Coded modulation scheme employing turbo
`codes
`
`P. Robertson and '1‘. Worz
`
`l'nu’e.\'irtg .remt.s.' Cont-riluririrnri cor.’e.r.
`
`.-’l4'na’ni::lir:n mrtliiig
`
`turbo coding scheme for bandwidth-
`it
`The authors present
`etlicienl modulation that outperforms turbo coding with Gray
`mapping by employing llngerbocek codes as component codes.
`Thc scheme can be decoded iteratively and achieves very good bit
`error rates at low signal to noise ratios after 2: small number of
`iterations. SPSK is used as an example. although the scheme can
`be extended to other constellations.
`
`turbo codes have been introduced [l]
`l'ritmd'm'tion.' Recently.
`which achieve good bit error rates (103 —
`ll] 5) at a low SNR.
`They are of interest in :1 wide range of telcooitttnunications appli-
`cations and are composed of two binary component codes. They
`were
`originally
`proposed
`for
`binary modulation
`(BPSKI.
`Approaches have been undertaken to combine binary turbo codes
`with higher order modulation leg. BPSK.
`l6QAM] and Gray
`mapping [2]. in contrast, in our approaclt we have employed two
`Ungerboeck codes [3] in combination with TCM in their recursive
`systematic form as component codes in a structure similar to
`binary turbo codes. We use SPSK as an example throughout this
`paper, although the method can easily be extended to other modu-
`lation formats (cg. lo and 6-4 QAM) with similar results. We will
`begin by presenting the encoder structure. Followed by a brief
`description of the decoder and conclude with simulation results.
`
`they use
`Encoder." An important property of turbo codes is that
`recursive systematic component codes that are simple and have
`interleaving between two such component encoders. which results
`in :1
`small error event probability. Urtgerboeclt codes were
`designed to provide high spectral and power efficiency through
`signal set expansion. The motivation for our appfoaclt was to
`replace the binary component codes
`in classical
`turbo code
`schemes with llngerbocck codes and retain the advantages of
`both.
`Major dif'l'ert.-noes to classical turbo codes are:
`
`ti) The interleaving now operates on pairs of bits (for SPSK)
`instead of single bits.
`
`(ii) To achieve the desired spectral efficiency of Zbitfsymbol. the
`mandatory puncturing of parity information is not quite as
`straightforward as in the binary turbo ending case.
`
`Let the size of the (pseudorandom) intcrleaver he N. also equal
`to the number of SPSK. symbols per block. and let the number of
`information bits trattsntittcd per block be ZN. The encoder is illus-
`trated in Fig. 1. where we have chosen a short interleaving length
`N = (1.
`
`sequence of
`_ _'1*‘1bi*J39'£5__ _ -
`5161 .0 2.d3 .d»s.d5.dsJ='.
`00Ut_]t}_O00tt_ __JI
`
`BPSK symbols _____ _ _
`|_ro'.‘§]‘:‘.]‘5T£'1,|
`E__g.3£.;.r1“'}l.l:
`
`
`
`even position to even position
`
`
`J
`E
`,1’. ‘t
`odd position to oddposilxon
`111!
`
`I
`on jl1.=lda.ds.d5.d2.d1 .2141
`s§qT|e_nEe_c'f i_nfobit pairs
`1"s?r,‘o_’aTofE‘,
`s:TqE€n'c§ St
`aPSK symbols
`
`
`
`l Err.-radar _t-itnivn for SPSK u-"lib t‘t.N?ll'J0fle’Jil' ("titles nrenir.-ry three
`Fig.
`and example ofFrrrcrl'eut‘Fng with N — 6 shoivn
`Underlined letters indicate that symbols or pairs of bits correspond to
`first encoder
`
`achieved by keeping only the largest term in each of the sums. By
`taking the logarithm above we obtain simplified detector (optimal
`for large average signal to noise ratios, SWF), which is
`2
`0
`2
`
`.
`‘
`Z Inn} ll. rtlkl _ Jr|'t[lc]3Il
`‘___0lEf"‘
`
`. 2
`'
`'
`> Z "3111! lr-rile) — .Irn(l-Jstl
`< k_n at.’-Pr,
`1
`This detector uses the Euclidean distances between the received
`
`'2
`
`In all the
`signal and the possible [fadedl channel symbols only.
`results below.
`this simplified front—t:nd dctoctor has been used
`throughout with small performance loss relative to the optimal
`C3317.
`
`Per on-marme e,rantple_r.' Both uncodetcl and coded tFig. 2] schemes
`are considered and the bit error probabilities estimated by compu-
`ter simulations. Starting with the uneoded case, all schemes have
`the same power Spectrum as BPSK. which serves as a reference.
`For large TWVR. the bit error probability behaves as FNR ‘, The
`remaining three schemes have repetition codes resulting in 2. 3 or
`dhits. which are delayed and mapped into QPSK. SPSK and
`IEQAM signal sets.
`respectively.
`It
`is found that
`the diversity
`orders are oi, — l. 2. 3 and 4. respectively, and that SJVR ‘it shows
`the nsymptotic bit error rate. Note. however. that significant per-
`formance gains are obtained even at fairly large bit error rates. At
`the IU-’ level. 10:13 of SNR is saved with at, -2. With an in. ft)
`block code. the diversity order is now at, _ nflc.
`i.e.
`the inverse
`code rate. In Fig. 1. two TCM schemes with eight states are also
`considered. The case with code rate 2.33 and SPSK is taken from
`[1] and represents state of the art for Zbitlchannel use. The new
`systcm user»; code rate 2.01 with |6QAl\«‘l_ This latter code was
`designed by hand and is probably not the best possible. In spite of
`this. an improvement of --ldB of3'N7? is observed as high as the
`20% error rate.
`
`(‘0r.=r?!r.trr'nn.s'.' Starting from the CB] concept due to Zehavi [1], a
`diversity increase is obtained in a very simple way by introducing
`more coded bits. To keep the power spectrum unchanged.
`the
`channel symbol set must be doubled for each new coded bit. Sig-
`nificant bit error rate improvements are demonstrated even at high
`error rates. The proposed. simple suboptimal detector performs
`close to optimal. even at low 3W?i'.
`
`© IEE I995
`tilt’:-rro:I:'cs Letters Onl':‘m* No.‘ l995J'05?
`
`.’9 June I995
`
`U. Hansson and T. Aulin ((.'!ral:m.»rs Univemty of Dchnolog)‘.
`(.'oni_mm*r i':'rtginet*rin;-,'. Telcconrinrniirmion Tlieory. S-412 96 Goteborg.
`SIt'r:re'en I
`I-Lntailz tor@ce.cha|mcr5.se
`
`References
`
`I
`
`‘8—PSK trellis codes for :1 Rayleigh channel‘. JEEE
`ZEHAW. E.:
`Tr.an.r., I992, COM-10. pp. 8'33 884
`2 Wll.‘5(lN.!i.t}.. and l.EUNII.'u.Y.S.I ‘Trellis-coded phase modulation on
`Rayleigh cl1atutels‘_ Pt-ac. I98? int. Cont’. Common. kattle. WA,
`USA. '.l—lU June I987, pp. 21.3.!--2|.'3.5
`SCIILEGEL. (1. and t:oSTELLo_I)..'
`‘Bandwidth efficienl coding for
`fading channels: Code construction and performrmce analysis‘.
`IEEE J. Sell.
`.=frm.r ('ormmrn..
`i989. SAC—'i'. pp. l35b—l368
`4 JEi.rt‘tc.B.r>__ and |t0\r'.S.: ‘Design of trellis coded QAM for flat
`fading and AGWN channels‘. IEEE TJ"mr.t‘..
`I994. VT-44. pp. 192-
`201
`
`3
`
`5
`
`tstimation and modulation theory‘
`‘Detection.
`V.-AN ‘l'ltF.ES. 1I.L.:
`(John Wiley &. Sons. New York. I968}. Part I
`
`1546
`
`ELECTRONICS LETTERS 31st August 1995 Vol. 31 N0. 18
`
`Ericsson Exhibit 1025
`
`Ericsson Exhibit 1025
`Ericsson v. IV
`IPR2014-00921
`
`Ericsson V. IV
`
`IPR2014—00921
`
`

`
`ch.) —' (00. 01. ll. I0. UU.
`In our cxarnplc. the sequence (tit. :11.
`ll) of information bit pairs is encoded in an llngerhoeck style
`encoder to yield the SPSK sequence (0, 3. T. 5. I. 6). The informa-
`tion bit pairs are interleaved and encoded again. We dc-interleave
`the output symbols of the second encoder to ensure that the order-
`ing of the two information bits partly defining catch symbol corre-
`sponds to that of the first encoder. Finally, we transmit the lirst
`symbol of the first encoder,
`the second symbol of the second
`encoder. the third symbol of the first cncoder, the fourth symbol
`of the second encoder etc. Thus each information bit pair is con-
`tained in only one SPSK symbol. and the parity bit is alternately
`chosen from the Iirst and second encoder (hold. not-bold. hold.
`...}. Furthennore. the kth infonnzttion bit pair exactly determines
`two of the three hits of the Icth symbol X... Additionally. we need
`to ensure that the interleaving and alternate selection at the output
`cause each symbol to appear once and only once at the encoder
`output. It is easily seen that the interleaver must map even posi-
`tions to even positions and odd positions to odd positions.
`
`Decoder.‘ The iterative decoder is similar to that used For binary
`turbo codes [I], except that there is at dillerencc in the nature of
`the information
`from one encoder to the other. and in the
`treatment of the lll'5K decoding step. A further problem is the fact
`that each decoder alternately sees the noisy output symbol of its
`corresponding encoder and that of the other encoder. The infor-
`mation hits. i.c. the systematic bits that partly resulted in the map-
`ping of each of these symbols. are correct
`in the sense of being
`identical in the outputs of both encoders. However, this is not true
`of the parity bits. since these belong to the other encoder every
`other symbol. We have indexed those symbols with "" and some-
`times call these symbols 'punctu1'ed‘.
`
`
`
`
`e -interleclver
`to
`
`
`
`lfitiil
`Fig. 2 ConIp.l't’i't” dt?('tm'r-'r
`* dcntitcs 'punclured' symbols for corresponding component decoder
`
`
`<e°"d5*'*5 t:.:r.;t:f.f:.‘::.
`
`
`
`it can be shown that the
`In the binary turbo coding scheme.
`output of the component decoder can be split into three additive
`parts: when in the logarithmic or log-likelihood ratio domain. the
`systematic component .r. the aprinri component a and the extrinsic
`component .2. Here we can only split the output into two different
`components:
`at prion" and extrinsic and systematic (e&.t'). Each
`component decoder must now pass the second component to the
`next decoder. The complete iterative decoder is depicted in Fig. 2
`where the fir-st decoder sees a ‘punctured’ symbol (output by the
`second encoder: "‘-mode‘), i.::. the Corresponding symbol from the
`first cticodcr was not
`transmitted. The first docodcr now ignores
`this symbol, indicated by the position of the upper switch. as far
`as the direct channel input is concerned. The only input for this
`step in the trellis is the G‘ prfnri
`infonnation a from the other
`decoder, which contains the systematic information .r. The output
`of the first decoder is the sum of this a prion‘ information it and
`the newly computed extrinsic information a. The latter is given to
`the second decoder as its :3 prion‘
`information. The variables
`passed between our dceoders are vcctors of four ]og—likclihoods;
`one
`for each possible information group value. The second
`decoder. however.
`sees
`a
`symbol
`that was generated by its
`encoder, hence it can compute eats which is used as the air’ priori
`input :1 of the first decoder in the next iteration. The selling of the
`
`switches will alternate from one pair of bits to another. but not
`from one decoding iteration to the next.
`The above does not apply to the first decoding of the First
`decoder if it is in “—modc‘ because no 0 prion" information from
`the second decoder is available. in this case the rt prion’ informa-
`tion must be calculated from the received symbol by calculating
`the probability of the information group (:1.
`talking into account
`the unknown parity output bit of the other encoder. This calculat-
`tion is indicated by ‘metric s‘ in Fig. 2.
`
`
`
`3-5
`
`4-0
`E5.iNo‘dB
`3 TT(I'M_,I'bI' HPSK. 2 bitr"sJ'mbol
`:3 N = 5900 HUUUO bits}. I3 iterations
`O N ‘ 5000 (IIJODU hits}. 4 iterations
`El N ‘ 1024 [2048 hits). 4 iterations
`O N = 2048 hits. Gray mapping. 4 iterations
`
`3'2
`
`!.'.-£.
`
`-5» 8
`E]
`
`Siriiuiratéan re'.t‘trt’.'s.- As examples, we have used SPSK (with N =
`1024 and 5000) transmitted over an AWGN channel. The compo-
`nent code we used was the same as the Ungcrhoeck recursive
`eight-state code: We found that optimising the 'puncturcd' mini-
`mutn distance yielded the same code in this case. The bit error rate
`(BER) curves are shown in Fig. 3 for different numbers of i[Bt'£l-
`tions. Also shown is a Gray mapping scheme as presented in [3].
`that has the same complexity (number of trellis branches per infor-
`mation bit] as our f0I.tr—itcration scheme and the same number of
`information bits per block: 2048. In all simulations. we used the
`symbol-by-symbol MAP algorithm [4]. Compared to TCM with
`[14-state Ungerboeck codes. we achieve gains of L? and 0.5dB
`compared to the Gray mapping scheme. at a BER of ID‘. The
`Shannon limit for Ebitfsyrnb-ol and SPSK is at 2.9dB I;}JNa.
`
`(‘win-’r.u-iorr.r.' We have presented a novel bandwidth—eflit:ienI turbo
`coding scheme that employs Ungerbo-eck codes as component
`codes and combines the advantages of both schemes. The codes
`can be decoded iteratively and achieve very good pcrlonnarlce
`after a small number of iterations.
`
`(*3 [BE I995
`Ei'ec'trom'c.t Letters Ontine Na: !99.Sh')o4‘
`
`3 July .’995
`
`'f'e’t.‘ril'!I£J‘|ltJ_|f"l'.
`P. Robertson and T. Wore Un.m'!rrte of (."ornmu.m'::atiou.r
`Gcrnran At’r0spttt't’ Rr:s¢'ar(‘tl!
`I-Lttrtrhiis-ltnrerrr [DLRL PO Box HM. D-
`H2239 Wt“.r.ttt':ig. Gemrany}
`
`References
`
`l
`
`(_il.r\\I'IL‘.UX..-\.. and THITI.\vl.-'\.TSH[Mr\.P.: ‘Near Shannon
`IIF.RRt.)U.('..
`limit error—t:orrc-cling coding and decoding; TtIrbo—codc5‘. Proc.
`tCC‘93. May 1993. pp.
`toa4—Io7o
`2 GOFI-'.S.L.. CuLa\'IELIx..-\. and Bt=.RttoIJ.C.: "['urbo—codes and high
`spectral elliciency modulation‘. Proc.
`lC'C'93. May 1994. pp. 545-
`649
`
`3
`
`‘Channel coding with multileveliphase signals‘.
`L.'NCiF.RBOE(_'K.(.i.:
`IEEE Trrin.-r.. 1982. 1T-28. pp. 55-6‘!
`
`ELECTRONICS LETTERS 31stAugust 7995 Vol. 31 No. 18
`
`1547