation-based Feature Selection
Iformatio-based Feature Selectio Farza Faria, Abbas Kazeroui, Afshi Babveyh Email: {faria,abbask,afshib}@staford.edu 1 Itroductio Feature selectio is a topic of great iterest i applicatios dealig with
More informationVariable selection in principal components analysis of qualitative data using the accelerated ALS algorithm
Variable selectio i pricipal compoets aalysis of qualitative data usig the accelerated ALS algorithm Masahiro Kuroda Yuichi Mori Masaya Iizuka Michio Sakakihara (Okayama Uiversity of Sciece) (Okayama Uiversity
More informationProvläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE
TECHNICAL REPORT CISPR 16-4-3 2004 AMENDMENT 1 2006-10 INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE Amedmet 1 Specificatio for radio disturbace ad immuity measurig apparatus ad methods Part 4-3:
More informationA statistical method to determine sample size to estimate characteristic value of soil parameters
A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig
More informationLecture 11: Decision Trees
ECE9 Sprig 7 Statistical Learig Theory Istructor: R. Nowak Lecture : Decisio Trees Miimum Complexity Pealized Fuctio Recall the basic results of the last lectures: let X ad Y deote the iput ad output spaces
More informationSession 5. (1) Principal component analysis and Karhunen-Loève transformation
200 Autum semester Patter Iformatio Processig Topic 2 Image compressio by orthogoal trasformatio Sessio 5 () Pricipal compoet aalysis ad Karhue-Loève trasformatio Topic 2 of this course explais the image
More informationPacket Video 99. A Corruption Model for Motion Compensated Video Subject to Bit Errors. Gustavo de los Reyes Amy R. Reibman Shih-Fu Chang
A Corruptio Model for Motio Compesated Video Subject to Bit Errors Gustavo de los Reyes Amy R. Reibma Shih-Fu Chag AT&T Labs AT&T Labs-Research Columbia Uiversity gdelosreyes@att.com amy@research.att.com
More informationVector Quantization: a Limiting Case of EM
. Itroductio & defiitios Assume that you are give a data set X = { x j }, j { 2,,, }, of d -dimesioal vectors. The vector quatizatio (VQ) problem requires that we fid a set of prototype vectors Z = { z
More informationDual Frame Motion Compensation with Optimal Long-term Reference Frame Selection and Bit Allocation
AER IDENTIFICATION NUMBER:33 Dual Frame Motio Compesatio with Optimal Log-term Referece Frame Selectio ad Bit Allocatio Da Liu, Debi Zhao, Xiagyag i, ad We Gao, Fellow, IEEE Abstract I dual frame motio
More informationInformation Theory and Coding
Sol. Iformatio Theory ad Codig. The capacity of a bad-limited additive white Gaussia (AWGN) chael is give by C = Wlog 2 ( + σ 2 W ) bits per secod(bps), where W is the chael badwidth, is the average power
More informationDouble Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution
Iteratioal Mathematical Forum, Vol., 3, o. 3, 3-53 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.9/imf.3.335 Double Stage Shrikage Estimator of Two Parameters Geeralized Expoetial Distributio Alaa M.
More informationElement sampling: Part 2
Chapter 4 Elemet samplig: Part 2 4.1 Itroductio We ow cosider uequal probability samplig desigs which is very popular i practice. I the uequal probability samplig, we ca improve the efficiecy of the resultig
More informationFastest mixing Markov chain on a path
Fastest mixig Markov chai o a path Stephe Boyd Persi Diacois Ju Su Li Xiao Revised July 2004 Abstract We ider the problem of assigig trasitio probabilities to the edges of a path, so the resultig Markov
More informationChannel coding, linear block codes, Hamming and cyclic codes Lecture - 8
Digital Commuicatio Chael codig, liear block codes, Hammig ad cyclic codes Lecture - 8 Ir. Muhamad Asial, MSc., PhD Ceter for Iformatio ad Commuicatio Egieerig Research (CICER) Electrical Egieerig Departmet
More informationLecture 11: Channel Coding Theorem: Converse Part
EE376A/STATS376A Iformatio Theory Lecture - 02/3/208 Lecture : Chael Codig Theorem: Coverse Part Lecturer: Tsachy Weissma Scribe: Erdem Bıyık I this lecture, we will cotiue our discussio o chael codig
More informationThere is no straightforward approach for choosing the warmup period l.
B. Maddah INDE 504 Discrete-Evet Simulatio Output Aalysis () Statistical Aalysis for Steady-State Parameters I a otermiatig simulatio, the iterest is i estimatig the log ru steady state measures of performace.
More informationEfficient Reverse Converter Design for Five Moduli
Joural of Computatios & Modellig, vol., o., 0, 93-08 ISSN: 79-765 (prit), 79-8850 (olie) Iteratioal Scietific ress, 0 Efficiet Reverse Coverter Desig for Five Moduli Set,,,, MohammadReza Taheri, Elham
More informationDigital Video Systems ECE 634
Digital Video Systems ECE 634 egieerig.purdue.edu/~reibma/ece634/idex.html Professor Amy Reibma MSEE 356 reibma@purdue.edu MulGple descripgo codig Layered codig vs. MDC Layered codig: Base layer is high
More informationAs metioed earlier, directly forecastig o idividual product demads usually result i a far-off forecast that ot oly impairs the quality of subsequet ma
Semicoductor Product-mix Estimate with Dyamic Weightig Scheme Argo Che, Ziv Hsia ad Kyle Yag Graduate Istitute of Idustrial Egieerig, Natioal Taiwa Uiversity Roosevelt Rd. Sec. 4, Taipei, Taiwa, 6 ache@tu.edu.tw
More informationResearch Article A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
Discrete Dyamics i Nature ad Society Article ID 210761 4 pages http://dxdoiorg/101155/2014/210761 Research Article A Uified Weight Formula for Calculatig the Sample Variace from Weighted Successive Differeces
More informationADVANCED SOFTWARE ENGINEERING
ADVANCED SOFTWARE ENGINEERING COMP 3705 Exercise Usage-based Testig ad Reliability Versio 1.0-040406 Departmet of Computer Ssciece Sada Narayaappa, Aeliese Adrews Versio 1.1-050405 Departmet of Commuicatio
More informationA New Multivariate Markov Chain Model with Applications to Sales Demand Forecasting
Iteratioal Coferece o Idustrial Egieerig ad Systems Maagemet IESM 2007 May 30 - Jue 2 BEIJING - CHINA A New Multivariate Markov Chai Model with Applicatios to Sales Demad Forecastig Wai-Ki CHING a, Li-Mi
More informationA New Solution Method for the Finite-Horizon Discrete-Time EOQ Problem
This is the Pre-Published Versio. A New Solutio Method for the Fiite-Horizo Discrete-Time EOQ Problem Chug-Lu Li Departmet of Logistics The Hog Kog Polytechic Uiversity Hug Hom, Kowloo, Hog Kog Phoe: +852-2766-7410
More informationGoodness-Of-Fit For The Generalized Exponential Distribution. Abstract
Goodess-Of-Fit For The Geeralized Expoetial Distributio By Amal S. Hassa stitute of Statistical Studies & Research Cairo Uiversity Abstract Recetly a ew distributio called geeralized expoetial or expoetiated
More informationReport on Private Information Retrieval over Unsynchronized Databases
Report o Private Iformatio Retrieval over Usychroized Databases Lembit Valgma Supervised by Vitaly Skachek May 25, 217 1 Problem Statemet There are may challeges cocerig olie privacy. Private iformatio
More information2D DSP Basics: 2D Systems
- Digital Image Processig ad Compressio D DSP Basics: D Systems D Systems T[ ] y = T [ ] Liearity Additivity: If T y = T [ ] The + T y = y + y Homogeeity: If The T y = T [ ] a T y = ay = at [ ] Liearity
More informationOFDM Precoder for Minimizing BER Upper Bound of MLD under Imperfect CSI
MIMO-OFDM OFDM Precoder for Miimizig BER Upper Boud of MLD uder Imperfect CSI MCRG Joit Semiar Jue the th 008 Previously preseted at ICC 008 Beijig o May the st 008 Boosar Pitakdumrogkija Kazuhiko Fukawa
More informationUniversal source coding for complementary delivery
SITA2006 i Hakodate 2005.2. p. Uiversal source codig for complemetary delivery Akisato Kimura, 2, Tomohiko Uyematsu 2, Shigeaki Kuzuoka 2 Media Iformatio Laboratory, NTT Commuicatio Sciece Laboratories,
More informationSimilarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall
Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig
More informationVector Permutation Code Design Algorithm. Danilo SILVA and Weiler A. FINAMORE
Iteratioal Symposium o Iformatio Theory ad its Applicatios, ISITA2004 Parma, Italy, October 10 13, 2004 Vector Permutatio Code Desig Algorithm Dailo SILVA ad Weiler A. FINAMORE Cetro de Estudos em Telecomuicações
More informationInformation Theory Tutorial Communication over Channels with memory. Chi Zhang Department of Electrical Engineering University of Notre Dame
Iformatio Theory Tutorial Commuicatio over Chaels with memory Chi Zhag Departmet of Electrical Egieerig Uiversity of Notre Dame Abstract A geeral capacity formula C = sup I(; Y ), which is correct for
More informationUC Berkeley CS 170: Efficient Algorithms and Intractable Problems Handout 17 Lecturer: David Wagner April 3, Notes 17 for CS 170
UC Berkeley CS 170: Efficiet Algorithms ad Itractable Problems Hadout 17 Lecturer: David Wager April 3, 2003 Notes 17 for CS 170 1 The Lempel-Ziv algorithm There is a sese i which the Huffma codig was
More informationScheduling under Uncertainty using MILP Sensitivity Analysis
Schedulig uder Ucertaity usig MILP Sesitivity Aalysis M. Ierapetritou ad Zheya Jia Departmet of Chemical & Biochemical Egieerig Rutgers, the State Uiversity of New Jersey Piscataway, NJ Abstract The aim
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationProperties and Hypothesis Testing
Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.
More informationOlli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5
Sigals ad Systems Sigals ad Systems Sigals are variables that carry iformatio Systemstake sigals as iputs ad produce sigals as outputs The course deals with the passage of sigals through systems T-6.4
More informationOptimally Sparse SVMs
A. Proof of Lemma 3. We here prove a lower boud o the umber of support vectors to achieve geeralizatio bouds of the form which we cosider. Importatly, this result holds ot oly for liear classifiers, but
More informationWHAT IS THE PROBABILITY FUNCTION FOR LARGE TSUNAMI WAVES? ABSTRACT
WHAT IS THE PROBABILITY FUNCTION FOR LARGE TSUNAMI WAVES? Harold G. Loomis Hoolulu, HI ABSTRACT Most coastal locatios have few if ay records of tsuami wave heights obtaied over various time periods. Still
More informationAPPLICATION OF CEPSTRUM ANALYSIS IN SPEECH CODING. Vahid Abolghasemi, Hossein Marvi
ICSV4 Cairs Australia 9- July, 7 APPLICATION OF CEPSTRUM ANALYSIS IN SPEECH CODING Vahid Abolghasemi, Hossei Marvi Faculty of Electrical & Robotic Egieerig, Shahrood Uiversity of Techology vahidabolghasemi@yahoo.com,
More informationShannon s noiseless coding theorem
18.310 lecture otes May 4, 2015 Shao s oiseless codig theorem Lecturer: Michel Goemas I these otes we discuss Shao s oiseless codig theorem, which is oe of the foudig results of the field of iformatio
More informationOn stratified randomized response sampling
Model Assisted Statistics ad Applicatios 1 (005,006) 31 36 31 IOS ress O stratified radomized respose samplig Jea-Bok Ryu a,, Jog-Mi Kim b, Tae-Youg Heo c ad Chu Gu ark d a Statistics, Divisio of Life
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationSeed and Sieve of Odd Composite Numbers with Applications in Factorization of Integers
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 319-75X. Volume 1, Issue 5 Ver. VIII (Sep. - Oct.01), PP 01-07 www.iosrjourals.org Seed ad Sieve of Odd Composite Numbers with Applicatios i
More informationSequential Monte Carlo Methods - A Review. Arnaud Doucet. Engineering Department, Cambridge University, UK
Sequetial Mote Carlo Methods - A Review Araud Doucet Egieerig Departmet, Cambridge Uiversity, UK http://www-sigproc.eg.cam.ac.uk/ ad2/araud doucet.html ad2@eg.cam.ac.uk Istitut Heri Poicaré - Paris - 2
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 2, Issue 5, November 2012
Iteratioal Joural of Egieerig ad Iovative Techology (IJEIT) Pre Improved Weighted Modulo 2 +1 Desig Based O Parallel Prefix Adder Dr.V.Vidya Devi, T.Veishkumar, T.Thomas Leoid PG Head/Professor, Graduate
More informationMOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND.
XI-1 (1074) MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND. R. E. D. WOOLSEY AND H. S. SWANSON XI-2 (1075) STATISTICAL DECISION MAKING Advaced
More informationThe Local Harmonious Chromatic Problem
The 7th Workshop o Combiatorial Mathematics ad Computatio Theory The Local Harmoious Chromatic Problem Yue Li Wag 1,, Tsog Wuu Li ad Li Yua Wag 1 Departmet of Iformatio Maagemet, Natioal Taiwa Uiversity
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationCS322: Network Analysis. Problem Set 2 - Fall 2009
Due October 9 009 i class CS3: Network Aalysis Problem Set - Fall 009 If you have ay questios regardig the problems set, sed a email to the course assistats: simlac@staford.edu ad peleato@staford.edu.
More informationChapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol Discrete-Event System Simulation
Chapter Output Aalysis for a Sigle Model Baks, Carso, Nelso & Nicol Discrete-Evet System Simulatio Error Estimatio If {,, } are ot statistically idepedet, the S / is a biased estimator of the true variace.
More informationThe Choquet Integral with Respect to Fuzzy-Valued Set Functions
The Choquet Itegral with Respect to Fuzzy-Valued Set Fuctios Weiwei Zhag Abstract The Choquet itegral with respect to real-valued oadditive set fuctios, such as siged efficiecy measures, has bee used i
More informationThe Maximum-Likelihood Decoding Performance of Error-Correcting Codes
The Maximum-Lielihood Decodig Performace of Error-Correctig Codes Hery D. Pfister ECE Departmet Texas A&M Uiversity August 27th, 2007 (rev. 0) November 2st, 203 (rev. ) Performace of Codes. Notatio X,
More informationGUIDELINES ON REPRESENTATIVE SAMPLING
DRUGS WORKING GROUP VALIDATION OF THE GUIDELINES ON REPRESENTATIVE SAMPLING DOCUMENT TYPE : REF. CODE: ISSUE NO: ISSUE DATE: VALIDATION REPORT DWG-SGL-001 002 08 DECEMBER 2012 Ref code: DWG-SGL-001 Issue
More informationDIRECT LINEAR CONVERSION OF LSP PARAMETERS FOR PERCEPTUAL CONTROL IN SPEECH AND AUDIO CODING
DIRECT LINEAR CONVERSION OF LSP PARAMETERS FOR PERCEPTUAL CONTROL IN SPEECH AND AUDIO CODING R Sugiura 1, Y Kamamoto 2, N Harada 2, H Kameoka 2, T Moriya 2 1 Graduate School of Iformatio Sciece ad Techology,
More informationAre Slepian-Wolf Rates Necessary for Distributed Parameter Estimation?
Are Slepia-Wolf Rates Necessary for Distributed Parameter Estimatio? Mostafa El Gamal ad Lifeg Lai Departmet of Electrical ad Computer Egieerig Worcester Polytechic Istitute {melgamal, llai}@wpi.edu arxiv:1508.02765v2
More informationEntropy and Ergodic Theory Lecture 5: Joint typicality and conditional AEP
Etropy ad Ergodic Theory Lecture 5: Joit typicality ad coditioal AEP 1 Notatio: from RVs back to distributios Let (Ω, F, P) be a probability space, ad let X ad Y be A- ad B-valued discrete RVs, respectively.
More informationRandomized Algorithms I, Spring 2018, Department of Computer Science, University of Helsinki Homework 1: Solutions (Discussed January 25, 2018)
Radomized Algorithms I, Sprig 08, Departmet of Computer Sciece, Uiversity of Helsiki Homework : Solutios Discussed Jauary 5, 08). Exercise.: Cosider the followig balls-ad-bi game. We start with oe black
More informationw (1) ˆx w (1) x (1) /ρ and w (2) ˆx w (2) x (2) /ρ.
2 5. Weighted umber of late jobs 5.1. Release dates ad due dates: maximimizig the weight of o-time jobs Oce we add release dates, miimizig the umber of late jobs becomes a sigificatly harder problem. For
More information1.0 Probability of Error for non-coherent BFSK
Probability of Error, Digital Sigalig o a Fadig Chael Ad Equalizatio Schemes for ISI Wireless Commuicatios echologies Sprig 5 Lectures & R Departmet of Electrical Egieerig, Rutgers Uiversity, Piscataway,
More informationRank Modulation with Multiplicity
Rak Modulatio with Multiplicity Axiao (Adrew) Jiag Computer Sciece ad Eg. Dept. Texas A&M Uiversity College Statio, TX 778 ajiag@cse.tamu.edu Abstract Rak modulatio is a scheme that uses the relative order
More informationThe Method of Least Squares. To understand least squares fitting of data.
The Method of Least Squares KEY WORDS Curve fittig, least square GOAL To uderstad least squares fittig of data To uderstad the least squares solutio of icosistet systems of liear equatios 1 Motivatio Curve
More informationProbability of error for LDPC OC with one co-channel Interferer over i.i.d Rayleigh Fading
IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 2278-2834,p- ISSN: 2278-8735.Volume 9, Issue 4, Ver. III (Jul - Aug. 24), PP 59-63 Probability of error for LDPC OC with oe co-chael
More informationEE260: Digital Design, Spring n MUX Gate n Rudimentary functions n Binary Decoders. n Binary Encoders n Priority Encoders
EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig MUXs, Ecoders, Decoders Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi at Māoa Overview of Ecoder ad Decoder MUX Gate
More informationArithmetic Distribution Matching
Arithmetic Distributio Matchig Sebastia Baur ad Georg Böcherer Istitute for Commuicatios Egieerig Techische Uiversität Müche, Germay Email: baursebastia@mytum.de,georg.boecherer@tum.de arxiv:48.393v [cs.it]
More informationStatistics 511 Additional Materials
Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability
More informationDiagnosis of Kinematic Vertical Velocity in HYCOM. By George Halliwell, 28 November ( ) = z. v (1)
Diagosis of Kiematic Vertical Velocity i HYCOM By George Halliwell 28 ovember 2004 Overview The vertical velocity w i Cartesia coordiates is determied by vertically itegratig the cotiuity equatio dw (
More informationNUMERICAL INVESTIGATION OF FEEDBACK CONTROL IN PLASMA PROCESSING REACTORS INTRODUCTION
NUMERICAL INVESTIGATION OF FEEDBACK CONTROL IN PLASMA PROCESSING REACTORS Shahid Rauf ad Mark J. Kusher Departmet of Electrical ad Computer Egieerig Uiversity of Illiois 1406 W. Gree Street, Urbaa, Illiois
More informationLecture 6: Source coding, Typicality, and Noisy channels and capacity
15-859: Iformatio Theory ad Applicatios i TCS CMU: Sprig 2013 Lecture 6: Source codig, Typicality, ad Noisy chaels ad capacity Jauary 31, 2013 Lecturer: Mahdi Cheraghchi Scribe: Togbo Huag 1 Recap Uiversal
More informationADVANCED DIGITAL SIGNAL PROCESSING
ADVANCED DIGITAL SIGNAL PROCESSING PROF. S. C. CHAN (email : sccha@eee.hku.hk, Rm. CYC-702) DISCRETE-TIME SIGNALS AND SYSTEMS MULTI-DIMENSIONAL SIGNALS AND SYSTEMS RANDOM PROCESSES AND APPLICATIONS ADAPTIVE
More informationWE study the problem of decentralized detection in a
IEEE SIGNAL PROCESSING LETTERS, VOL.XX, NO.X Double-detector for Sparse Sigal Detectio from Oe Bit Compressed Sesig Measuremets Hadi Zayyai, Farza Haddadi, Member, IEEE, ad Mehdi Korki, Studet Member,
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals
More informationFree Space Optical Wireless Communications under Turbulence Channel Effect
IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue 3, Ver. III (May - Ju. 014), PP 01-08 Free Space Optical Wireless Commuicatios uder Turbulece
More informationNumber of fatalities X Sunday 4 Monday 6 Tuesday 2 Wednesday 0 Thursday 3 Friday 5 Saturday 8 Total 28. Day
LECTURE # 8 Mea Deviatio, Stadard Deviatio ad Variace & Coefficiet of variatio Mea Deviatio Stadard Deviatio ad Variace Coefficiet of variatio First, we will discuss it for the case of raw data, ad the
More informationMedian and IQR The median is the value which divides the ordered data values in half.
STA 666 Fall 2007 Web-based Course Notes 4: Describig Distributios Numerically Numerical summaries for quatitative variables media ad iterquartile rage (IQR) 5-umber summary mea ad stadard deviatio Media
More informationComplex Algorithms for Lattice Adaptive IIR Notch Filter
4th Iteratioal Coferece o Sigal Processig Systems (ICSPS ) IPCSIT vol. 58 () () IACSIT Press, Sigapore DOI:.7763/IPCSIT..V58. Complex Algorithms for Lattice Adaptive IIR Notch Filter Hog Liag +, Nig Jia
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should be doe
More information6.3 Testing Series With Positive Terms
6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial
More informationStudy on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm
Joural of ad Eergy Egieerig, 05, 3, 43-437 Published Olie April 05 i SciRes. http://www.scirp.org/joural/jpee http://dx.doi.org/0.436/jpee.05.34058 Study o Coal Cosumptio Curve Fittig of the Thermal Based
More informationEstimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable
Iteratioal Joural of Probability ad Statistics 01, 1(4: 111-118 DOI: 10.593/j.ijps.010104.04 Estimatio of Populatio Mea Usig Co-Efficiet of Variatio ad Media of a Auxiliary Variable J. Subramai *, G. Kumarapadiya
More informationNumber Representation
Number Represetatio 1 Number System :: The Basics We are accustomed to usig the so-called decimal umber system Te digits :: 0,1,2,3,4,5,6,7,8,9 Every digit positio has a weight which is a power of 10 Base
More informationBayesian and E- Bayesian Method of Estimation of Parameter of Rayleigh Distribution- A Bayesian Approach under Linex Loss Function
Iteratioal Joural of Statistics ad Systems ISSN 973-2675 Volume 12, Number 4 (217), pp. 791-796 Research Idia Publicatios http://www.ripublicatio.com Bayesia ad E- Bayesia Method of Estimatio of Parameter
More informationSymmetric Two-User Gaussian Interference Channel with Common Messages
Symmetric Two-User Gaussia Iterferece Chael with Commo Messages Qua Geg CSL ad Dept. of ECE UIUC, IL 680 Email: geg5@illiois.edu Tie Liu Dept. of Electrical ad Computer Egieerig Texas A&M Uiversity, TX
More informationECE 901 Lecture 12: Complexity Regularization and the Squared Loss
ECE 90 Lecture : Complexity Regularizatio ad the Squared Loss R. Nowak 5/7/009 I the previous lectures we made use of the Cheroff/Hoeffdig bouds for our aalysis of classifier errors. Hoeffdig s iequality
More informationLecture 10: Universal coding and prediction
0-704: Iformatio Processig ad Learig Sprig 0 Lecture 0: Uiversal codig ad predictio Lecturer: Aarti Sigh Scribes: Georg M. Goerg Disclaimer: These otes have ot bee subjected to the usual scrutiy reserved
More information567. Research of Dynamics of a Vibration Isolation Platform
567. Research of Dyamics of a Vibratio Isolatio Platform A. Kilikevičius, M. Jurevičius 2, M. Berba 3 Vilius Gedimias Techical Uiversity, Departmet of Machie buildig, J. Basaavičiaus str. 28, LT-03224
More informationsubject to A 1 x + A 2 y b x j 0, j = 1,,n 1 y j = 0 or 1, j = 1,,n 2
Additioal Brach ad Boud Algorithms 0-1 Mixed-Iteger Liear Programmig The brach ad boud algorithm described i the previous sectios ca be used to solve virtually all optimizatio problems cotaiig iteger variables,
More informationSupport vector machine revisited
6.867 Machie learig, lecture 8 (Jaakkola) 1 Lecture topics: Support vector machie ad kerels Kerel optimizatio, selectio Support vector machie revisited Our task here is to first tur the support vector
More informationImage Segmentation on Spiral Architecture
Image Segmetatio o Spiral Architecture Qiag Wu, Xiagjia He ad Tom Hitz Departmet of Computer Systems Uiversity of Techology, Sydey PO Box 3, Broadway Street, Sydey 007, Australia {wuq,sea,hitz}@it.uts.edu.au
More informationCS276A Practice Problem Set 1 Solutions
CS76A Practice Problem Set Solutios Problem. (i) (ii) 8 (iii) 6 Compute the gamma-codes for the followig itegers: (i) (ii) 8 (iii) 6 Problem. For this problem, we will be dealig with a collectio of millio
More informationREGRESSION (Physics 1210 Notes, Partial Modified Appendix A)
REGRESSION (Physics 0 Notes, Partial Modified Appedix A) HOW TO PERFORM A LINEAR REGRESSION Cosider the followig data poits ad their graph (Table I ad Figure ): X Y 0 3 5 3 7 4 9 5 Table : Example Data
More information