Polar codes
Reliability sequence for 5G
Below is the reliability sequence $Q_0, Q_1, \ldots, Q_{1023}$ of the length-$1024$ polar code used in 5G, in ascending order of reliability. The entry in row $r$ and column $c$ is $Q_{r + c}$.
Source: ETSI18, Table 5.3.1.2-1, pp. 16–18.
| $r \backslash c$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ |
|---|---|---|---|---|---|---|---|---|
| $0$ | $0$ | $1$ | $2$ | $4$ | $8$ | $16$ | $32$ | $3$ |
| $8$ | $5$ | $64$ | $9$ | $6$ | $17$ | $10$ | $18$ | $128$ |
| $16$ | $12$ | $33$ | $65$ | $20$ | $256$ | $34$ | $24$ | $36$ |
| $24$ | $7$ | $129$ | $66$ | $512$ | $11$ | $40$ | $68$ | $130$ |
| $32$ | $19$ | $13$ | $48$ | $14$ | $72$ | $257$ | $21$ | $132$ |
| $40$ | $35$ | $258$ | $26$ | $513$ | $80$ | $37$ | $25$ | $22$ |
| $48$ | $136$ | $260$ | $264$ | $38$ | $514$ | $96$ | $67$ | $41$ |
| $56$ | $144$ | $28$ | $69$ | $42$ | $516$ | $49$ | $74$ | $272$ |
| $64$ | $160$ | $520$ | $288$ | $528$ | $192$ | $544$ | $70$ | $44$ |
| $72$ | $131$ | $81$ | $50$ | $73$ | $15$ | $320$ | $133$ | $52$ |
| $80$ | $23$ | $134$ | $384$ | $76$ | $137$ | $82$ | $56$ | $27$ |
| $88$ | $97$ | $39$ | $259$ | $84$ | $138$ | $145$ | $261$ | $29$ |
| $96$ | $43$ | $98$ | $515$ | $88$ | $140$ | $30$ | $146$ | $71$ |
| $104$ | $262$ | $265$ | $161$ | $576$ | $45$ | $100$ | $640$ | $51$ |
| $112$ | $148$ | $46$ | $75$ | $266$ | $273$ | $517$ | $104$ | $162$ |
| $120$ | $53$ | $193$ | $152$ | $77$ | $164$ | $768$ | $268$ | $274$ |
| $128$ | $518$ | $54$ | $83$ | $57$ | $521$ | $112$ | $135$ | $78$ |
| $136$ | $289$ | $194$ | $85$ | $276$ | $522$ | $58$ | $168$ | $139$ |
| $144$ | $99$ | $86$ | $60$ | $280$ | $89$ | $290$ | $529$ | $524$ |
| $152$ | $196$ | $141$ | $101$ | $147$ | $176$ | $142$ | $530$ | $321$ |
| $160$ | $31$ | $200$ | $90$ | $545$ | $292$ | $322$ | $532$ | $263$ |
| $168$ | $149$ | $102$ | $105$ | $304$ | $296$ | $163$ | $92$ | $47$ |
| $176$ | $267$ | $385$ | $546$ | $324$ | $208$ | $386$ | $150$ | $153$ |
| $184$ | $165$ | $106$ | $55$ | $328$ | $536$ | $577$ | $548$ | $113$ |
| $192$ | $154$ | $79$ | $269$ | $108$ | $578$ | $224$ | $166$ | $519$ |
| $200$ | $552$ | $195$ | $270$ | $641$ | $523$ | $275$ | $580$ | $291$ |
| $208$ | $59$ | $169$ | $560$ | $114$ | $277$ | $156$ | $87$ | $197$ |
| $216$ | $116$ | $170$ | $61$ | $531$ | $525$ | $642$ | $281$ | $278$ |
| $224$ | $526$ | $177$ | $293$ | $388$ | $91$ | $584$ | $769$ | $198$ |
| $232$ | $172$ | $120$ | $201$ | $336$ | $62$ | $282$ | $143$ | $103$ |
| $240$ | $178$ | $294$ | $93$ | $644$ | $202$ | $592$ | $323$ | $392$ |
| $248$ | $297$ | $770$ | $107$ | $180$ | $151$ | $209$ | $284$ | $648$ |
| $256$ | $94$ | $204$ | $298$ | $400$ | $608$ | $352$ | $325$ | $533$ |
| $264$ | $155$ | $210$ | $305$ | $547$ | $300$ | $109$ | $184$ | $534$ |
| $272$ | $537$ | $115$ | $167$ | $225$ | $326$ | $306$ | $772$ | $157$ |
| $280$ | $656$ | $329$ | $110$ | $117$ | $212$ | $171$ | $776$ | $330$ |
| $288$ | $226$ | $549$ | $538$ | $387$ | $308$ | $216$ | $416$ | $271$ |
| $296$ | $279$ | $158$ | $337$ | $550$ | $672$ | $118$ | $332$ | $579$ |
| $304$ | $540$ | $389$ | $173$ | $121$ | $553$ | $199$ | $784$ | $179$ |
| $312$ | $228$ | $338$ | $312$ | $704$ | $390$ | $174$ | $554$ | $581$ |
| $320$ | $393$ | $283$ | $122$ | $448$ | $353$ | $561$ | $203$ | $63$ |
| $328$ | $340$ | $394$ | $527$ | $582$ | $556$ | $181$ | $295$ | $285$ |
| $336$ | $232$ | $124$ | $205$ | $182$ | $643$ | $562$ | $286$ | $585$ |
| $344$ | $299$ | $354$ | $211$ | $401$ | $185$ | $396$ | $344$ | $586$ |
| $352$ | $645$ | $593$ | $535$ | $240$ | $206$ | $95$ | $327$ | $564$ |
| $360$ | $800$ | $402$ | $356$ | $307$ | $301$ | $417$ | $213$ | $568$ |
| $368$ | $832$ | $588$ | $186$ | $646$ | $404$ | $227$ | $896$ | $594$ |
| $376$ | $418$ | $302$ | $649$ | $771$ | $360$ | $539$ | $111$ | $331$ |
| $384$ | $214$ | $309$ | $188$ | $449$ | $217$ | $408$ | $609$ | $596$ |
| $392$ | $551$ | $650$ | $229$ | $159$ | $420$ | $310$ | $541$ | $773$ |
| $400$ | $610$ | $657$ | $333$ | $119$ | $600$ | $339$ | $218$ | $368$ |
| $408$ | $652$ | $230$ | $391$ | $313$ | $450$ | $542$ | $334$ | $233$ |
| $416$ | $555$ | $774$ | $175$ | $123$ | $658$ | $612$ | $341$ | $777$ |
| $424$ | $220$ | $314$ | $424$ | $395$ | $673$ | $583$ | $355$ | $287$ |
| $432$ | $183$ | $234$ | $125$ | $557$ | $660$ | $616$ | $342$ | $316$ |
| $440$ | $241$ | $778$ | $563$ | $345$ | $452$ | $397$ | $403$ | $207$ |
| $448$ | $674$ | $558$ | $785$ | $432$ | $357$ | $187$ | $236$ | $664$ |
| $456$ | $624$ | $587$ | $780$ | $705$ | $126$ | $242$ | $565$ | $398$ |
| $464$ | $346$ | $456$ | $358$ | $405$ | $303$ | $569$ | $244$ | $595$ |
| $472$ | $189$ | $566$ | $676$ | $361$ | $706$ | $589$ | $215$ | $786$ |
| $480$ | $647$ | $348$ | $419$ | $406$ | $464$ | $680$ | $801$ | $362$ |
| $488$ | $590$ | $409$ | $570$ | $788$ | $597$ | $572$ | $219$ | $311$ |
| $496$ | $708$ | $598$ | $601$ | $651$ | $421$ | $792$ | $802$ | $611$ |
| $504$ | $602$ | $410$ | $231$ | $688$ | $653$ | $248$ | $369$ | $190$ |
| $512$ | $364$ | $654$ | $659$ | $335$ | $480$ | $315$ | $221$ | $370$ |
| $520$ | $613$ | $422$ | $425$ | $451$ | $614$ | $543$ | $235$ | $412$ |
| $528$ | $343$ | $372$ | $775$ | $317$ | $222$ | $426$ | $453$ | $237$ |
| $536$ | $559$ | $833$ | $804$ | $712$ | $834$ | $661$ | $808$ | $779$ |
| $544$ | $617$ | $604$ | $433$ | $720$ | $816$ | $836$ | $347$ | $897$ |
| $552$ | $243$ | $662$ | $454$ | $318$ | $675$ | $618$ | $898$ | $781$ |
| $560$ | $376$ | $428$ | $665$ | $736$ | $567$ | $840$ | $625$ | $238$ |
| $568$ | $359$ | $457$ | $399$ | $787$ | $591$ | $678$ | $434$ | $677$ |
| $576$ | $349$ | $245$ | $458$ | $666$ | $620$ | $363$ | $127$ | $191$ |
| $584$ | $782$ | $407$ | $436$ | $626$ | $571$ | $465$ | $681$ | $246$ |
| $592$ | $707$ | $350$ | $599$ | $668$ | $790$ | $460$ | $249$ | $682$ |
| $600$ | $573$ | $411$ | $803$ | $789$ | $709$ | $365$ | $440$ | $628$ |
| $608$ | $689$ | $374$ | $423$ | $466$ | $793$ | $250$ | $371$ | $481$ |
| $616$ | $574$ | $413$ | $603$ | $366$ | $468$ | $655$ | $900$ | $805$ |
| $624$ | $615$ | $684$ | $710$ | $429$ | $794$ | $252$ | $373$ | $605$ |
| $632$ | $848$ | $690$ | $713$ | $632$ | $482$ | $806$ | $427$ | $904$ |
| $640$ | $414$ | $223$ | $663$ | $692$ | $835$ | $619$ | $472$ | $455$ |
| $648$ | $796$ | $809$ | $714$ | $721$ | $837$ | $716$ | $864$ | $810$ |
| $656$ | $606$ | $912$ | $722$ | $696$ | $377$ | $435$ | $817$ | $319$ |
| $664$ | $621$ | $812$ | $484$ | $430$ | $838$ | $667$ | $488$ | $239$ |
| $672$ | $378$ | $459$ | $622$ | $627$ | $437$ | $380$ | $818$ | $461$ |
| $680$ | $496$ | $669$ | $679$ | $724$ | $841$ | $629$ | $351$ | $467$ |
| $688$ | $438$ | $737$ | $251$ | $462$ | $442$ | $441$ | $469$ | $247$ |
| $696$ | $683$ | $842$ | $738$ | $899$ | $670$ | $783$ | $849$ | $820$ |
| $704$ | $728$ | $928$ | $791$ | $367$ | $901$ | $630$ | $685$ | $844$ |
| $712$ | $633$ | $711$ | $253$ | $691$ | $824$ | $902$ | $686$ | $740$ |
| $720$ | $850$ | $375$ | $444$ | $470$ | $483$ | $415$ | $485$ | $905$ |
| $728$ | $795$ | $473$ | $634$ | $744$ | $852$ | $960$ | $865$ | $693$ |
| $736$ | $797$ | $906$ | $715$ | $807$ | $474$ | $636$ | $694$ | $254$ |
| $744$ | $717$ | $575$ | $913$ | $798$ | $811$ | $379$ | $697$ | $431$ |
| $752$ | $607$ | $489$ | $866$ | $723$ | $486$ | $908$ | $718$ | $813$ |
| $760$ | $476$ | $856$ | $839$ | $725$ | $698$ | $914$ | $752$ | $868$ |
| $768$ | $819$ | $814$ | $439$ | $929$ | $490$ | $623$ | $671$ | $739$ |
| $776$ | $916$ | $463$ | $843$ | $381$ | $497$ | $930$ | $821$ | $726$ |
| $784$ | $961$ | $872$ | $492$ | $631$ | $729$ | $700$ | $443$ | $741$ |
| $792$ | $845$ | $920$ | $382$ | $822$ | $851$ | $730$ | $498$ | $880$ |
| $800$ | $742$ | $445$ | $471$ | $635$ | $932$ | $687$ | $903$ | $825$ |
| $808$ | $500$ | $846$ | $745$ | $826$ | $732$ | $446$ | $962$ | $936$ |
| $816$ | $475$ | $853$ | $867$ | $637$ | $907$ | $487$ | $695$ | $746$ |
| $824$ | $828$ | $753$ | $854$ | $857$ | $504$ | $799$ | $255$ | $964$ |
| $832$ | $909$ | $719$ | $477$ | $915$ | $638$ | $748$ | $944$ | $869$ |
| $840$ | $491$ | $699$ | $754$ | $858$ | $478$ | $968$ | $383$ | $910$ |
| $848$ | $815$ | $976$ | $870$ | $917$ | $727$ | $493$ | $873$ | $701$ |
| $856$ | $931$ | $756$ | $860$ | $499$ | $731$ | $823$ | $922$ | $874$ |
| $864$ | $918$ | $502$ | $933$ | $743$ | $760$ | $881$ | $494$ | $702$ |
| $872$ | $921$ | $501$ | $876$ | $847$ | $992$ | $447$ | $733$ | $827$ |
| $880$ | $934$ | $882$ | $937$ | $963$ | $747$ | $505$ | $855$ | $924$ |
| $888$ | $734$ | $829$ | $965$ | $938$ | $884$ | $506$ | $749$ | $945$ |
| $896$ | $966$ | $755$ | $859$ | $940$ | $830$ | $911$ | $871$ | $639$ |
| $904$ | $888$ | $479$ | $946$ | $750$ | $969$ | $508$ | $861$ | $757$ |
| $912$ | $970$ | $919$ | $875$ | $862$ | $758$ | $948$ | $977$ | $923$ |
| $920$ | $972$ | $761$ | $877$ | $952$ | $495$ | $703$ | $935$ | $978$ |
| $928$ | $883$ | $762$ | $503$ | $925$ | $878$ | $735$ | $993$ | $885$ |
| $936$ | $939$ | $994$ | $980$ | $926$ | $764$ | $941$ | $967$ | $886$ |
| $944$ | $831$ | $947$ | $507$ | $889$ | $984$ | $751$ | $942$ | $996$ |
| $952$ | $971$ | $890$ | $509$ | $949$ | $973$ | $1000$ | $892$ | $950$ |
| $960$ | $863$ | $759$ | $1008$ | $510$ | $979$ | $953$ | $763$ | $974$ |
| $968$ | $954$ | $879$ | $981$ | $982$ | $927$ | $995$ | $765$ | $956$ |
| $976$ | $887$ | $985$ | $997$ | $986$ | $943$ | $891$ | $998$ | $766$ |
| $984$ | $511$ | $988$ | $1001$ | $951$ | $1002$ | $893$ | $975$ | $894$ |
| $992$ | $1009$ | $955$ | $1004$ | $1010$ | $957$ | $983$ | $958$ | $987$ |
| $1000$ | $1012$ | $999$ | $1016$ | $767$ | $989$ | $1003$ | $990$ | $1005$ |
| $1008$ | $959$ | $1011$ | $1013$ | $895$ | $1006$ | $1014$ | $1017$ | $1018$ |
| $1016$ | $991$ | $1020$ | $1007$ | $1015$ | $1019$ | $1021$ | $1022$ | $1023$ |