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  • 7/25/2019 Fc-pi-5 Clause 5 Bit Error Rate Test Suitev1.0

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    Fibre Channel Consortium

    FC-PI-5 Clause 5

    Bit Error Rate Test Suite

    Version 1.0

    Technical Document

    Last Updated: September 30, 2014

    Fibre Channel Consortium 121 Technology Drive, Suite 2

    InterOperability Laboratory Durham, N !"#2$

    %niversity o& Ne' ampshire (hone) *1+!"+#2+!!-!

    Fa.) *1+!"+#2+$1#1

    http)//'''0iol0unh0eu/consortiums/&c

    2014 University of New Hampshire InterOperability Laboratory

    http://www.iol.unh.edu/consortiums/fchttp://www.iol.unh.edu/consortiums/fc
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    Table of ContentsTable of Contents2

    !"#nowle$%ments4Intro$&"tion'

    (ro&p 1) *it +rror ,ate-

    Test .'11) +le"tri"al *it +rror ,ate /*+,

    Test .'12) Opti"al *it +rror ,ate /*+,10!ppen$i !) Test 3et&p12

    !ppen$i *) Test atterns15

    !ppen$i C) *it +rror ,ate 6eas&rement17

    8ibre Channel Consorti&m 2 8C9I9' *it +rror ,ate Test 3&ite v10

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    Modification Record !&%&st 14: 2014 ;

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    AcknowledgmentsThe University of New Hampshire would like to acknowledge the efforts of the following individuals in the

    development of this test suite.

    =aniel (ray University of New Hampshire

    =aniel ,eynol$s University of New Hampshire

    8ibre Channel Consorti&m 4 8C9I9' *it +rror ,ate Test 3&ite v10

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    IntroductionOverview

    The University of New Hampshire>s InterOperability Laboratory /UNH9IOL is an instit&tion $esi%ne$ to improvethe interoperability of stan$ar$s base$ pro$&"ts by provi$in% an environment where a pro$&"t "an be teste$ a%ainst

    other implementations of a stan$ar$ This parti"&lar s&ite of tests has been $evelope$ to help implementers eval&ate

    the hysi"al Layer f&n"tionality of their opti"al 8ibre Channel pro$&"ts

    These tests are $esi%ne$ to $etermine if a 8ibre Channel pro$&"t "onforms to spe"ifi"ations of the FC-!-"#ev $.%&

    8ibre Channel 3tan$ar$ /hereafter referre$ to as ?8C9I9'@ 3&""essf&l "ompletion of all tests "ontaine$ in this

    s&ite $oes not %&arantee that the teste$ $evi"e will operate with other $evi"es However: "ombine$ with satisfa"tory

    operation in the IOL>s interoperability test be$: these tests provi$e a reasonable level of "onfi$en"e that the $evi"e&n$er test /=UT will f&n"tion properly in many 8ibre Channel environments

    Organi'ation of Tests

    The tests "ontaine$ in this $o"&ment are or%aniAe$ to simplify the i$entifi"ation of information relate$ to a test an$to fa"ilitate in the a"t&al testin% pro"ess +a"h test "ontains an i$entifi"ation se"tion that $es"ribes the test an$

    provi$es "ross9referen"e information The $is"&ssion se"tion "overs ba"#%ro&n$ information an$ spe"ifies why the

    test is to be performe$ Tests are %ro&pe$ in or$er to re$&"e set&p time in the lab environment +a"h test "ontains

    the followin% information)

    Test Num(er

    The Test N&mber asso"iate$ with ea"h test follows a simple %ro&pin% str&"t&re Liste$ first is the Cla&se followe$

    by the Test (ro&p N&mber followe$ by the testBs n&mber within the %ro&p This allows for the a$$ition of f&t&re

    tests to the appropriate %ro&ps of the test s&ite witho&t re&irin% the ren&mberin% of the s&bse&ent tests

    urpose

    The p&rpose is a brief statement o&tlinin% what the test attempts to a"hieve The test is written at the f&n"tional

    level

    #eferences

    This se"tion spe"ifies all referen"e material externalto the test s&ite: in"l&$in% the spe"ifi" s&b"la&ses referen"es for

    the test in &estion: an$ any other referen"es that mi%ht be helpf&l in &n$erstan$in% the test metho$olo%y an$Dor test

    res&lts +ternal so&r"es are always referen"e$ by a bra"#ete$ n&mber /e%: E1F when mentione$ in the test

    $es"ription !ny other referen"es in the test $es"ription that are not in$i"ate$ in this manner refer to elements within

    the test s&ite $o"&ment itself /e%: ?!ppen$i 7!@: or ?Table 71191@

    #esource #e)uirements

    The re&irements se"tion spe"ifies the test har$ware an$Dor software nee$e$ to perform the test This is %enerally

    epresse$ in terms of minim&m re&irements: however in some "ases spe"ifi" e&ipment man&fa"t&rerDmo$elinformation may be provi$e$

    *ast +odification

    This spe"ifies the $ate of the last mo$ifi"ation to this test

    ,iscussion

    The $is"&ssion "overs the ass&mptions ma$e in the $esi%n or implementation of the test: as well as #nown

    limitations Other items spe"ifi" to the test are "overe$ here

    8ibre Channel Consorti&m ' 8C9I9' *it +rror ,ate Test 3&ite v10

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    Test etup

    The set&p se"tion $es"ribes the initial "onfi%&ration of the test environment 3mall "han%es in the "onfi%&ration

    sho&l$ be in"l&$e$ in the test pro"e$&re

    rocedure

    The pro"e$&re se"tion of the test $es"ription "ontains the systemati" instr&"tions for "arryin% o&t the test It

    provi$es a "oo#boo# approa"h to testin%: an$ may be intersperse$ with observable res&lts

    O(serva(le #esults

    This se"tion lists the spe"ifi" observable res&lts that "an be eamine$ by the tester in or$er to verify that the =UT is

    operatin% properly Ghen m&ltiple val&es for an observable are possible: this se"tion provi$es a short $is"&ssion on

    how to interpret them The $etermination of a pass or fail o&t"ome for a parti"&lar test is often base$ on the

    s&""essf&l /or &ns&""essf&l $ete"tion of a "ertain observable

    ossi(le ro(lems

    This se"tion "ontains a $es"ription of #nown iss&es with the test pro"e$&re: whi"h may affe"t test res&lts in "ertainsit&ations It may also refer the rea$er to test s&ite appen$i"es an$Dor whitepapers that may provi$e more $etail

    re%ar$in% these iss&es

    8ibre Channel Consorti&m 7 8C9I9' *it +rror ,ate Test 3&ite v10

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    Group 1: Bit Error Rate

    Overview

    This %ro&p of tests verifies the +le"tri"al an$ Opti"al *it +rror ,ate /*+,: as $efine$ in Cla&se ' of 8C9I9' These

    tests "annot provi$e a %&arantee that the $evi"e "onforms to the *it +rror ,ate: in all "on$itions: as $efine$ in

    Cla&se ' of 8C9I9': b&t "an provi$e "onfi$en"e that the $evi"e an$ the *it +rror ,ate Tester /*+,T "onform to

    the appli"able *it +rror ,ate

    8ibre Channel Consorti&m - 8C9I9' *it +rror ,ate Test 3&ite v10

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    Test /".%.% 0lectrical 1it 0rror #ate 210#3

    urpose

    To verify that the *it +rror ,ate of the =UT is within the "onforman"e limit

    #eferences

    E1F 8C9I9' 9 Cla&se '1

    E2F Ibi$ ; Cla&se 1E5F 8C963J ; !nne !

    E4F 8C963J3 ; Cla&se

    #esource #e)uirements

    +le"tri"al 9*+,T Capable of han$lin% &p to 17(8C si%nalin%

    /4 36!D36! "ables

    *ast Updated 6ay 04: 200

    ,iscussion

    In or$er to ens&re the overall &ality of the 8ibre Channel lin#: it is important to establish a maim&m allowable

    *it +rror ,ate /*+, that $evi"es m&st a"hieve The 8C98395 proto"ol is $efine$ to operate a"ross "onne"tions

    havin% a bit error ratio /*+, $ete"te$ at the re"eivin% port of less than 10 912 The *+, obKe"tive is 10912 ! T,

    Conne"tion bit error rate /*+, of 10 912as meas&re$ at its re"eiver is s&pporte$ The basis for the *+, is theen"o$e$ serial $ata stream on the transmission me$i&m $&rin% system operation

    !ll 8ibre Channel T, Conne"tions $es"ribe$ in referen"e E2F shall operate within the *+, obKe"tive /10 912

    atterns for this test are $efine$ by 8C963J E5F for 4(8C an$ 8C963J3 E4F for (8C an$ 17(8C The

    implementation of spe"ifi" patterns is mentione$ in the ro"e$&re: an$ is $etermine$ by the spee$ of the $evi"e

    &n$er test

    Test etup

    The =UT sho&l$ be set&p as $efine$ in!ppen$i ! Confi%&re the =UT for the appropriate spee$ The =UTsho&l$ be transitione$ into the monitorin%Da"tive state If the =UT s&pports s"ramblin%) the s"rambler D $e9s"rambler

    m&st be $isable$

    rocedure

    a LMortDNMortD8Mort =evi"e

    1 Instr&"t the 9*+,T to transmit a L* to the =UT

    2 Instr&"t the 9*+,T to be%in so&r"in% I$le "ontin&o&sly5 6eas&re the *it +rror ,ate over the transmission of 51012transmitte$ bits

    4 ,epeat steps 195 for ea"h port

    ' 8or 4( an$ ( /not s&pportin% s"ramblin% =evi"es

    1 ,epeat steps 194 for CT!T: C,!T an$ C3!T7 8or ( =evi"es s&pportin% s"ramblin%

    1 ,epeat steps 194 for 3!T an$ T3!T

    - 8or 17( =evi"es

    1 ,epeat steps 194 &sin% ,*3: ,*351: an$ 3"ramble$ I$le

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    b NMortD8Mort =evi"e

    1 3et&p the =UT to retransmit &naltere$ traffi" thro&%h the T, Conne"tion2 Instr&"t the 9*+,T to be%in so&r"in% I$le "ontin&o&sly

    5 6eas&re the *it +rror ,ate over the transmission of 51012transmitte$ bits

    4 ,epeat steps 195 for ea"h port

    ' 8or 4( an$ ( /not s&pportin% s"ramblin% =evi"es

    1 ,epeat steps 194 for CT!T: C,!T an$ C3!T7 8or ( =evi"es s&pportin% s"ramblin%

    1 ,epeat steps 194 for 3!T an$ T3!T

    - 8or 17( =evi"es

    1 ,epeat steps 194 &sin% ,*3: ,*351: an$ 3"ramble$ I$le

    O(serva(le #esults

    The *it +rror ,ate /*+, over all traffi" shall not e"ee$ 10 912/ie not errors shall be $ete"te$ over the 51012

    transmitte$ bits

    ossi(le ro(lems None

    8ibre Channel Consorti&m 8C9I9' *it +rror ,ate Test 3&ite v10

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    Test /".%.4 Optical 1it 0rror #ate 210#3

    urpose

    To verify that the *it +rror ,ate of the =UT is within the "onforman"e limit

    #eferences

    E1F 8C9I9' 9 Cla&se '1

    E2F Ibi$ ; Cla&se 71E5F 8C963J ; !nne !

    E4F 8C963J3 ; Cla&se

    #esource #e)uirements

    Opti"al 9*+,T Capable of han$lin% &p to 17(8C si%nalin%

    /1 8iber Cable

    *ast Updated 6ay 04: 200

    ,iscussion

    In or$er to ens&re the overall &ality of the 8ibre Channel lin#: it is important to establish a maim&m allowable

    *it +rror ,ate /*+, that $evi"es m&st a"hieve The 8C98395 proto"ol is $efine$ to operate a"ross "onne"tions

    havin% a bit error ratio /*+, $ete"te$ at the re"eivin% port of less than 10 912 The *+, obKe"tive is 10912 ! T,

    Conne"tion bit error rate /*+, of 10 912as meas&re$ at its re"eiver is s&pporte$ The basis for the *+, is theen"o$e$ serial $ata stream on the transmission me$i&m $&rin% system operation

    8ibre Channel lin#s shall not e"ee$ the *+, obKe"tive /10912 &n$er any "ompliant "on$itions atterns for this

    test are $efine$ by 8C963J E5F for 4(8C an$ 8C963J3 E4F for (8C an$ 17(8C The implementation of

    spe"ifi" patterns is mentione$ in the ro"e$&re: an$ is $etermine$ by the spee$ of the $evi"e &n$er test

    Test etup

    The =UT sho&l$ be set&p as $efine$ in!ppen$i ! Confi%&re the =UT for the appropriate spee$ The =UT

    sho&l$ be transitione$ into the monitorin%Da"tive state

    rocedure

    a LMortDNMortD8Mort =evi"e

    1 Instr&"t the 9*+,T to transmit a L* to the =UT

    2 Instr&"t the 9*+,T to be%in so&r"in% I$le "ontin&o&sly

    5 6eas&re the *it +rror ,ate over the transmission of 51012transmitte$ bits

    4 ,epeat steps 195 for ea"h port' 8or 4( an$ ( /not s&pportin% s"ramblin% =evi"es

    1 ,epeat steps 194 for CT!T: C,!T an$ C3!T

    7 8or ( =evi"es s&pportin% s"ramblin%

    1 ,epeat steps 194 for 3!T an$ T3!T- 8or 17( =evi"es

    1 ,epeat steps 194 &sin% ,*3: ,*351: an$ 3"ramble$ I$le

    8ibre Channel Consorti&m 10 8C9I9' *it +rror ,ate Test 3&ite v10

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    b NMortD8Mort =evi"e1 3et&p the =UT to retransmit &naltere$ traffi" thro&%h the T, Conne"tion

    2 Instr&"t the 9*+,T to be%in so&r"in% I$le "ontin&o&sly

    5 6eas&re the *it +rror ,ate over the transmission of 51012transmitte$ bits4 ,epeat steps 195 for ea"h port

    ' 8or 4( an$ ( /not s&pportin% s"ramblin% =evi"es

    1 ,epeat steps 194 for CT!T: C,!T an$ C3!T

    7 8or ( =evi"es s&pportin% s"ramblin%

    1 ,epeat steps 194 for 3!T an$ T3!T- 8or 17( =evi"es

    1 ,epeat steps 194 &sin% ,*3: ,*351: an$ 3"ramble$ I$le

    O(serva(le #esults

    The *it +rror ,ate /*+, over all traffi" shall not e"ee$ 10 912/ie not errors shall be $ete"te$ over the 51012

    transmitte$ bits

    ossi(le ro(lems None

    8ibre Channel Consorti&m 11 8C9I9' *it +rror ,ate Test 3&ite v10

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    Appendi A: Test !etup

    8ibre Channel Consorti&m 12 8C9I9' *it +rror ,ate Test 3&ite v10

    Figure % 0lectrical Test etup

    I9*+,T

    =UT/4ort *ypasse$ orLoopba"# 6o$e

    TN TN9

    TN TN9

    Opti"al 8iber

    36!D36! +le"tri"al Cable

    *egend

    ,N ,N9

    ,N ,N9

    Figure 4 Optical Test etup

    I9*+,T

    =UT/4ort *ypasse$ orLoopba"# 6o$e

    TN

    TN

    Opti"al 8iber

    36!D36! +le"tri"al Cable

    *egend

    ,N

    ,N

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    Appendi B: Test "atterns

    #eferences

    E1F 63J ; Table !: !11: !15

    E2F 63J3 ; Cla&se 12: 15

    8or 17(8C $evi"es: patterns &se$ are $efine$ by Cla&se of 8C963J3 4(8C an$ (8C patterns &se$ are as

    follows)

    Table 1 9 CT!T /T!T in a 8C "ompliant frame format

    Table 2 9 C,!T /,!T in a 8C "ompliant frame format

    Table 5 9 C3!T /3!T in a 8C "ompliant frame format

    8ibre Channel Consorti&m 15 8C9I9' *it +rror ,ate Test 3&ite v10

    Primitive Count

    (Idle) BC 95 B5 B5 6

    (SOFn3) BC B5 36 36 1

    BE D7 23 47

    166B 8F B3 14

    5E FB 35 59

    (CRC) EE 23 55 16 1

    BC B5 D5 D5 1(EOFn)

    Primitive Count

    (Idle) BC 95 B5 B5 6

    (SOFn3) BC B5 36 36 1

    7E 7E 7E 7E 41

    7E 7E 7E 74 1

    7E AB B5 B5 1

    B5 B5 B5 B5 12

    B5 5E 4A 7E 1

    7E 7E 7E FE 1

    (CRC) F5 2E F6 DD 1

    BC B5 D5 D5 1(EOFn)

    Primitive Count

    (Idle) BC 95 B5 B5 6

    (SOFn3) BC B5 36 36 1

    7F 7F 7F 7F 512(CRC) F1 96 DB 97 1

    BC 95 D5 D5 1(EOFn)

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    8ibre Channel Consorti&m 14 8C9I9' *it +rror ,ate Test 3&ite v10

    Figure 5 67T 2scram(led 8itter pattern3 94:

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    8ibre Channel Consorti&m 1' 8C9I9' *it +rror ,ate Test 3&ite v10

    Figure ; 6T7T 26itter tolerance scram(led pattern3 94:

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    Appendi C: Bit Error Rate Measurement

    urpose To $evelop a pro"e$&re for bit error rate meas&rement thro&%h the appli"ation of statisti"al metho$s

    #eferences

    E1F 6iller: Irwin an$ ohn + 8re&n$: robability an$ 3tatisti"s for +n%ineers /3e"on$ +$ition: renti"e9Hall:

    1--: pp 149210: 240924'

    *ast +odification November 4: 2004 /

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    b k ;n , p=Cn , kpk

    1p

    nk /+&ation *91

    Note that in this "ase: a s&""essf&l o&t"ome is a bit error The "oeffi"ient Cn:#

    is referre$ to as the binomial

    "oeffi"ient or ?n9"hoose9#@ It is the n&mber of "ombinations of # s&""esses in n trials ,et&rnin% to "oin toss

    analo%y: there are 5 ways to %et 2 hea$s from 5 "oin tosses) /tails: hea$s: hea$s: /hea$s: tails: hea$s: an$ /hea$s:

    hea$s: tails Therefore: C5:2

    wo&l$ be 5 ! more pre"ise mathemati"al $efinition is %iven in e&ation *92

    cn , k= n !

    k ! nk !/+&ation *92

    This mo$el refle"ts the fa"t that for a %iven probability: p: a test in whi"h n bits are sent "o&l$ yiel$ manypossible o&t"omes However: some o&t"omes are more li#ely than others an$ this li#elihoo$ prin"iple allows &s to

    ma#e "on"l&sions abo&t the *+, for a %iven test res&lt

    *5 ; Hypothesis Test

    The statisti"al metho$ of hypothesis testin% will allow &s to establish a val&e of n: the n&mber of bits to be sent:

    for the *+, meas&rement Nat&rally: the test be%ins with a hypothesis In this "ase: we will hypothesiAe that theprobability of a bit error: p: for the system is less than some tar%et *+,:

    0 This hypothesis is state$ formally in

    e&ation *95

    H0: pP0 /+&ation *95

    Ge now "onstr&"t a test for this hypothesis In this "ase: we will ta#e the obvio&s approa"h of sen$in% n bits

    an$ "o&ntin% the n&mber errors: # Ge will interpret the test res&lts as shown in table *91

    Table *91) !""eptan"e an$ reKe"tions re%ions for H0

    Test #esult Conclusion

    # Q 0 H0is tr&e

    # R 0 H0is false

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    Ge now a"#nowle$%e the possibility that o&r "on"l&sion is in error 3tatisti"ians $efine two $ifferent "ate%oriesof error ! type I error is ma$e when the hypothesis is reKe"te$ even tho&%h it is tr&e ! type II error is ma$e when

    the hypothesis is a""epte$ even tho&%h it is false The probability of a type I an$ a type II error are $enote$ as aan$

    brespe"tively Table *92 $efines type I an$ type II errors in the "ontet of this test

    Table *92) =efinitions of type I an$ type II errors

    Type ! 0rror # R 0 even tho&%h p *+,

    Type !! 0rror # Q 0 even tho&%h p R *+,

    ! type II error is ar%&ably more serio&s an$ we will $efine n so that the probability of a type II error: b: is

    a""eptable The probability of a type II error is %iven in e&ation *94

    =1pn1P0n

    /+&ation *94

    +&ation *94 ill&strates that the &pper bo&n$ on the probability of a type II error is a f&n"tion of the tar%et bit

    error rate an$ n *y solvin% this e&ation for n: we "an $etermine the minim&m n&mber of bits that nee$ to sent in

    or$er to verify that p is less than a %iven 0for a %iven probability of type II error

    nln

    ln1P0/+&ation *9'

    Let &s now eamine the probability of a type I error The $efinition of ais %iven in e&ation *97

    =11pn11P0n

    /+&ation *97

    +&ation *97 shows that while we in"rease n to ma#e bsmall: we sim&ltaneo&sly raise the &pper bo&n$ on a

    This ma#es sense sin"e the li#elihoo$ of observin% a bit error in"reases with the n&mber of bits that yo& sen$: nomatter how small bit error rate is Therefore: while the hypothesis test is very &sef&l in $eterminin% a reasonable

    val&e for n: we m&st be very "aref&l in interpretin% the res&lts 3pe"ifi"ally: if we sen$ n bits an$ observe no errors:

    we are "onfi$ent that p is less than o&r tar%et bit error rate /o&r level of "onfi$en"e $epen$s on how small we ma$e

    b However: if we $o observe bit errors: we "annot be &i"# to ass&me that the system $i$ not meet the *+, tar%et

    sin"e the probability of a type I error is so lar%e In the "ase of # R 0: a "onfi$en"e interval "an be &se$ to help &s

    interpret #

    8ibre Channel Consorti&m 1 8C9I9' *it +rror ,ate Test 3&ite v10

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    *4 ; Confi$en"e Interval

    The statisti"al metho$ of "onfi$en"e intervals will be &se$ to establish a lower bo&n$ on the bit error rate %iven

    that # R 0 ! "onfi$en"e interval is a ran%e of val&es that is li#ely to "ontain the a"t&al val&e of some parameter of

    interest The interval is $erive$ from the meas&re$ val&e of the parameter: referre$ to as the point estimate: an$ the

    "onfi$en"e level: /19a: the probability that the parameter>s a"t&al val&e lies within the interval

    ! "onfi$en"e interval re&ires a statisti"al mo$el of the parameter to be bo&n$e$ In this "ase: we &se thestatisti"al mo$el for # %iven in e&ation *91 If we were to "omp&te the area &n$er the binomial "&rve for some

    interval: we wo&l$ be "omp&tin% the probability that # lies within that interval This "on"ept is shown in fi%&re *91

    8i%&re *91) Comp&tin% the probability that A 9174' /stan$ar$ normal $istrib&tion

    To "omp&te the area &n$er the binomial "&rve: we nee$ a val&e for the parameter p To "omp&te a "onfi$en"e

    interval for #: yo& ass&me that #Dn: the point estimate for p: is the a"t&al val&e of p

    Note that fi%&re *91 ill&strates the "omp&tation of the lower toleran"e bo&n$ for #: a spe"ial "ase where the

    "onfi$en"e interval is E#l: F ! lower toleran"e bo&n$ implies that in a per"enta%e of f&t&re tests: the val&e of #

    will be %reater than #l In other wor$s: a"t&al val&e of # is %reater than #

    lwith probability e&al to the "onfi$en"e

    level Therefore: if #lDn is %reater than

    0: we "an say that the system $oes not meet the tar%et bit error rate with

    probability /19a *y re$&"in% a: we re$&"e the probability of ma#in% a type I error

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    To $etermine the val&e of #l: it is &sef&l to ass&me that the binomial $istrib&tion "an be approimate$ by a

    normal /(a&ssian $istrib&tion when n is lar%e The mean an$ varian"e of this e&ivalent $istrib&tion are the mean

    an$ varian"e of the "orrespon$in% binomial $istrib&tion /%iven in e&ations *9- an$ *9

    k=np /+&ation *9-

    k2=np1p /+&ation *9

    Now: let abe the probability that S Aawhere S is a stan$ar$ normal ran$om variable ! stan$ar$ ran$om

    variable is one whose mean is Aero an$ whose varian"e is one The ran$om variable "an be stan$ar$iAe$ as shown

    in e&ation *9

    Z=K k k

    /+&ation *9

    Note that S is %reater than Aawith probability /19a: the "onfi$en"e level Ge apply this ine&ality to e&ation

    *9 an$ solve for to %et e&ation *910

    K kz k

    Knpznp 1p

    /+&ation *910

    !s mentione$ before: we ass&me that p is #Dn Ge "an now %enerate an epression for #l: the val&e that will

    e"ee$ with probability /19a This epression is %iven in e&ation *911

    kl=kznk/ n1k/n

    n/+&ation *911

    8inally: we ar%&e that if e"ee$s #l: then the a"t&al val&e of p m&st e"ee$ #lDn Therefore: we "an %enerate

    an epression for pl: the val&e that p will e"ee$ with probability /19a: an$ "ompare it to the tar%et bit error rate *y

    applyin% this "omparison /%iven in e&ation *912 the probability of a type I error "an be %reatly re$&"e$ 8or

    eample: by settin% Aa

    to ;174': the probability of a type I error is re$&"e$ to '

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    P0pl=kln=

    k

    nz

    k/n1k/n

    n/+&ation *912

    *' ; 3ample Test Constr&"tion

    Ge now "ompress the theory presente$ in se"tions *92 thro&%h *94 into two ine&alities that may be &se$ to

    "onstr&"t a bit error rate test 8irst: we ta#e e&ation *9' an$ ass&me that ln/1-0 is ;

    0/vali$ for

    0m&"h less

    than one The res&lt is e&ation *915

    nln

    P0/+&ation *915

    3e"on$: we eamine e&ation *912 !ss&min% that /19#Dn is very "lose to 1 an$ s&bstit&tin% ;ln/bD0for n: we

    %et e&ation *914

    lnkzk /+&ation *914

    The lar%est val&e of # that satisfies e&ation *914 is #l The benefit of these two e&ations is that a bit error rate

    test is &ni&ely $efine$ by ban$ a an$ that the test s"ales with 0 Table *95 $efines n an$ #

    lin terms of ban$ a.

    Table *95) n an$ #las a f&n"tion of ban$ a

    < -ln2

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    (iven that a ' "han"e of a type II error is a""eptable: we fin$ that #lis - If more than - errors are "o&nte$: we

    are "onfi$ent that the bit error rate is %reater than 10912 However: what if between 1 an$ - errors are "o&nte$P These

    "ases may be han$le$ several $ifferent ways One option is to ma#e a statement abo&t the bit error rate /whether it isless than or %reater than 10912 at a lower level of "onfi$en"e !nother option wo&l$ be to state that the test res&lt is

    s&""ess sin"e we "annot establish with an a""eptable probability of error that the *+, is %reater than 10912 3&"h a

    statement implies that we faile$ to meet the b&r$en of proof for the "onKe"t&re that the *+, e"ee$ 10912 Of "o&rse:

    the b&r$en of proof "o&l$ be shifte$ to the $evi"e &n$er test whi"h wo&l$ imply that any o&t"ome other than # Q 0

    wo&l$ "orrespon$ to fail&re /the $evi"e &n$er test faile$ to prove to &s that the *+, was no more than 10 912 Ifneither of these sol&tions are a""eptable: it is always an option to perform a more vi%oro&s bit error rate test in or$er

    to "larify the res&lt

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