History of Belief-propagation thresholds of regular LDPC codes on the binary erasure channel

 Display properties:   number-header: $\epsilon^{\mathrm{BP}}_{l,r}$-Numbers: []+Numbers:+- params:+    l: '3'+    r: '4'+  number: '0.6474256494010103699433673115176290794176741107650388581643454178949251946404222573497173063291285627'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,4}=0.441742430504$.+- params:+    l: '3'+    r: '5'+  number: '0.5175701819014950776573150128369529845784690039348490084539515956945751460723288248871259995838820798'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,5}=0.328093462089$.+- params:+    l: '3'+    r: '6'+  number: '0.4294398144194918371556095283314474261570741280102327674982252297778539595778854667886948322839447969'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,6}=0.260571072907$. Kudekar,+    Richardson and Urbanke give $\epsilon^{\mathrm{BP}}_{3,6}\approx 0.42944$ CITE{KRU}.+- params:+    l: '3'+    r: '7'+  number: '0.3664191795204672190054844740538174783547992084743690982984788018673415506734775838588358227824760715'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,7}=0.215987266858$.+- params:+    l: '3'+    r: '8'+  number: '0.3193121153498562380628066051322261591981582956154777910588018999149484632662304891389124833126536665'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,8}=0.184389835313$.+- params:+    l: '3'+    r: '9'+  number: '0.2828368323849195683202375811045292618215463222739268519494902916046974085811068318243660360321094594'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,9}=0.160839303572$.+- params:+    l: '3'+    r: '10'+  number: '0.2537883708018809667532335500702106657528194685686144015831277786559442100036324469334302337054245866'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,10}=0.142614216099$.+- params:+    l: '3'+    r: '11'+  number: '0.2301218323212584284986642045941442567014493529772342160418634618740971447529743260234083428882897306'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,11}=0.128094106724$.+- params:+    l: '3'+    r: '12'+  number: '0.2104754161202487813349595049899685765930835926308175169312570894619199313305232082470429284422308274'+  comment: The double fixed point is $x^{\mathrm{BP}}_{3,12}=0.116254634433$.+- params:+    l: '4'+    r: '5'+  number: '0.6001109521010464656499858617730463383383880806922300388641488073162519666444753774847972952765523524'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,5}=0.447178781923$.+- params:+    l: '4'+    r: '6'+  number: '0.5061323461778445767230851604158820509733169739598299428042821537288047943048420150162027255250528358'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,6}=0.363349503139$.+- params:+    l: '4'+    r: '7'+  number: '0.4365973733885906978937682724018898835252463116049600796868301571402046702405036478068799761190369744'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,7}=0.305653674412$.+- params:+    l: '4'+    r: '8'+  number: '0.3834465723217366076713832595502640761171472547763852706474898686755986714428632574482601247414380972'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,8}=0.263641195507$.+- params:+    l: '4'+    r: '9'+  number: '0.3416363173952012807450502125841236782416334896147780221340235468358284855417700460001922748679668034'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,9}=0.231724294029$.+- params:+    l: '4'+    r: '10'+  number: '0.3079448626463704483076579180073641200025958485449853954989549962238362259343062742300033378054747497'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,10}=0.206671364907$.+- params:+    l: '4'+    r: '11'+  number: '0.2802441556862722274341775835157686654723284080974125100903651232745423059753541253772197996778775523'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,11}=0.186490985393$.+- params:+    l: '4'+    r: '12'+  number: '0.2570810044002002062878130397566264096083022653941202514618306309924457648424711316261757005291041602'+  comment: The double fixed point is $x^{\mathrm{BP}}_{4,12}=0.169891588461$.+- params:+    l: '5'+    r: '6'+  number: '0.5510035343592071877001978562847294544651830312216153731364836008490865456653675113073303443443939787'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,6}=0.423346634329$.+- params:+    l: '5'+    r: '7'+  number: '0.4786068038434105556178854556205779846526315167489651889407588241456539569637023146872102815771754087'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,7}=0.359329197651$.+- params:+    l: '5'+    r: '8'+  number: '0.4224462340617003241436373701113741934274632137803969757057708643919887781382348374246104758416248662'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,8}=0.311907937730$.+- params:+    l: '5'+    r: '9'+  number: '0.3778045406996808318680869260973492223193382754316516604426166551081576109585842540316854636870743317'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,9}=0.275442493047$.+- params:+    l: '5'+    r: '10'+  number: '0.3415500230422898616119782202561890673706299233815931950029602324826762254567458430428227687717286480'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,10}=0.246559219310$.+- params:+    l: '5'+    r: '11'+  number: '0.3115613668707418904096704881272331616188026452622918315309667600557217571584471249587444744980884923'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,11}=0.223129866466$.+- params:+    l: '5'+    r: '12'+  number: '0.2863638191408606265061135584132343079208264474259569899868222172425607932593914682836128693536610976'+  comment: The double fixed point is $x^{\mathrm{BP}}_{5,12}=0.203749968730$.+- params:+    l: '6'+    r: '7'+  number: '0.5078931849564840370145190056941074999602568618222345012752539048133021753115719794580482496826508765'+  comment: The double fixed point is $x^{\mathrm{BP}}_{6,7}=0.396594280939$.+- params:+    l: '6'+    r: '8'+  number: '0.4499266014156229849804014629697984467294823240966564608181002128167669813337428912672943747827178889'+  comment: The double fixed point is $x^{\mathrm{BP}}_{6,8}=0.345806583477$.+- params:+    l: '6'+    r: '9'+  number: '0.4034896617599236421382849526538677671220618814348480870333448145428664213849033885129327059944081884'+  comment: The double fixed point is $x^{\mathrm{BP}}_{6,9}=0.306406485969$.+- params:+    l: '6'+    r: '10'+  number: '0.3655576802459955413403089064393596127437660343371445050087197292516013105815031632188793463428709615'+  comment: The double fixed point is $x^{\mathrm{BP}}_{6,10}=0.274992604778$.+- params:+    l: '6'+    r: '11'+  number: '0.3340399429542679649596109362591965728790962684472775849392287336260061644402960792804585171718729510'+  comment: The double fixed point is $x^{\mathrm{BP}}_{6,11}=0.249380043956$.+- params:+    l: '6'+    r: '12'+  number: '0.3074622614781001286506942179484307980678259368037273002773986521277249486856936927537786859057259164'+  comment: The double fixed point is $x^{\mathrm{BP}}_{6,12}=0.228107723378$.+- params:+    l: '7'+    r: '8'+  number: '0.4708776764367653180080414660808348676898325435659472266483030186298481905356430975552569713199600387'+  comment: The double fixed point is $x^{\mathrm{BP}}_{7,8}=0.371562423694$.+- params:+    l: '7'+    r: '9'+  number: '0.4231886405149950444888261511366039792202241027810258141202052780434646915939602758357528427570365077'+  comment: The double fixed point is $x^{\mathrm{BP}}_{7,9}=0.330081990786$.+- params:+    l: '7'+    r: '10'+  number: '0.3840537633660437191600799252554193238295467299887766912931413598652076754977298971537488457673580010'+  comment: The double fixed point is $x^{\mathrm{BP}}_{7,10}=0.296838488968$.+- params:+    l: '7'+    r: '11'+  number: '0.3514199823576594701384389639210459891691112996996064104914255344287078345986366999303150923235012510'+  comment: The double fixed point is $x^{\mathrm{BP}}_{7,11}=0.269625553242$.+- params:+    l: '7'+    r: '12'+  number: '0.3238224384249304119408323168009798830948027320051705281874757234651074646271270728304934201356450144'+  comment: The double fixed point is $x^{\mathrm{BP}}_{7,12}=0.246951723225$.+- params:+    l: '8'+    r: '9'+  number: '0.4390466829307120666245868416212772034594638315329363048099521653002392036138786627616403393689664728'+  comment: The double fixed point is $x^{\mathrm{BP}}_{8,9}=0.349089111349$.+- params:+    l: '8'+    r: '10'+  number: '0.3989979708441433017922917527240491279033052446349398242872941710234726016245663464524707218083056878'+  comment: The double fixed point is $x^{\mathrm{BP}}_{8,10}=0.314444692598$.+- params:+    l: '8'+    r: '11'+  number: '0.3655029966349869928469911768826772127930431349594401129301536193206165361650335745293344540194136640'+  comment: The double fixed point is $x^{\mathrm{BP}}_{8,11}=0.285991809376$.+- params:+    l: '8'+    r: '12'+  number: '0.3371100093630909745047015169932057557397384429361947947573332994696209700137294863850605354782287224'+  comment: The double fixed point is $x^{\mathrm{BP}}_{8,12}=0.262222656528$.+- params:+    l: '9'+    r: '10'+  number: '0.4114755018414529615295155139647411173285158295955574993619146649245643652592891436132638216606286903'+  comment: The double fixed point is $x^{\mathrm{BP}}_{9,10}=0.329112357358$.+- params:+    l: '9'+    r: '11'+  number: '0.3772899057397068364290390283540364704544118530464464440269904042022080047891731003966468567479474885'+  comment: The double fixed point is $x^{\mathrm{BP}}_{9,11}=0.299661147716$.+- params:+    l: '9'+    r: '12'+  number: '0.3482529088467711548182209211858629708317778468850640815717558852251178757800754450291825343685525169'+  comment: The double fixed point is $x^{\mathrm{BP}}_{9,12}=0.275003404411$.+- params:+    l: '10'+    r: '11'+  number: '0.3873919295931600570180140714300080706543443814296091657551792094255238532308188318832053099990127742'+  comment: The double fixed point is $x^{\mathrm{BP}}_{10,11}=0.311355180190$.+- params:+    l: '10'+    r: '12'+  number: '0.3578190375174394542399300814069318585794094607321170936820173527151865145417347822894569931196571523'+  comment: The double fixed point is $x^{\mathrm{BP}}_{10,12}=0.285956506693$.+- params:+    l: '11'+    r: '12'+  number: '0.3661801706661561881089519003920240893017581910073416632009498146646784722630737870566683726752469087'+  comment: The double fixed point is $x^{\mathrm{BP}}_{11,12}=0.295515258010$.