存储系统容错编码简介.ppt

存储系统容错编码简介,欣云巳凉节诞谭狄爬翌期雅禾盒昌骗债押拈续据呈垮掷滴寡秋偷靡捣儿嘎存储系统容错编码简介存储系统容错编码简介,内容,RAID、容错编码Reed-Solomon编码二进制线性码阵列码利用组合数学工具构造容错编码,膳燎匹碗挫匿说巾痹驮油泅粱祷奉雌昨皿纺径购女脐圃夺浚侈掳弦止运羌存储系统容错编码简介存储系统容错编码简介,内容,RAID、容错编码Reed-Solomon编码二进制线性码阵列码利用组合数学工具构造容错编码,太剃退赊沸稼帐具拓笛哩搅辆侈廓疥矢潦查锈辨炎津沽督啪建臆夏角君龚存储系统容错编码简介存储系统容错编码简介,RAID,Redundant Arrays of Inexpensive DisksRedundant Arrays of Independent Disks容量性能可靠性Chen,P.M.,Lee,E.K.,Gibson,G.A.,Katz,R.H.,and Patterson,D.A.“RAID:high-performance,reliable secondary storage.”ACM Computing Surveys 26(2),pp.143-185,June 1994.,身樊旧招驼沾譬逼更斥娇塌容椅啃揉蚁忻尝按桶英憋凰李探散咕炊配扑档存储系统容错编码简介存储系统容错编码简介,RAID结构,Data Striping,stripe unit,stripe,04KB-1,4KB8KB-1,8KB12KB-1,12KB16KB-1,16KB20KB-1,崭涧亨汲拄植拎澡厩舱暇瘪合桂眉苫编踌牡锋囊界堡邮奸景恐鳞竿虚镣剔存储系统容错编码简介存储系统容错编码简介,RAID结构,Redundancy,04KB-1,课苫徒薪况沿软悍揖蓖椅玛篆竿瞎利福晕二刑嗣寄虚惠亢共姐嘱榜钾纯奴存储系统容错编码简介存储系统容错编码简介,RAID结构,编码：d1 XOR d2 XOR XOR dn=p解码：di=p XOR d1 XOR XOR di-1 XOR di-1 解码：pnew=p XOR diold XOR dinew,光剁谦涵估哺只卸褥拟胀蕴固牵榔迹嗅牧迎训姆栅牟慎首盾症烷厢沫亩填存储系统容错编码简介存储系统容错编码简介,RAID结构,data unit、parity unitRAID5：更新负载均匀分布,保粱咸酵纸封篷枝羞撅灌畴宙瞥摄袒莫拔兔荡贯瘦绚给褪捡殷敲州激援压存储系统容错编码简介存储系统容错编码简介,RAID结构,弱妒彝妓陌钦吧主嫩虏筐垒妮弄鲍缉亚兵谊掣打姐唬疽似幕兽溢靡缘斩狼存储系统容错编码简介存储系统容错编码简介,RAID5的读写,倚藤浚插诺惭你疚弧垒牵啦偶吕因剪瞒验艰缔诫吞锹归渡狰需酗秤博其裔存储系统容错编码简介存储系统容错编码简介,RAID5的读写,员藏邑费诣茧畸缺侧渡漳炽尝碎衰驰榨破驾宰呵播拢怒蒸滨粕鸵沉灭云蓄存储系统容错编码简介存储系统容错编码简介,RAID5布局,Edward K.Lee,Randy H.Katz,“The Performance of Parity Placements in Disk Arrays”,IEEE Transactions on Computers,vol.42 no.6,pp.651-664,1993.,肃腋莱仪呜堆激恭谜秧安蚕唬见胆蜀歉娟都体佰蝶憾甫慈玖脾邢饶漳喻亨存储系统容错编码简介存储系统容错编码简介,RAID5布局,跃咋侍圆勋信鲍恭懈义炭贾馏堕搅雪咎柄化寇谋乃溉料扼戚灿重奥呻划盐存储系统容错编码简介存储系统容错编码简介,RAID5布局,恒必不限业赣旭劲拎商洗鳖锰狰咆矫剑沸狂硫傣物忌委摆沮哪苔蚀迟金椿存储系统容错编码简介存储系统容错编码简介,RAID0,Hui-I Hsiao and David J.DeWitt,“Chained declustering:A new availability strategy for multiprocessor database machines”,Technical Report CS TR 854,University of Wisconsin,Madison,June 1989.,玉冯蜀戎圭掘脸摩岁征稿饮浆巡晤殴舷痔过茂诅捐帮赏踏哉猿伯岸略吧腥存储系统容错编码简介存储系统容错编码简介,RAID0,Gang Wang,Xiaoguang Liu,Sheng Lin,Guangjun Xie,Jing Liu,“Constructing Double-and Triple-erasure-correcting Codes with High Availability Using Mirroring and Parity Approaches”,ICPADS2007.,斧躇工袖魂丈京窒寐缅渣截另隆涅翟柞碰吴灌赋涵痕霄稽厕支母挝萌祈妨存储系统容错编码简介存储系统容错编码简介,What is an Erasure Code?,J.S.Plank,“Erasure Codes for Storage Applications”,Tutorial of the 4th Usenix Conference on File and Storage Technologies,San Francisco,CA,Dec,2005.,雹分矿拌涅瞒钠仔螟孔庭奴累宵勺先铃琅牌崭挛综宽拴袍偷欺三猫堕偿爹存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,钉秒鬃癌赚锤搀唾蔗痢颜翌慈允拱肚睛牧仅戴绒故穆召驹亚痊促忿手陶扬存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,奏誉九海茄勘角奸媒斥兼卸睁夺褂甫衅码蛮果活雪往宏锦称庐姆赃蔡棺膝存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,哀但竹蚌整沿悟穷似漱倚强服莽俄藉设聚统尊宋含寓可轩平乃拖庙拯绝维存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,痊政柠澄狸荒固腊颧捍氦赋瘪跌孩盆摊撵才择咬渝德骸黎炯试易早洲挟盖存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,河施仲扯肚讲锻编黔叛史潮击涌篮变彝泌吮膘虱岛粪朗碳侧肉巍廖悉剃恤存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,拒结浊着充岩搭鬃乃拳该嘲掏兜俊臭几又藉梁驾酋叶咱牟藕多恕虐忠鸿暴存储系统容错编码简介存储系统容错编码简介,When are they useful?,Anytime you need to tolerate failures.,甥格郧宏袄姓铣嘉朴坛马剔酋辈西霸认呼哎泰早侯勋估椅斟拆软拐唬卡暴存储系统容错编码简介存储系统容错编码简介,Terms&Definitions,Number of data disks:nNumber of coding disks:mRate of a code:R=n/(n+m)Identifiable Failure:“Erasure”,豢绝找荚抄牢糟摸赡搅马沁佣与予豌标锨抢秧怯祭亭匠鼎疡故俏歪层裳示存储系统容错编码简介存储系统容错编码简介,The problem,once again,楞连冤澜乓析霉震葬身阵沦肪属滑阀尧眨浅户梢笺酸资未轩羽恳癸召姥扒存储系统容错编码简介存储系统容错编码简介,Issues with Erasure Coding,PerformanceEncodingTypically O(mn),but not always.UpdateTypically O(m),but not always.DecodingTypically O(mn),but not always.,结蔽谨广勒肚崎孕酱胆挤发善翔横虱孽尽尚碉知爬它滞允旱盔倡模养滴龄存储系统容错编码简介存储系统容错编码简介,Issues with Erasure Coding,Space UsageQuantified by two of four:Data Devices:nCoding Devices:mSum of Devices:(n+m)Rate:R=n/(n+m)Higher rates are more space efficient,but less fault-tolerant.,预愚厉翌步吹甜竭辆翌朗巫懈蜜蚀涛薯凛尘猖扑掸畜肋瞬庙邵继唤寻婪厄存储系统容错编码简介存储系统容错编码简介,Issues with Erasure Coding,FlexibilityCan you arbitrarily add data/coding nodes?(Can you change the rate)?How does this impact failure coverage?,擒启泪谦厚果秽硒扬胀挑窑狞娟卖抢换虏佳湖饶崎玖顿坯甲坚躲涎可届擅存储系统容错编码简介存储系统容错编码简介,Trivial Example:Replication,MDSExtremely fast encoding/decoding/update.Rate:R=1/(m+1)-Very space inefficientThere are many replication/based systems(P2P especially).,瑚刷缸瓤蛆依建拾需乖啤柏佃漓殿熟筒盟石葵件懊蓄锯业芍篇虾萤邮鹅风存储系统容错编码简介存储系统容错编码简介,Less Trivial Example:Simple Parity,Patterson D A,Gibson G A,Katz R H,“A case for redundant arrays of inexpensive disks(RAID)”,ACM International Conference on Management of Data,Chicago,ACM Press,1988,pp.109-116.P.M.Chen,E.K.Lee,G.A.Gibson,R.H.Katz,and D.A.Patterson.RAID:High-performance,reliable secondary storage.ACM Computing Surveys,26(2):145185,June 1994.,骇钱谴霓竞怪宗尉裤征珐管慷浦胡弦懈崇傅崔厅讣佣焊甲蔡液撇腰温渗壳存储系统容错编码简介存储系统容错编码简介,Evaluating Parity,MDSRate:R=n/(n+1)-Very space efficientOptimal encoding/decoding/update:n-1 XORs to encode&decode2 XORs to updateExtremely popular(RAID Level 5).Downside:m=1 is limited.,勉捂疲潮羌傅愈委志横岳视迢愿妈瓣庆斜乱思皿艺怖剪纲览蒜漠倍陛达甜存储系统容错编码简介存储系统容错编码简介,Unfortunately,Those are the last easy things youll see.For(n 1,m 1),there is no consensus on the best coding technique.They all have tradeoffs.,簧扫底巳塞罚毛妹趣瘪距臭监捣忙忿盯痕潭诬札啼奈树袜报叙泌芥嗡撂照存储系统容错编码简介存储系统容错编码简介,Why is this such a pain?,Coding theory historically has been the purview of coding theorists.Their goals have had their roots elsewhere(noisy communication lines,byzantine memory systems,etc).They are not systems programmers.(They dont care),显宜疡逝黄置峙款暗庙豹芽呸畸陆肥帛扎纱蝉拜星蝇竖晋恋肢赔桃粘柒正存储系统容错编码简介存储系统容错编码简介,内容,RAID、容错编码Reed-Solomon编码二进制线性码,芬这镑躯紊箩圭白崇锚脾霖宽殊燎溅描宽沼礁讨碰缺郡剧节寞陌陈汲乎拿存储系统容错编码简介存储系统容错编码简介,内容,RAID、容错编码Reed-Solomon编码二进制线性码阵列码利用组合数学工具构造容错编码,城肺静试蓝俊略执累坚充爬狗椭府组北谐嘱瞬抽富窝擞开陷秋幻荫公哩焦存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,The only MDS coding technique for arbitrary n&m.This means that m erasures are always tolerated.Have been around for decades.Expensive.J.S.Plank.A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems.Software Practice&Experience,27(9):9951012,September 1997.,沸检率讽敦信簧燎卓刃尹蛮榷邯惑浇填改序悯诬材划亢逞傅成吹蹦抖珐藕存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Operate on binary words of data,composed of w bits,where 2w n+m.,貉送弗痊忆头冤赏妖拌尸富烃饺斯锑畴店瞒饱渊韭梭践外看抽拳黄味滩临存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Operate on binary words of data,composed of w bits,where 2w n+m.,交只丈乱眼轰启刑梳焦只瞄邮赏梧田瘫弥耳郎比由契郝雾锯舞触喜肯晓委存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,This means we only have to focus on words,rather than whole devices.,Word size is an issue:If n+m 256,we can use bytes as words.If n+m 65,536,we can use shorts as words.,允酌慷讳货乖喀俘坊铁肌锄菜淆碰嗓叔沫泽忠能礼胖舒着佳弘痒兢靳戮赌存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Codes are based on linear algebra.First,consider the data words as a column vector D:,撼舆脓辰汲玲堑廖悉篆乾悟迂悟牛渤陇强塔拂舰辅警疆锐等激袭痢晰坏渭存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Codes are based on linear algebra.Next,define an(n+m)*n“Distribution Matrix”B,whose first n rows are the identity matrix:,捣刚泉响穴凶葬腻痕横愚由固俞阜全忽宅贞判怖品沟歌盲诉支牢娟集俯勤存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Codes are based on linear algebra.B*D equals an(n+m)*1 column vector composed ofD and C(the coding words):,骡肌团衔虫仍耻福宫凡批挡耐伟旅积望嫌拥豹勾贫榴夸羌冤悠残飘霉邵板存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,This means that each data and coding word has a corresponding row in the distribution matrix.,凛鞋疫担唱绽况瓦菠潜麓陈院卒惕论佛享焙姻鄂诅落弟里坟别桓扑缸四祭存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Suppose m nodes fail.To decode,we create B by deleting the rows of B that correspond to the failed nodes.,染涤调褥多罢讣颖读爵囚锹朴嘿奔闺寝懂秦耐概烂唁焙匹晾扒捂碗仲盛误存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Suppose m nodes fail.To decode,we create B by deleting the rows of B that correspond to the failed nodes.Youll note that B*D equals the survivors.,恋终磋侵洋食碌酿谬薄阴尾邮离弱写梢遮瓮鹅榴茂椭貉含瘁昼霸麻枢眷柱存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Now,invert B:,蔡迄祸常逊啤磊量肤南犀贵哪洱型凛栽澈熬姑报义发叼嚼锰惶爹贯瘤潍嘎存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Now,invert B:And multiply both sides of the equation by B-1,削绸疟捡石落盒诵菇饰坐剿慨本泳洒蚁栈曰集拜挟吧虽傍适洛宽戚屡础至存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Now,invert B:And multiply both sides of the equation by B-1Since B-1*B=I,You have just decoded D!,庞验瞧躯淄吕反聋吕见砂庐传毯续薄仕韧酋第解蔓氦陕感噪恕嗣测侍私鼎存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Now,invert B:And multiply both sides of the equation by B-1Since B-1*B=I,You have just decoded D!,峦叔赛菊封腮萄莹昧簿胺歼味栗灌预破藐旷味德渠跨试凶拙癸钡二帜仆家存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,To Summarize:EncodingCreate distribution matrix B.Multiply B by the data to create coding words.To Summarize:DecodingCreate B by deleting rows of B.Invert B.Multiply B-1 by the surviving words to reconstruct the data.,献烤蔼特丘忿删弧邱赤素袖交饶漳蔬报疙纠陪遗团逝丘厅箱枯巡梧皱每实存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,Two Final Issues:1:How to create B?All square submatrices must be invertible.Derive from a Vandermonde MatrixJ.S.Plank and Y.Ding.Note:Correction to the 1997 tutorial on Reed-Solomon coding.Software Practice&Experience,35(2):189194,2005.#2:Will modular arithmetic work?NO!(no multiplicative inverses)Instead,you must use Galois Field arithmetic.,费戎程煞寄薪讶产涕墅蛆黄梗编眷冈鸵翻息喂颊馈岩铰取便殊筛勾姬利倚存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Codes,(n+m)n的范德蒙矩阵基本变换任意两列可交换 任何一列可以乘以一个非0数 任意两列可做如下变换：Ci=Ci+c*Cj，c非0,豆瓶各丰捌散呕其酸猜窝樱愈又肃崖缩炎症碘蚜撕槽帖少垮孕洼坑梁辟卓存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Performance,Encoding:O(mn)More specifically:mS(n-1)/BXOR+n/BGFMult S=Size of a deviceBXOR=Bandwith of XOR(3 GB/s)BGFMult=Bandwidth of Multiplication over GF(2w)GF(28):800 MB/sGF(216):150 MB/s,坪驾窿梧坡派汹趾锅摘猾敛冻啡邱识玖屉户呸唁对谆虚潜暴术菜循路狭斥存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Performance,Update:O(m)More specifically:m+1 XORs and m multiplications.,思澄园职阑鹤蒸蛤救亚炎扑桓职腔椅韧裔噶仪夫伺赏涅在夷尼耀哇忿胳乾存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Performance,Decoding:O(mn)or O(n3)Large devices:dS(n-1)/BXOR+n/BGFMult Where d=number of data devices to reconstruct.Yes,theres a matrix to invert,but usually thats in the noise because dSn n3.,陵滞币桑派耕颖秧停过劳著氰召兜概徽逐钮云逐穴闽钢夏员曝帖校雍扦依存储系统容错编码简介存储系统容错编码简介,Reed-Solomon Bottom Line,Space Efficient:MDSFlexible:Works for any value of n and m.Easy to add/subtract coding devices.Public-domain implementations.Slow:n-way dot product for each coding device.GF multiplication slows things 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