ETSI ETS 300 575 ed.2 (1995-07)
European digital cellular telecommunications system (Phase 2); Channel coding (GSM 05.03)
European digital cellular telecommunications system (Phase 2); Channel coding (GSM 05.03)
RE/SMG-020503P
Evropski digitalni celični telekomunikacijski sistem (faza 2) – Kodiranje kanalov (GSM 05.03)
General Information
Standards Content (Sample)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.European digital cellular telecommunications system (Phase 2); Channel coding (GSM 05.03)35.040Nabori znakov in kodiranje informacijCharacter sets and information coding33.070.50Globalni sistem za mobilno telekomunikacijo (GSM)Global System for Mobile Communication (GSM)ICS:Ta slovenski standard je istoveten z:ETS 300 575 Edition 2SIST ETS 300 575 E2:2003en01-december-2003SIST ETS 300 575 E2:2003SLOVENSKI
STANDARD
SIST ETS 300 575 E2:2003
EUROPEANETS 300 575TELECOMMUNICATIONJuly 1995STANDARDSecond EditionSource: ETSI TC-SMGReference: DE/SMG-020503PICS:33.060.30Key words:European digital cellular telecommunications system, Global System for Mobile communications(GSM)European digital cellular telecommunications system (Phase 2);Channel coding(GSM 05.03)ETSIEuropean Telecommunications Standards InstituteETSI SecretariatPostal address: F-06921 Sophia Antipolis CEDEX - FRANCEOffice address: 650 Route des Lucioles - Sophia Antipolis - Valbonne - FRANCEX.400: c=fr, a=atlas, p=etsi, s=secretariat - Internet: secretariat@etsi.frTel.: +33 92 94 42 00 - Fax: +33 93 65 47 16Copyright Notification: No part may be reproduced except as authorized by written permission. The copyright and theforegoing restriction extend to reproduction in all media.© European Telecommunications Standards Institute 1995. All rights reserved.SIST ETS 300 575 E2:2003New presentation - see History box
Page 2ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)Whilst every care has been taken in the preparation and publication of this document, errors in content,typographical or otherwise, may occur. If you have comments concerning its accuracy, please write to"ETSI Editing and Committee Support Dept." at the address shown on the title page.SIST ETS 300 575 E2:2003
Page 3ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)ContentsForeword.51.1Scope.71.2Normative references.71.3Definitions and abbreviations.72.General.82.1General Organization.82.2Naming Convention.103Traffic Channels (TCH).103.1Speech channel at full rate (TCH/FS).103.1.1Parity and tailing for a speech frame.113.1.2Convolutional encoder.113.1.3Interleaving.113.1.4Mapping on a Burst.123.2Speech channel at half rate (TCH/HS).123.2.1Parity and tailing for a speech frame.123.2.2Convolutional encoder.123.2.3Interleaving.133.2.4Mapping on a burst.133.3Data channel at full rate, 12.0 kbit/s radio interface rate (9.6 kbit/s services(TCH/F9.6)).143.3.1Interface with user unit.143.3.2Block code.143.3.3Convolutional encoder.143.3.4Interleaving.143.3.5Mapping on a Burst.153.4Data channel at full rate, 6.0 kbit/s radio interface rate (4.8 kbit/s services (TCH/F4.8)).153.4.1Interface with user unit.153.4.2Block code.153.4.3Convolutional encoder.153.4.4Interleaving.153.4.5Mapping on a Burst.153.5Data channel at half rate, 6.0 kbit/s radio interface rate (4.8 kbit/s services (TCH/H4.8))163.5.1Interface with user unit.163.5.2Block code.163.5.3Convolutional encoder.163.5.4Interleaving.163.5.5Mapping on a Burst.163.6Data channel at full rate, 3.6 kbit/s radio interface rate (2.4 kbit/s and less services(TCH/F2.4)).163.6.1Interface with user unit.163.6.2Block code.163.6.3Convolutional encoder.163.6.4Interleaving.173.6.5Mapping on a Burst.173.7Data channel at half rate, 3.6 kbit/s radio interface rate (2.4 kbit/s and less services(TCH/H2.4)).173.7.1Interface with user unit.173.7.2Block code.173.7.3Convolutional encoder.173.7.4Interleaving.173.7.5Mapping on a Burst.17SIST ETS 300 575 E2:2003
Page 4ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)4.Control Channels.184.1Slow associated control channel (SACCH).184.1.1Block constitution.184.1.2Block code.184.1.3Convolutional encoder.184.1.4Interleaving.184.1.5Mapping on a Burst.194.2Fast associated control channel at full rate (FACCH/F).194.2.1Block constitution.194.2.2Block code.194.2.3Convolutional encoder.194.2.4Interleaving.194.2.5Mapping on a Burst.194.3Fast associated control channel at half rate (FACCH/H).204.3.1Block constitution.204.3.2Block code.204.3.3Convolutional encoder.204.3.4Interleaving.204.3.5Mapping on a Burst.204.4Broadcast, Paging, Access grant and Cell broadcast channels (BCCH, PCH, AGCH,CBCH).214.5Stand-alone dedicated control channel (SDCCH).214.6Random access channel (RACH).214.7Synchronization channel (SCH).224.8Handover Access Burst.22Annex A (informative):Summary of Channel Types.28Annex B (informative):Summary of Polynomials Used for Convolutional Codes.29History.30SIST ETS 300 575 E2:2003
Page 5ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)ForewordThis European Telecommunication Standard (ETS) has been produced by the Special Mobile Group(SMG) Technical Committee (TC) of the European Telecommunications Standards Institute (ETSI).This ETS specifies the channel coding of used within the European digital cellular telecommunicationssystem (Phase 2).This ETS correspond to GSM technical specification, GSM 05.03 version 4.2.0.The specification from which this ETS has been derived was originally based on CEPT documentation,hence the presentation of this ETS may not be entirely in accordance with the ETSI/PNE rules.Reference is made within this ETS to GSM Technical Specifications (GSM-TSs) (NOTE).NOTE:TC-SMG has produced documents which give the technical specifications for theimplementation of the European digital cellular telecommunications system.Historically, these documents have been identified as GSM Technical Specifications(GSM-TSs). These TSs may have subsequently become I-ETSs (Phase 1), or ETSs(Phase 2), whilst others may become ETSI Technical Reports (ETRs). GSM-TSs are,for editorial reasons, still referred to in GSM ETSs.Proposed transposition datesDate of adoption of this ETS:30 July 1995Date of latest announcement of this ETS (doa):31 October 1995Date of latest publication of new National Standardor endorsement of this ETS (dop/e):30 April 1996Date of withdrawal of any conflicting National Standard (dow):30 April 1996SIST ETS 300 575 E2:2003
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Page 7ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)1.1ScopeA reference configuration of the transmission chain is shown in GSM 05.01. According to this referenceconfiguration, this technical specification specifies the data blocks given to the encryption unit.It includes the specification of encoding, reordering, interleaving and the stealing flag. It does not specifythe channel decoding method.The definition is given for each kind of logical channel, starting from the data provided to the channelencoder by the speech coder, the data terminal equipment, or the controller of the MS or BS. Thedefinitions of the logical channel types used in this technical specification are given in GSM 05.02, asummary is in annex 1.1.2Normative referencesThis ETS incorporates by dated and undated reference, provisions from other publications. Thesenormative references are cited at the appropriate places in the text and the publications are listedhereafter. For dated references, subsequent amendments to or revisions of any of these publicationsapply to this ETS only when incorporated in it by amendment or revision. For undated references, thelatest edition of the publication referred to applies.[1]GSM 01.04 (ETR 100): "European digital cellular telecommunication system(Phase 2); Definitions, abbreviations and acronyms".[2]GSM 04.08 (ETS 300 557): "European digital cellular telecommunication system(Phase 2); Mobile radio interface layer 3 specification".[3]GSM 04.21 (ETS 300 562): "European digital cellular telecommunication system(Phase 2); Rate adaption on the Mobile Station - Base Station System (MS -BSS) interface ".[4]GSM 05.01 (ETS 300 573): "European digital cellular telecommunication system(Phase 2); Physical layer on the radio path
General description".[5]GSM 05.02 (ETS 300 574): "European digital cellular telecommunication system(Phase 2); Multiplexing and multiple access on the radio path".[6]GSM 05.05: (ETS 300 577): "European digital cellular telecommunicationsystem (Phase 2); Radio Transmission and Reception".[7]GSM 06.10 (ETS 300 580-2): "European digital cellular telecommunicationsystem (Phase 2); Full rate speech transcoding".[8]GSM 06.20 (ETS 300 581-2): "European digital cellular telecommunicationsystem; Half rate speech Part 2: Half rate speech transcoding".1.3Definitions and abbreviationsDefinitions and abbreviations used in this specification are listed in GSM 01.04.SIST ETS 300 575 E2:2003
Page 8ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)2.General2.1General OrganizationEach channel has its own coding and interleaving scheme. However, the channel coding and interleavingis organized in such a way as to allow, as much as possible, a unified decoder structure.Each channel uses the following sequence and order of operations:-The information bits are coded with a systematic block code,uilding words of information + paritybits.-These information + parity bits are encoded with a convolutional code, building the coded bits.-Reordering and interleaving the coded bits, and adding a stealing flag, gives the interleaved bits.All these operations are made block by block, the size of which depends on the channel. However, mostof the channels use a block of 456 coded bits which is interleaved and mapped onto bursts in a verysimilar way for all of them. Figure 1 gives a diagram showing the general structure of the channel coding.This block of 456 coded bits is the basic structure of the channel coding scheme. In the case of full ratespeech TCH, this block carries the information of one speech frame. In case of control channels, it carriesone message.In the case of half rate speech TCH, the information of one speech frame is carried in a block of 228coded bits.In the case of FACCH, a coded message block of 456 bits is divided into eight sub-blocks. The first foursub-blocks are sent by stealing the even numbered bits of four timeslots in consecutive frames used forthe TCH. The other four sub-blocks are sent by stealing the odd numbered bits of the relevant timeslot infour consecutive used frames delayed 2 or 4 frames relative to the first frame. Along with each block of456 coded bits there is, in addition, a stealing flag (8 bits), indicating whether the block belongs to the TCHor to the FACCH. In the case of SACCH, BCCH or CCCH, this stealing flag is dummy.Some cases do not fit in the general organization, and use short blocks of coded bits which are sentcompletely in one timeslot. They are the random access messages of the RACH on uplink and thesynchronization information broadcast of the SCH on downlink.SIST ETS 300 575 E2:2003
Page 9ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)speech frame112 bits3.2 speech frame260 bits3.1 message184 bits4.1.1data frameN0 bits3.n.1messageP0 bits4.6, 4.7interface1interface2TCH/HS(half ratespeech TCH)TCH/FS(full ratespeech TCH)SACCH, FACCH,BCCH, CBCH, PCHAGCH, SDCCHdata TCHsRACH,SCHcyclic code+ tailin: 260 bitsout: 267 bits3.1.1cyclic code+ tailin: 112 bitsout: 121 bits3.2.1Fire code+tailin: 184 bitsout: 228 bits4.1.2+tailin: N0 bitsout: N1 bits3.n.2cyclic code+ tailin: P0 bitsout: P1 bits4.6, 4.7interface3interface4TCH/F2.4othersTCH/FS, FACCHTCH/F2.4othersencryption unitdiagonal interleaving+ stealing flagsin: 456 bitsout: 4 blocksdiagonally interleavedto depth 19, startingon consecutive bursts3.n.4reordering and partitioning+stealing flagin: 456 bitsout: 8 blocks3.1.3, 4.1.4, 4.3.4block rectangularinterleavingin: 8 blocksout: pairs of blocks4.1.4block diagonalinterleavingin: 8 blocksout: pairs of blocks3.1.3, 4.3.4reordering and partitioning+stealing flagin: 228 bitsout: 4 blocks3.2.3block diagonalinterleavingin: 4 blocksout: pairs of blocks3.2.3convolutionalcodek=7, 2 classesin: 121 bitsout: 228 bits3.2.2convolutionalcodek=5, 2 classesin: 267 bitsout: 456 bits3.1.2convolutionalcodek=5, rate 1/2in: 228 bitsout: 456 bits4.1.3convolutionalcodek=5, rate rin: N1 bitsout: 456 bits3.n.3convolutionalcodek=5, rate 1/2in: P1 bitsout: 2*P1 bits4.6, 4.7Figure 1: Channel Coding and Interleaving OrganisationIn each box, the last line indicates the chapter defining the function.In the case of
RACH, P0=8 andP1=18; in the case of SCH, P0=25 and P1=39. In the case of data TCHs, N0, N1 and n depend onthe type of data TCH.Interfaces:1)information bits (d)2)information + parity + tail bits (u)3)coded bits (c)4)interleaved bits (e)SIST ETS 300 575 E2:2003
Page 10ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)2.2Naming ConventionFor ease of understanding a naming convention for bits is given for use throughout the technicalspecification:- General naming"k" and "j" for numbering of bits in data blocks and bursts."Kx" gives the amount of bits in one block, where "x" refers to the data type"n" is used for numbering of delivered data blocks where"N" marks a certain data block"B" is used for numbering of bursts or blocks where"B0" marks the first burst or block carrying bits from the data block with n = 0 (first data block in thetransmission)-Data delivered to the encoding unit (interface 1 in figure 1):d(k)fork = 0,1,.,Kd-1-Data after the first encoding step (block code, cyclic code; interface 2 in figure 1):u(k)fork = 0,1,.,Ku-1-Data after the second encoding step (convolutional code ; interface 3 in figure 1):c(n,k) or c(k)fork = 0,1,.,Kc-1n = 0,1,.,N,N+1,.-Interleaved data:i(B,k)fork = 0,1,.,Ki-1B = B0, B0+1,.-Bits in one burst (interface 4 in figure 1):e(B,k)fork = 0,1,.,114,115B = B0, B0 + 1,.3Traffic Channels (TCH)Two kinds of traffic channel are considered: speech and data. Both of them use the same generalstructure (see fig.1), and in both cases, a piece of information can be stolen by the FACCH.3.1Speech channel at full rate (TCH/FS)The speech coder delivers to the channel encoder a sequence of blocks of data. In case of a full ratespeech TCH, one block of data corresponds to one speech frame. Each block contains 260 informationbits,including 182 bits of class 1 (protected bits), and 78 bits of class 2 (no protection), (see Table 2).The bits delivered by the speech coder are received in the order indicated in GSM 06.10 and have to berearranged according to Table 2 before channel coding as defined in 3.1.1 to 3.1.4. The rearranged bitsare labelled {d(0),d(1),.,d(259)}, defined in the order of decreasing importance.SIST ETS 300 575 E2:2003
Page 11ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)3.1.1Parity and tailing for a speech framea) Parity bits:The first 50 bits of class 1 are protected by three parity bits used for error detection. These paritybits are added to the 50 bits, according to a degenerate (shortened) cyclic code (53,50,2), using thegenerator polynomial:g(D) = D3 + D + 1The encoding of the cyclic code is performed in a systematic form, which means that, in GF(2), thepolynomial:d(0)D52 + d(1)D51 +. + d(49)D3 + p(0)D2 + p(1)D+ p(2)where p(0), p(1), p(2) are the parity bits, when divided by g(D), yields a remainder equal to:1 + D + D2b)Tailing bits and reordering:The information and parity bits of class 1 are reordered, defining 189 information + parity + tail bitsof class 1, {u(0),u(1),.,u(188)} defined by:u(k)= d(2k)andu(184-k) = d(2k+1)for k = 0,1,.,90u(91+k)= p(k)for k = 0,1,2u(k)= 0for k = 185,186,187,188 (tail bits)3.1.2Convolutional encoderThe class 1 bits are encoded with the 1/2 rate convolutional code defined by the polynomials:G0 = 1 + D3+ D4G1 = 1 + D + D3+ D4The coded bits {c(0), c(1),., c(455)} are then defined by:- class 1 :c(2k)= u(k) + u(k-3) + u(k-4)c(2k+1)= u(k) + u(k-1) + u(k-3) + u(k-4)for k = 0,1,.,188u(k) = 0 for k < 0- class 2 :c(378+k)= d(182+k)fork = 0,1,.,773.1.3InterleavingThe coded bits are reordered and interleaved according to the following rule :i(B,j)
= c(n,k),fork = 0,1,.,455n = 0,1,.,N,N+1,.B = B0 + 4n + (k mod 8)j = 2((49k) mod 57) + ((k mod 8) div 4)See table 1. The result of the interleaving is a distribution of the reordered 456 bits of a given data block, n= N, over 8 blocks using the even numbered bits of the first 4 blocks (B = B0 + 4N + 0, 1, 2, 3) and oddnumbered bits of the last 4 blocks (B = B0 + 4N + 4, 5, 6, 7). The reordered bits of the following datablock, n = N+1, use the even numbered bits of the blocks B = B0 + 4N + 4, 5, 6, 7 (B = B0 + 4(N+1) + 0, 1,2, 3) and the odd numbered bits of the blocks B= B0 + 4(N+1) + 4, 5, 6, 7. Continuing with the next datablocks shows that one block always carries 57 bits of data from one data block (n = N) and 57 bits of datafrom the next block (n = N+1), where the bits from the data block with the higher number always are theeven numbered data bits, and those of the data block with the lower number are the odd numbered bits.The block of coded data is interleaved "block diagonal", where a new data block starts every 4th block andis distributed over 8 blocks.SIST ETS 300 575 E2:2003
Page 12ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)3.1.4Mapping on a BurstThe mapping is given by the rule :e(B,j) = i(B,j)ande(B,59+j) = i(B,57+j)for j = 0,1,.,56ande(B,57) = hl(B)ande(B,58) = hu(B)The two bits, labelled hl(B) and hu(B) on burst number B are flags used for indication of control channelsignalling. For each TCH/FS block not stolen for signalling purposes:hu(B) = 0 for the first 4 bursts(indicating status of even numbered bits)hl(B) = 0 for the last 4 bursts(indicating status of odd numbered bits)For the use of hl(B) and hu(B) when a speech frame is stolen for signalling purposes see section 4.2.5.3.2Speech channel at half rate (TCH/HS)The speech coder delivers to the channel encoder a sequence of blocks of data. In case of a half ratespeech TCH, one block of data corresponds to one speech frame. Each block contains 112 bits, including95 bits of class 1 (protected bits), and 17 bits of class 2 (no protection), see Tables 3a and 3b.The bits delivered by the speech coder are received in the order indicated in GSM 06.20 and have to bearranged according to either Table 3a or Table 3b before channel encoding as defined in sections 3.2.1 to3.2.4. The rearranged bits are labelled {d(0),d(1),.,d(111)}. Table 3a has to be taken if parameterMode=0 (which means that the speech encoder is in unvoiced mode), while Table 3b has to be taken ifparameter Mode=1, 2 or 3 (which means that the speech encoder is in voiced mode)3.2.1Parity and tailing for a speech framea)Parity bits:The most significant 22 class 1 bits d(73),d(74),.,d(94) are protected by three parity bits used forerror detection. These bits are added to the 22 bits, according to a cyclic code using the generatorpolynomial:g(D) = D3 + D + 1The encoding of the cyclic code is performed in a systematic form, which means that, in GF(2), thepolynomial:d(73)D24 + d(74)D23 + . + d(94)D3 + p(0)D2 + p(1)D + p(2)where p(0), p(1), p(2) are the parity bits, when divided by g(D), yields a remainder equal to:1+D+D2.b)Tail bits and reordering:The information and parity bits of class 1 are reordered, defining 104 information + parity + tail bitsof class 1, {u(0),u(1),.,u(103)} defined by:u(k) = d(k)for k = 0,1,.,94u(k) = p(k-95)for k = 95,96,97u(k) = 0for k = 98,99,.,103 (tail bits)3.2.2Convolutional encoderThe class 1 bits are encoded with the punctured convolutional code defined by the mother polynomials:G4 = 1 + D2 + D3 + D5 + D6G5 = 1 + D + D4 + D6SIST ETS 300 575 E2:2003
Page 13ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)G6 = 1 + D + D2 + D3 + D4 + D6and the puncturing matrices:(1,0,1)for {u(0),u(1),.,u(94)} (class 1 information bits);and {u(98),u(99),.,u(103)} (tail bits).(1,1,1)for {u(95),u(96),u(97)} (parity bits)In the puncturing matrices, a 1 indicates no puncture and a 0 indicates a puncture.The coded bits {c(0),c(1),.,c(227)} are then defined by:class 1 information bits:c(2k)= u(k)+u(k-2)+u(k-3)+u(k-5)+u(k-6)c(2k+1)= u(k)+u(k-1)+u(k-2)+u(k-3)+u(k-4)+u(k-6)for k = 0,1,.,94;u(k) = 0 for k<0parity bits:c(3k-95)= u(k)+u(k-2)+u(k-3)+u(k-5)+u(k-6)c(3k-94)= u(k)+u(k-1)+u(k-4)+u(k-6)c(3k-93)= u(k)+u(k-1)+u(k-2)+u(k-3)+u(k-4)+u(k-6)for k = 95,96,97tail bits:c(2k+3)= u(k)+u(k-2)+u(k-3)+u(k-5)+u(k-6)c(2k+4)= u(k)+u(k-1)+u(k-2)+u(k-3)+u(k-4)+u(k-6)for k = 98,99,.,103class 2 information bits:c(k+211)= d(k+95)for k = 0,1,.,163.2.3InterleavingThe coded bits are reordered and interleaved according to the following rule:i(B,j) = c(n,k)fork = 0,1,.,227n = 0,1,.,N,N+1,.B = B0 + 2n + bThe values of b and j in dependance of k are given by Table 4.The result of the interleaving is a distribution of the reordered 228 bits of a given data block, n=N, over 4blocks using the even numbered bits of the first 2 blocks (B=B0+2N+0,1) and the odd numbered bits ofthe last 2 blocks (B=B0+2N+2,3). The reordered bits of the following data block, n=N+1, use the evennumbered bits of the blocks B=B0+2N+2,3 (B=B0+2(N+1)+0,1) and the odd numbered bits of the blocksB=B0+2(N+1)+2,3. Continuing with the next data blocks shows that one block always carries 57 bits ofdata from one data block (n=N) and 57 bits from the next block (n=N+1), where the bits from the datablock with the higher number always are the even numbered data bits, and those of the data block withthe lower number are the odd numbered bits. The block of coded data is interleaved "block diagonal",where a new data block starts every 2nd block and is distributed over 4 blocks.3.2.4Mapping on a burstThe mapping is given by the rule:e(B,j) = i(B,j) and e(B,59+j) = i(B,57+j) for j = 0,1,.,56ande(B,57) = hl(B)
and
e(B,58)=hu(B)SIST ETS 300 575 E2:2003
Page 14ETS 300 575: July 1995 (GSM 05.03 version 4.2.0)The two bits, labelled hl(B) and hu(B) on burst number B are flags used for indication of control channelsignalling. For each TCH/HS block not stolen for signalling purposes:hu(B) = 0for the first 2 bursts (indicating status of the even numbered bits)hl(B) = 0for the last 2 bursts (indicating status of the odd numbered bits)For the use of hl(B) and hu(B) when a speech frame is stolen for signalling purposes, see section 4.3.5.3.3Data channel at full rate, 12.0 kbit/s radio interface rate (9.6 kbit/s services (TCH/F9.6))The definition of a 12.0 kbit/s radio interface rate data flow for data services is given in GSM 04.21.3.3.1Interface with user unitThe user unit delivers to the encoder a bit stream organized in blocks of 60 information bits (data frames)every 5 ms. Four such blocks are dealt with together in the coding process {d(0),.,d(239)}. For non-transparent services those four blocks shall align with one 240-bit RLP frame.3.3.2Block codeThe block of 4 * 60 information bits is not encoded, but only increased with 4 tail bits equal to 0 at the endof the block.u(k) = d(k)for k = 0,1,.,239u(k) = 0for k = 240,241,242,243 (tail bits)3.3.3Convolutional encoderThis block of 244 bits {u(0),.,u(243)} is encoded with the 1/2 rate convolutional code defined by thefollowing polynomials:G0 = 1 + D3 + D4G1 = 1 + D + D3+ D4resulting in 488 coded bits {C(0), C(1),., C(487)} withC(2k) = u(k) + u(k-3) + u(k-4)C(2k+1) = u(k) + u(k-1) + u(k-3) + u(k-4)for k = 0,1,.,243 ; u(k) = 0 for
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