i
`
`I ELECTRONICS iA
`
`_
`
`,
`
`CONTENTS
`pages 1 - 96
`
`A NTENNAS
`Accurate modelling of anti-
`resonant dipole antennas
`using the method of moments
`D.H. Werner and
`RJ. Allard (USA)
`Dual-polarised uniplanar conical-
`beam antennas for HIPERLAN
`E.M. Ibrahim, N..J. McEwan,
`RA. Abd-Alhameed and
`RS. Excel) (United Kingdom)
`
`CIRCUIT THEORY& DESIGN
`Analogue CMOS high-frequency
`continuous wavelet transform
`circuit
`E.W. Justh and F.J. Kub (USA)
`Apparent power transducer for
`three-phase three-wire system
`S. Kusui and M. Kogane
`(Japan)
`Efficient and fast iterative reweighted
`least-squares nonrecursive filters
`Yue-Dar Jou, Chaur—Heh Hsieh
`and Chung-Ming Kuo (Taiwan)
`Input switch configuration
`suitable for rail-to-rail
`operation of switched
`opamp circuits
`M. Dessouky and
`A. Kaiser (France)
`Unified model of PWM switch
`including inductor in DCM
`Sung—Soo Hong (Korea)
`
`COMMUNICATIONS & SIGNAL
`PROCESSING
`Adaptive multiwavelet prefilter
`Yang Xi nxing and
`Jiao Licheng (China)
`Decision feedback equalisation
`of coded l-O QPSK in mobile
`radio environments
`A. Adinoyi, S. Al-Semari
`and A. Zerguine (Saudi Arabia)
`Detection algorithm and initial
`laboratory results using
`V-BLAST space-time
`communication architecture
`G.D. Golden, C.J. Foschini,
`FLA. Valenzuela and
`F’.W. Wolniansky (USA)
`
`7th January 1999 Vol. 35 No. 1
`
`Efficient complexity reduction
`technique in trellis decoding
`algorithm
`Sooyoung Kim Shin
`and S00 In Lee (Korea)
`Extended complex HBF and
`its application to M—QAM
`in presence of co—channel
`interterence
`Ki Yong Lee and
`Souhwan Jung (Korea)
`Fair queueing algorithm with
`rate independent delay for
`ATM networks
`S. Ho, 8. Chan and
`KT. Ko (Hong Kong)
`Integrated space-time equaliser
`for DSICDMA receiver with
`unequal reduced lengths
`V.D. Pham and T.B. Vu
`(Australia)
`Investigation of sensor failure
`with respect to ambiguities
`in linear arrays
`V. Lefkaditis and A. Manikas
`(United Kingdom)
`Learning algorithms for minimum
`cost, delay bounded multicast
`routing in dynamic environments
`.1. Reeve, P. Mars and
`T. Hodgkinson (United Kingdom)
`Multiple target tracking using
`constrained MAP data association
`Hong Jeong and
`JeongvHo Park (Korea)
`Passband flattening and
`broadening techniques for
`high spectral efficiency
`wavelength demultiplexers
`E.G. Churin and
`P. Bayvel (United Kingdom)
`Performance of CDMA/PRMA
`protocol for Nakagami-m
`frequency selective fading
`channel
`Fl.P,F. Hoefe) and
`C, de Almeida (Brazil)
`Tbit/s switching scheme
`for ATM/WDM networks
`J. Nir, I. Elhanany
`and D. Sadot (israef)
`
`_
`
`(continued on back cover)
`
`Apple 1103
`Apple 1103
`
`

`
`ii
`
`CONTENTS
`(continued from front cover)
`
`ELECTROMAGNETIC WAVES
`Electromagnetic penetration into
`2D multiple slotted rectangular
`cavity: TE-wave
`H.H. Park and H..J. Eom (Korea)
`
`IMAGE PROCESSING
`Encoding edge blocks by partial
`blocks of codevectors in vector
`quantisation
`Hui-Hsun Huang, Cheng—Wen K0
`and Chien-Ping Wu (Taiwan)
`Technique for accurate correspondence
`estimation in object borders and
`occluded image regions
`E. Izquierdo M. (United Kingdom)
`
`INFORMATION THEORY
`Analysis of turbo codes with
`asymmetric modulation
`Young Min Choi and
`Pi) Joong Lee (Korea)
`Improved group signature
`scheme based on discrete
`logarithm problem
`Yuh-Min Tseng and
`Jinn-Ke Jan (Taiwan)
`Low density parity check codes with
`semi-random parity check matrix
`Li Ping, W.K. Leung (Hong Kong)
`and Nam Pharndo (USA)
`Non-binary convolutional
`codestor turbo coding
`Cafigrrou and M. Jézéquel (France)
`
`-
`
`.
`
`INTEGRATEDOPTOELECTRONICS
`'
`' 46'Gl-iz bandwidth monolithic
`InPllnGaAs pinISHBT photoreceiver
`D. Huber, M. Bitter, T. Morf.
`C. Bergarnaschi, H. Melchior
`and H. Jackal (Switzerland)
`
`'
`
`r
`
`LASERS
`1.5pm |nGaAlAs-strained MOW ridge-
`waveguide laser diodes with hot-
`carrier injection suppression structure
`H. Fukano, Y. Noguchi
`and S. Kondo (Japan)
`9.5W CW output power from high
`brightness 980 nm lnGaAsIAlGaAs
`tapered laser arrays
`F.J. Wilson, J.J. Lewandowski,
`B.K. Nayar, D.J. Robbins.
`P..J. Williams. N. Carr and
`FD. Robson (United Kingdom)
`Investigation of data transmission
`characteristics of polarisation-
`controlled 850nm GaAs-based
`VCSELs grown on (311)B substrates
`H. Uenohara, K. Tateno,
`T. Kagawa, Y. Ohiso,
`H. Tsuda, T. Kurokawa
`and C. Amano (Japan)
`Low current and highly reliable
`operation at 80"C of 650nm
`5mW LDs for DVD applications
`M. Ohya, H. Fujii,
`K. Do) and K. Endo (Japan)
`Modelocked distributed
`Bragg reflector laser
`H. Fan, N.K. Dutta, U. Koren,
`C.H. Chen and AB. Piccirilli (USA)
`
`Near room-temperature continuous-
`wave operation of electrically
`pumped 1.55pm vertical cavity
`lasers with InGaAsPI|nP bottom
`mirror
`8. Rapp, F. Salomonsson,
`J. Bentell (Sweden),
`I. Sagnes, H. Moussa,
`C. Meriadec, R. Raj (France).
`K. Streubel and
`M. Hammar (Sweden)
`Record high characteristic
`temperature (1; = 12K) of 155nm
`strain-compensated A|GaInAsI
`A|Ga|nAs MOW lasers with
`AIAS/AllnAs multiqua ntum barrier
`N. Ohnoki, G. Okazaki,
`F. Koyama and K. Iga (Japan)
`Red light generation by sum frequency
`mixing of ErlYb fibre amplifier
`output in OPM LiNbO3
`D.L. Hart, L. Goldberg
`and W.K. Burns (USA)
`
`MICROWAVE GUIDES &
`COMPONENTS
`Lurnped DC—50GHz amplifier
`using lnPIInGaAs HBTS
`A. Huber, D. Huber,
`C. Bergamaschi, T. Moi‘)
`and H. Jackal (Switzerland)
`RF tunable attenuator and moduiator
`using high Tc superconducting filter
`Lu Jian, Tan Chin Yaw, C.K. Ong
`and Chew Siou Teck (Singapore)
`
`NEURAL NETWORKS
`Compact building blocks for
`artificial neural networks
`M. Melendez-Rodriguez and
`J. Silva-Martinez (Mexico)
`
`OPTICAL COMMUNICATIONS
`40GbitI5 single channel dispersion
`managed pulse propagation in
`standard fibre over 5l'l9km
`S.B. Alleston, F’. Harper,
`|.S. Penketh, I. Bennion and
`N.J. Doran (United Kingdom)
`All-optical ZR regeneration based
`on interferometric structure
`incorporating semiconductor
`optical amplifiers
`D. Wolfson, P.B. Hansen.
`A. Kioch and K.E. Stubkjaer
`(Denmark)
`Demonstration of time interweaved
`photonic four-channel WDM
`sampler for hybrid analogue-
`digital converter
`J.U. Kang and RD. Esman (USA)
`Design of short dispersion decreasing
`fibre for enhanced compression of
`higher-order soliton pulses around
`1550nm
`M.D. Pelusi, Y. Matsui
`and A. Suzuki (Japan)
`Experimental measurement of
`group velocity dispersion in
`photonic crystal fibre
`M.J. Gander, R. McBride,
`J.D.C. Jones, D. Mogilevtsev,
`T.A. Birks, J.C. Knight and
`P.St.J. Russell (United Kingdom)
`
`(continued on inside back cover)
`
`

`
`iiiiii
`
`ELECTRONICS
`LETTERS
`
`T H E
`
`I N S T I T U T I O N
`
`O F
`
`E L E C
`
`Fl
`
`I C A L
`
`E N G I N E E R S
`
`7 JANUARY 1999
`ELLEAK 35(1)
`
`VOLUME 35
`1 — 96
`
`NUMBEH1
`ISSN 0013-5194
`
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`
`the proposed
`
`ar1ct1_r.vi.r: Some possible attacks against
`.S'ec'trri't_i'
`scheme are presented below.
`Armz-A’ 1: Although the group authority has the knowledge of (r_.
`3,. k,). the group signature cannot be Iiorgcd withottt the secret kc}
`.\'_. of U. It is impossible to obtain .r. from _I‘. without being able to
`solve the discrete logarithm problem lVlt)l't.30\L‘|'. because the gen-
`erator Ct, = g“ *1 mod p. A’. e 7,," and it e 7.)‘. both or. and tr have
`the same order q. Therct‘ore. forging (R. S) is as dillicult as break-
`ing ElGarnal‘s scheme [3-3. Since the group autliority cannot forge
`the group signature.
`I‘orger_v by an :tdvei'sary is even more dith-
`cult. Thus. the impersonation attack can not be successful.
`Arm:-A’ 2: The signer (.5, can be identilied if we can obtain 11 from
`the signature -I R. S. limit. A. B. C’. D. 5:. Since the receiver does
`not know the (r,. .5}. ft.) of the group authority. he cannot check the
`equation D” - _r,‘
`- E 5 1)“ mod p, Obtaining (r,.
`A1) from given
`{A. B. C. D. E $ depends on the discrete logarithm.
`Arm:-A’ 3: The group authority niay publish the infortnation (r,. .v,.
`_r,} for the message m‘s signature to enable a verifier to check the
`identity of
`This does not darnagc the anonymity of Us previ-
`ous group signatures because the itilmtiitititiii
`[r,_ .\‘,. _I',l
`is only
`provided for the spccitic group signature :R. S. i'i(m]. /I. B. ('. D.
`E. For di!Tcrcnt messages. if will have chosen dit‘ferent random
`integers (I and It
`to generate group signatures. If an adversary
`wants to obtain (1,
`/2 and try. r.) from given {.41. B. C D. E‘ .this is
`as dillictih as solving the discrete logarithm.
`
`Diii'ras‘.sinii.' The improved schenic preserves the main merits inher-
`ent in most of the Lee-(‘hang scheine. In the case of a later dis-
`pute. the group authority ma_\- publish the information (rr. RT. _r.)
`to enable a vcrilier to check the identity of the signer. although
`this does not damage the anon_vmity of the other previous signa-
`tures of the signer. Meanu-ltile.
`the group authority need not
`renew any key of the signer The reason is that the iiiforrnatioti
`(t',. .s',.
`1",)
`is only provided for the specific group signature :R. S.
`from.
`.4. B.
`('. 1).
`I51. C'onipared to the original scheme.
`the
`improved scheme requires some additional cost
`in terms of com-
`ptttational time and the size oi‘ the group signature. For generating
`a group signature. the signer I", may precoinputc sc\'ct‘ttl diITerent
`:ot,.
`.-1. B. (L I).
`II‘, using ti-_.
`.r,) to reduce the real-time computa-
`tional time.
`
`CtJII(’.lN.\'i(.W.\'.' We haxe proposed an improved group signature
`scheme based on the discrete logarithm. in our improvement. a
`group signature can be opened to reveal the identity of the signer.
`the anon_v1nity of the other previous signatures signed by this
`group member are not daniagcd. Meaiiwhile. the group ztutliority
`also need not renew the keys of the signer. We have demonstrated
`some possible attacks against the proposed scheme, Under the ditl
`Iicttlty of computing the discrete logarithm problem. he llavc
`shown that the improved scheme is secure against these attacks.
`
`35"‘ IEE [999
`Et't'¢'rrrurit'.\ Lt'l'.'(‘l'\' (}m'.im= No: I‘/99t){)7!
`
`3.3’ Ot‘mI')t'r I‘-t‘)..\‘
`
`..l!utt'imi::Ii't'.\‘.
`Ytlh-Min Tseng and Jinn-Kc Jan ('1'n.vtfri.rIv of Ap,nfi'm'
`N'ziri'r:iztit'
`('i'u.rng !i'.ri'.v-ig
`t.="tii"i‘er.rtt_t‘, Ttttdtirrig. 7'unmii W13. Rv,'itififi'i- of
`(illflltll
`
`Jinn-Ke Jan: corresponding author
`
`E—mail: jl(V]'£ll1./i1“Et1'l‘l.”ltl].l‘lCll1l.€dLl.1\\
`
`References
`
`Pfrlr‘.
`
`sigiiauu-es‘.
`
`‘Group
`ur.\'sT. F.:
`and
`( Hn\t'\1 I)..
`E(.'R(J(R)'PT'91, I993. pp, 257 265
`( H!-.\
`|.. and Pt:tJt.i<sI N. T r: ‘New group signature ~.c|ieiues‘_ I’:-mu
`t':"L'ROCRl'PT'9-I. l995. pp.
`l-Fl
`ltil
`LL(iA.\lAL. T.1 ‘A public key crypto s'_\slc‘IT1 and a sigii-attire st-lit-me
`based on discrete iogtiritltms‘. IEEE Trmi.\.
`Irtfl Ilirurt.
`1‘)-\‘5. 31.
`HI. pp. 469-473
`‘Fill-It.‘lCl1'l group sigiiatttrc scltcmc based
`LLE. \\ B. and t'H-\\('i. C C;
`on the discrete logttritliilf. [HE Prur
`(imipm i'Jt_L't'!.
`'i’l't1’i,
`I995‘.
`145.11). pp. is is
`-.ignature
`for
`\I‘)'B1-'R(i.K. anti RlTl‘l’I.I..R..\Z ‘Message reco\‘eI‘_\'
`schemes based on the discrete logarithm prublcilt. Dt'.\:_<,'.-ii.
`(‘writ-.n
`amt’ (‘r_i'p!og:i‘cipft1‘. 1996. 7. pp. 61 HI
`
`l
`
`I.)
`
`R
`
`-1-
`
`3
`
`38
`
`Low density parity check codes with semi-
`random parity check matrix
`
`Li Ping. W.K. Leung and Nam Phamdo
`
`A sr:mi-random approach to low density pztrit} L‘l'lCCl\' code LlL‘\'lg]1
`is shown to achieve essentially the sanie perfonnance as an
`existing method. but with considerably reduced comple.xit§_..
`
`[ItII'r1ti'Ir('{ftJI1.' Recently. there has been revived interest in the low
`dcnsity parity check (LDPC] codes originally introduced in 1961
`by Gallager [1]. It has been shown that such codes can achieve
`tery good performances {within 1.5dB of theoretical limits) with
`modest decoding coniplestity [2].
`An LDPC code is defined from a randoinl_v generated parity
`check matrix H [2]. For the purpose of encoding. it is iicccssttr} to
`transfer H into Hm. the equivalent systeinatic form of H. which
`can be accomplished by Gaussian elimination. For it rate R = k H
`(R : infonnation length. it : coded length]. the size of H is tn k] x
`ii. When it is large. Gaussian elimination can be costly in tcrnis of
`both memory and the operations lI1\L1l\‘l.'(l. Besides. a considerable
`amount of memory is required to store II...
`in the encoder. which
`is not necessarily sparse even though H is ttsually designed so.
`In this Letter. we report a moditicd approach to LDPC code
`design. We adopt a semi-random technique. i.c, only part of H is
`generated randomly. and the remaining part is deterministic. The
`new method can achieve essentially the sanic peitorniaiice as the
`standard LDPC encoding method with sigtiiiicaiitly reduced coin-
`plexity.
`
`Prupowd r1ppi'mm'r: For simplicity we will only consider binary
`codes. Decompose the codeword c as c = [p. d]'‘. where p anti d
`contain the parity and iiitbriuatioii bits. respectively. Accordingly.
`we decompose H into H = [H". H"]. Then
`
`(II
`tH".H“)CD 7 0
`In the proposed method. HI‘
`is constructed in some deterministic
`form. Empirieally. we found the following a good choice (recall
`that HI‘ must be a sqttatrc matrix [3]):
`I
`I
`
`II
`
`H“ =
`
`I
`
`.
`
`.
`
`(‘ll
`
`II
`
`1
`
`1
`
`We adopt the following rules to create ll‘. Let I be 11 preset integer
`constrttincd by [ii (divides rt-A’ and (ii) I7-Ix’ divides kt. Partition H”
`{which has n A rows) into I equal sub-blocks as
`
`II" a
`
`Hdl
`
`7
`H(l'
`
`I3}
`
`-r. tte randomly create exactly
`I
`In each sub-block H“; i : I. 2 »
`one element 1 per column and kt.-tii—k) Is per row. The partition in
`con. 3 is to best incre'.tse the recurrence distance of each bit in the
`encoding chain tsec below) and. intuitively. reduces the correlation
`during the decoding process. The resultant H“ has a column
`weight of r and a row weight oi‘A'J«(n—-A) (the weight of a vector is
`the number of Is among its elements).
`Basetl on eons.
`I and 2.
`’ to: can easily be calculated from a
`given (I
`' M: as
`F
`-2-‘ .’i'I',r/',
`
`pi
`
`:tn«i
`
`_u_. -1»,
`
`i
`
`I
`
`2-! It‘-‘ix/.
`
`tI1uIIl—’.|
`tli
`
`the above
`('omp:u'ed with the standard LDPC code design [2].
`method has several advantages. First. the encoding process in eqn.
`4 is much simpler than a full Gaussian elimination. Secondly. a
`random H" can be singular. which causes additional programming
`L‘0I‘n}‘)lt.‘Z'tll_\' in realising a specified rate. On the other hand. HI‘
`in
`cqn. 2 is always non-singular so the new method can realise any
`given rate directly and precisely. Thirdly.
`it requires very little
`nicmor_v to store H“ in the encoder if H“ is sparse (this can be
`ensured using sniztll II.
`
`ELECTRONICS LETTERS
`
`7th January 1999
`
`Vol. 35 No.
`
`1
`
`

`
`decoders passing the result of their work to each other. at each
`iterative step.
`
`!
`
`X
`systematic
`part
`
`
`
`data --
`
` \
`i interleaving i
`
`
`
`Y1
`
`redundancy
`
`0.5
`
`1.0
`
`1.3
`
`1.4
`Eb/N0.dB
`
`2.2
`
`95-~
`
`f’t~i'f2»t'nn.uit-<-.~ of LDPC mdt-s gt=itt=i'umt' ht‘ uwt.'-mttt.'~n: /Ituflt
`l
`Fig.
`t‘I'.lt‘c'.i\‘ Htr.'t‘t't\‘t’.\
`tt til) ti‘
`3t'HJUU
`
`Oltrl‘
`IR I
`AR—2
`
`,4I.r.4
`
`1 contains the simulated perfonnttnces of
`.S':'nm/utiuii mu/_t‘.‘ Fig.
`the proposed encoding method for \'-ttrious rates (1 3.
`l2. 2 3}
`using ! : 4. The decoding algorithm follotvs that in [2]. The results
`are cssetitittll} the same as those obtained using fully random H.
`
`ilth been sl]0\\n that a semi»r-andom approach to
`It
`("um-iltmfmi.‘
`I.[)i’(‘ code design can :tchie\'e essettti-.tl¥_t' the same perfomtaitcc
`21s the existing method with cotistderabl_\ reduced compleytity.
`
`IKE: W9‘)
`1
`.’:’t’t't‘rt'uiiit‘.\ f.:'.'m'\ Uitltr.-:'
`
`\’ri.‘
`
`IUWU-‘J05
`
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`[ J'tiI‘z't'.\H_t' «if Hru.r_q f\'nIJ_t{.
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`l;"!ct‘.'rir‘uf wit.’ ('nrttpt.wr' Ell'Qtfl'L’(’t‘tl'1g,
`.\ttm Phatntdo tilt-,rmi'rnmir of
`Stalin’ [‘l.|t't‘t'."ti.'t‘ crt";\7t'tt
`i'rM'.t'x at S.'rut'_t' h'i'rmA'_ .5'.tmr_t' Brriri/(,
`,‘\a }"
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`3.350. (‘‘\'-I)
`
`("fry
`
`References
`
`I
`
`2
`
`‘.1
`4
`
`tt.\LI «oi R R (.2 ‘Low tlcttsily pttrity cheek eodesfi IRE It’:-mi.»-.
`'1"/in-:1't'.
`I963. IT-8, pp. ll 38
`\t.tt~it.M'. |)..|.( .. and t\'t-.-\I.. R.‘\t.‘ ‘Nettr Sttztntton limit performance of
`low tlcttsit} pttt'it_\-‘ cheek codes‘,
`I;'i'¢'n‘mri
`I,r.'t‘.,
`I997. 33. to]. pp.
`457 458
`|'R()»‘\l\l\. .t ti’. ‘Digital eotnmtittietttions‘ (Mc("ir;t\\~i lill. I995)
`i't—tt.ttst>.\. ww. zmtl wt I DUN I
`.I.
`it
`. ‘tinor-correcting codes‘ (MIT
`|’I'css. Ctttnbridgc. Mztsstteltttsetts. 1972; Zntl edit.
`
`Infj
`
`Non-binary convolutional codes for turbo
`coding
`
`C. Berrou and M. Jézeqttel
`
`The 'ttlllitUl‘.\ cott~.it_lcr tltc use of rton—bitt;tt}' contolutionztl codes in
`turbo ending.
`It
`ts ~ilto\\n
`that
`L]ll‘.t.lt.‘t'ltttT_\
`codes can be
`;TLi\'L'tI1l&.1_t._‘_c'ULt>.
`both
`from perTot'tn.mee
`and
`eontptewity
`standpoints. but
`that
`ltiglter-order codes in-.:_\ not bring titrtlier
`tl‘t1pl'0\ emcnt.
`
`least
`Immdm-riuri.' Turbo codes are error correctin-__v codes vtith att
`two (liI‘J‘ICt1SlOt1S ti.e. each dattuin is encoded at least
`twice). The
`decoding of turbo codes is based on an iteratix-‘e procedure using
`the concept of extrinsic ittformttttott. Fig.
`1 gives an example of at
`t\=;o-dimensional turbo code built t‘ront It pztntllel eonetttenntioit otl
`two identical recursive systentatie convolutional (RS(‘] Codes with
`generators
`l5.
`l3 (octal notation). The global
`(tton-iterative)
`decoding of such 22 code is too complex to be envisaged becitnsc ot‘
`the very large number of states induced by the intct'lcttvcr. /\n iter-
`ative procedure is therefore used.
`the two codes being decoded
`alternately‘
`itt
`their own dimensions and the two associated
`
`
`
`Fig.1.
`
`1 THH-t.l't'mt'n.\tuu .'t.'t'/Ir» (‘m.lt'
`
`§55('l
`|l if/I t{t'.'tc'i'ut‘m'.s I5. I3
`
`at block of
`(’U(t't’.\'. Fig. la I’t:?pI‘€St$nl>t
`B."m1i‘_t‘ rru/tar t'¢'t‘.t'tr.\' £_,'£t'h't'L'F't'f(t't’_t
`si/c A‘ encoded by the code ol' Fig.
`t. This block is seen as a two-
`diinettsiotial V‘I'\' X \-‘It’ block and for simplicity we consider that the
`intcrleax-er is at rcgttlur one:
`the sequence is encoded lirst by C',,
`following the liori/,ontal or linewise dimension. and secondly by
`('3. tollowittg lltc \-ertieul or columriwise dintension, Tlte dashes on
`both ditncnsions syttibolise the pttli] error packets at the output of
`the two decoders. at
`it pztrticttlar step of the iterative process.
`These packets do not contain only erroneous decisions but they
`indicate where it wrong pltlit
`lttts been chosen either by the
`decoder ot" ('1 or by the decoder of (E. This eorre.~‘.pottds to a cer«
`tttin path error density per dimension. which is the sttnte itt both
`dimensions it‘ the component codes are identical.
`
`xlfi
`
`
`
`5531'
`
`Fig. 2 Path t'H‘m‘ ,'!.:.rr/t:'.t’.t
`it Biliary codes
`I: Qttatermtr} codes
`
`in !mt'Iri (!'t‘(’nr/int.’
`
`:7:
`systematic pan
`
`
`
`£jt1t'!!'t’.‘l'Htlt'_l.‘
`Fig. 3 »\‘—wurt‘
`(mic ire"!/r \L'(’fI(‘l"(lft)l‘.f 1.1". [3
`
`i'cr=trr'5i't'c'
`
`.t'_t‘.&miict.'."r
`
`t‘ont'm'ttti'omt.’
`
`tRS'('_1
`
`redundancy
`
`The perfot'tttattee of turbo decoding is strongly dependent on
`the path ClTt)t' density per dimension. Obviously. the more numer-
`ous and the longer the horizontal and vertical dashes in the sqttare
`box are. the harder the convergence to the Correct codeword is.
`Now For each component code. replace the biliary code of Fig.
`l
`by the qttaterttat'y code of Fig. 3. The data are thus encoded and
`interleaved in couples. The size of the block is Ir/‘2 couples and the
`sqttat‘c box now lids the dimensions NW2 X \‘‘'/\'/2 (Fig. 211). When a
`decoder selects a path in the decoding trellis. the same amount of
`itttortnation is used in the cases of both binary and quaternary’
`codes. theret‘ore with halt‘ the number of transitions in the Case of
`.-t L|tt2llL‘l‘t‘|‘¢lF}' code. giving path error packets which are halt" the
`
`ELECTRONICS LETTERS
`
`7th January 1999 Vol. 35 No. 1
`
`39