TANARE AND FARVAIDIN: 5UliAN'b ttmte coerrta
`
`the srtbhand veriancet
`Apart from'the encededdala.
`need to be transmitted to side (overlteadl lnfortnatton. In
`addition. for System A the predictor coellieients need to
`be tsansrttitted while.
`in System B. the variances of the
`DCT eoelrltienta and the mean of the he eoefiidient need
`to be transmitted. Nple that lfthe-.vstiance itttorrnatinn Is
`available lo the receiver. the bit allocation procedure cm
`be repeated there and hence noadditlnnal information for
`the parameters of tlte (UTQt I-IC) pairs is neceasuy.
`Assuming that we needtwo bytes [16 hits) for each real-
`valued parameter. 36 bytes (16 ttuhbaotla-and two cone-
`Iatinn coefficients) need to be trartsetttted for System A.
`This eorrespcnds to CLW4 b_/p for e B6 3-! 256 image
`and £1.00! bfp for a 512 X 512 image. In Systetn B. in
`.sdditien to the variances of the stthbantls. the variances
`of the DC!‘ ooelflcienta and thl traean of the do eoal7fl-
`clent need to be transmitted. Therefore, for an L x L
`blocltsize, the side infnrrttetiott is 10.2‘ + 16) bytes. For
`tlte chosen blocltalze ore tt dtltls antouttta to 0.008 h/p
`and 0.002 13/1: for 256 x 156 and 512 x 512 images.
`respectively. Therefore.
`for all cases of
`-tlerest
`the
`amount of size intmttotlon is less than 0.Dl -
`!p—a nep-
`ligible axnount.
`
`V. Ttuuvstttsstorv Esutott Rrrecrs
`in Systems A and B. ttariablevlength ending is used es~
`tensiveiy.- It is well-icnown that this to theseqttentlttl na-
`ture of decoding such codes. channel errors wold result
`In the lost of syttehtonisattoti and. hence. severe degra-
`dation in system perfonnaoee. Fttttherrnote. predictive
`coding (used in System A and the W-0 scheme) is ltncvrn
`to s1.td'er from channel error propagation problems. Fi-
`nally.
`in 2-D DC.'l' oodlnp (used in System 3), channel
`er-rota propagate throughout the block. These facts indi-
`cate that the stthband coding schemes studied in Section
`iv may sull'er serious dlllleultles lo the presence of trans-
`rnissiott {or should) noise. oteettrae. due to the extensive
`use of variable-lengdt coding in Systems A and B. one
`would expect a greater sensitivity toehanttel noise in Sys-
`terns A. and 3 as compared to the w—o acetate.’ In this
`section. we will present simulation results for the perfor-
`mance of Systems A and B as well as the W--O scheme in
`the presence of channel noise.
`To prevent the infinite propagation of deoodlng errors.
`we havepscketlzed the codeword aeqnertt.-ea before trans-
`missiun. In what follows. we describe dte details of the
`pecketization scheme.
`
`-
`
`A. Packeriaorlon Scheme
`The main motivation in paeketieation of codewords is
`to confine the propagation of channel noise to within a
`packet. To do so. we must malte certain that our packets
`
`‘The W-O scheme also uses varlaltle-tnpslt codes for set.-eels; some
`srteeases tsee Ill); however.
`the LFS ls noodd hp fitted-Lurgrlr wees.
`line: LES has us: lIl[l‘|¢l| variance l.ll|llI| a.I| suelunrlg. tn; gnungl none
`efiectt in the LFS should result In the most dramatic degradations in system
`petforlnanet.
`
`" ,
`
`-to
`
`'“ ‘M
`contain information about a fixed (or lt.l'IDW|‘l
`eeiver) nuttsb-er of Filth 50 “Ill Pllilfll-'l°'P“k°'
`I K.
`station of the I-Ittlftttan decoding error is prevented.
`the pixels are encoded ll! "||lIb1°"=flB1-1" °°‘~1“' “''.° F"
`eta cannot be of listed length 1'l°W\'¢|'- 1" d“"i""3 M"
`pacltetlzation scheroe we will '1'!‘
`'0 _i°°P 'h° awrflg
`packet length that so that fair oolltpartsons can be In
`between dllferent systems. It is important to remember
`that the severity of error propagation is directly related 10
`the paeltet lettgtlt.-
`_
`_
`In the pacltetlzatiott scheme adopted in this wotit. the
`hen consist oftsvo pasta: 1) a length indlcetar lndtt:at-
`l’..‘.f the length at the tnromtton portion (in bin): 11"‘ “l
`the infinrrrscrlon portion consisting of a sequence of hlnery
`codewords. While the length of the length lrtdiestor is
`tired. that of the inforteatloa portion of the P|d‘¢‘ ‘mm
`vat1r—hettee resulting in torleble-lengtll p¢¢*“-|'- F‘-'7'
`therroore. all codewords tr-sntrnteed ln a packet tattoos '0
`the same atthhand.' To be mun! l!'°°'5°- '°‘ “" °°''''“" “
`pacltet used for encoding the llh attlsheod.Le1 |lI ll-|PP°‘:_
`thattheplxelsinthltsttbhsodsteencodedbv M“-"5:
`l-IC‘r of order i'|r at s tletllfl W ‘W °f "P s"F1’°"’ ‘
`'3
`ofllae.lnt‘orntat.lott portion of thfl puck“ *'
`average length
`_
`,
`- 1, hits. Then. the number of codewords lll tmt r-=|=== E‘
`given by:
`'
`(6)
`5 I
`'
`"'-‘ '7 E
`where |':'i is out to denote the smallest lrIl¢l=|' trr-M
`oanoreqrutwx.rtmuut,treudmdrruIdmI=¢
`lmovvtt front the results of the hit allocation procedflln
`u.,. can he deterntltted tn the receiver aide. maim-
`enoedingtlte ltlt snhlsand. alt-'-ll
`bet contains the infor-
`mation fer rt,_. - rtrtt.._t 1'-‘lflll-‘
`I
`E
`I M for tn, damn}... Pmccu,‘
`following ntes ll
`applied.
`'
`'
`'
`'
`'
`1) ooendtngoreodwurds in a Picket W“ "“' ‘fl
`inttatpsetnstsornsrttrsttuntruam«_adIns__err=!r|l°°=
`W3. nt:lf'ohttBdewordl its a rm-Its‘! m°°l*'°‘ ""“‘
`thettlt nthlsaod terratl.tu'tes when one oftlte follolrllll Ill!“
`eeortltions is met.
`'-
`'9-Ir
`== '
`
`'
`
`rda are
`_ code
`)
`III¢l|¢I1"=°““°“P""‘°'
`3) ;ll:I.’lawl:Iwl(l!IB
`(known from the length lndleatotl-
`_
`c) A bit string which cannot be decoded is
`teted. In this case. deco-flint ts unwed ‘mm
`-ately. and all pixels that cannot be decoded are
`retraersscrutred ll'l¢!O-
`
`In what follows. I-'3 W1“ 9'33"‘ 3i|'“'-"“'°" '“fm'S;"
`the performance of the thlffl
`°°‘'|5id‘'‘d "'
`'
`titan [V when the channel is noisy.
`
`M‘-
`_
`|_
`'te srsmn a. each of the traealtme cumr.-teats is treated at It NM‘
`3...... ...t puke! mum oodavorda from only am trim“-H" ‘°"'
`cififill pseitela used foretteotlilj the ill: stthhlnd Iunlflifl ’'r.- 9“‘'' ‘“'F
`namely the lastone which conlalll only IIII N--i-i-I W"-
`
`
`
`Page 266 of 437
`
`Page 266 of 437
`
`

`
`Ill! iottesutt on enter.-rel: Assn its oomuuutcmons. vet. to. no. s. time ml.
`TABLE VI
`‘
`PENN ltestloes-macs liaswrs (Ill til) I-0| "-i.£NA“
`
`
`
`31.59
`23.92
`ts st
`1;:
`1 L39
`33.71
`l3.lT
`its
`test
`Liiii
`use
`lat
`avttnvstttt
`31.55
`36.5?
`J6.‘-"'.'
`1.64
`35.16
`54.66
`ill!
`t.2‘.'
`32.00
`. JL99
`l&.23
`lo.d9
`A MAX-PSNI
`20.19
`l‘.l.Il
`an
`t.ss
`2131'
`13.17
`IIL19
`6.-21
`test
`test
`tt.st
`9.tr
`7”“ sttti-rstra
`4.95
`4.45
`I as
`0.34
`4.3:
`3.4!
`its
`0.32
`3.0:
`has
`ttao
`a.-to.
`ETD-rsfllt
`tr.-it
`11.01
`sons
`tins
`s4.17
`tut
`toss
`tsso
`at.s4
`sun
`st.tt
`lI.3J
`AVE-PSNI
`systems mt:-tvstnt
`ts.-to
`:s.o'i
`!l.9J
`32.19
`|«l.'l-i
`zt.ss
`trot
`35.32
`ts.s:
`ss.tz : _ss.t4
`asst
`ttxo loItN~PSNl
`_
`ts.4_r
`ts.s2
`23.3:
`24.5: mt
`nus
`sass
`:s.ts ‘
`tins
`ts..is
`13.2: ms
`STD-MN!
`0.54
`1.30
`2.19
`L}?
`0.0!
`LS!
`1.91‘
`' 1.44
`0.5]
`L4!
`3.03
`t.I:I
`
`AVE-Pall]
`teas
`rite:
`tint
`sets
`2‘.i.Dl
`21.51
`29.11
`29.9:
`21.9:
`asst -
`sans
`33.91
`MAX-PSNI.
`ll-.09
`1l.D3
`2I.hS
`11.65
`14.3!
`29.0’)
`29.94
`Zli.9-I
`ZJJI
`31.00
`l3.9-I
`3l.l:il
`w_°
`MIN-PSNII
`2I.le mo
`zs.ss
`rut
`tuna
`17.19
`29.51
`29.1:
`zone
`and
`32.1:
`ss.t:t
`
`on on one Mid and out one D.Dt am one tutsro-mitt D.l'l
`
`
`
`
`
`
`
`
`
`
`
`
`S
`
`.
`
`B. Simtdqliarr Results over Noisy Ciro.-their
`We stssume that the chsnnel
`is a rrtemoryiess binary
`symmetric channel (BC) with a bit error tats (BER) or
`P,. For ottrsitnuiatiotts in this section. we have consid-
`ered P. - 10". 10-’. to“. and to". To make certain
`that our results are meaningfttl. for each encoding scheme.
`hit rate. attd channel BER, we have repeated our simula-
`tions 50 times and comprised the average PSNR (AVE-
`PSNR). mutimum Paint (MAX-PSNR). minimum PSNR
`(MIN-PSNR1. . and standard deviation of the PSNR
`[STD-PSNR). sintttlatlesas are carried out for en-
`code-dby syatetnaaatal natal thaw-0 scheme“'attte-
`sign bit rates of 0.25. 0.3. and I b/p. The sitntdstion
`results are surnrnarirted in Table Vi. A few important ob-
`servations about these results are in order.
`i) System A is eitlretstely sensitive to channel errors.
`Also. the STD-PSNR of System A is fairly large (espe-
`cially for low BER's) implying that. even at low-cltanttei
`BER‘: there is a possibility at’ severe perfornunce deg-
`radation [e.g.. - 14 dB dlltetence between JWE-PSNR
`and MIN-PSNR. for System A II 1 Is/p with P. - 10").
`2) Syrterrl E is also very sensitive to channel errors.
`However. it performs considerably better than System A.
`In all cases considered. the MIN-PSNII of System B was
`significantly lII]|s1-[Q-3 d3) tltlrl that of System A: 'the
`AVE-PSNR of System B was also larger than that ofSys-
`tem A. especially for larger values of the channel BER.
`Final|y,tll'te STD-PSNR of System B is smaller than that
`of System A.
`3) The -W—O scheme exhibits the highest degree of to-
`bustness in the presence of channel noise. in most cases.
`the eifect ol channel noise is negligible for P, < lO"]
`Also. contrary scour observation for systems A and is.
`the STD-PSNR in this case is very small. In almost all
`cases. the ‘H-0 system petrortns better than System B
`
`'“In all orour simulation for noisy shsnnels. the avenge puke! length
`it little hita. Thu is not an optimized length but. um rut. theultt provide
`an appmpriste ttedeofl bemoan the channel error streets and the inet-me
`of aid: inlnrtetlatitsa.
`
`-
`
`with the etcctsption ofa fewfissee where the channel noise
`is very SI'l'll.|l (P, - ID").
`' in Fig. 9. an exsmplc of reconstructed images front the
`three systems is presented Eorsrt encoding rate of 0.5 is/p
`sndii, - iO":ti'teseitstagescot1erpondtorltt:-secasesin
`our simulation which result in rttlnitnunt PSNR. Clearly.
`the sttbiecrive perfonnutcs of the three systems closely
`lbilovrs the trend suggested by the PSNR results of Table
`vi.
`The results ofTsltle Vi [also supported by Fig. 9) sug-
`gest that systems A and is. despite their superior perfor-
`mance for noiseless channels. exhibit an unacceptable
`level ofsetuitivity to channel errors and hence should not
`be used over tasiay channels (st lesst over the range of
`channel BER’: ‘considered here). in the next section. we
`will describe 3 combined sourocfchanael coding method-
`ology to reduce this severe sensitivity to channel noise.
`Vi. Cotaatttso Souacs.-‘Cranmer. Comm:
`systerna A and 3 exhibit a high degree of sensitivity to
`channel noise because they have been designer to mini-
`nilze _lhe source coding distortion Issunting a noiseless
`channel. It is a well-ltnowtt fact that. in general. the more
`eiiiclent the source coding scheme is. the more sensitive
`it "will be to channel noise unless some corrective rues-
`sunes are taltett. Specitlcaliy. it is shown In [Isl for zero-
`rnernoty qttatrtlaets and in [16] and [IT] for predictive
`coding and transform coding or images that. in the pres-
`site: of channel noise: increasing the accuracy oi‘: source
`encoder could result in an overall performance degrada-
`tion.
`.
`One possible method of mitigating the channel error ef-
`fects is use of error control coding. in this manner. of all
`bits used for encoding the image. some will be used in
`source wdliig while the rest will he kept to provide pro-
`tection against channel noise.
`in [I6] and [ii]. an ap-
`proach in which specific source encoders and channel en-
`coders are combined is cntttidercd: in this approach. the
`..rates of the source code and channel code are adjusted so I
`Is to minimize the MSE. in [IS]. all approach for chart-
`
`Page 267 of 437
`
`Page 267 of 437
`
`

`
`TANtlI'E AND FAIVAIDIT-It SUIIHHD ‘MAO! UDDING
`
`
`
` -_ U11
`
`important questicn»ls'hovr to distribute the bits among the '
`source coding and channel coding opererions for the dir-
`ferenr sttbbettdtt so as to minimize the overall distottiflfl
`caused by quantization noise and channel noise. The main
`dlflicultsr in doing this stems from the fact that vst'ieb|e-
`length codes are used in Systems A and B. In this use.
`the analysts of channel error efieets end its itnpuct on the
`event]! distortion is a fostttideble task {If not Impossible}.
`Another importsrtt problem in our sysresns is the! of bit
`allomttion among the tliferent strbblttde. Clearly. the bit
`aflocation used under the rtoieehn channel assumption
`need not be opli1'ml.fo1' noisy cheeneis. To be title to de-
`tenrttrte the optimal bit allocation. we need to be able to
`determine the distortion-rste perforrnsrtce of the U'FQ'3
`followed by s HC and an error correcting code (ECG)-
`Agsin. due to the inherent problerrts of psclterized virt-
`ttble-lengtlt cadet. the nnslyticsl ootttputetiort oftltete dis-
`tortion-rste performance results is not possible.
`In what follows. its will describe e srettttetton-ham‘
`procedure to determine the best (UTQ. HC. ECC1 triple
`fa‘: encoding s otettturyleas source ever a BSC It s given
`encoding me. This procedure will lend to the detelt'rI1'-
`nstion of the distortion-rste perfernsenee functions that we
`- need for optimei bit allocation mun: suhlsttttds.
`
`Al. Selection of HJTQ, HC, ECCJ Tifple and Bit
`Allocation
`
`For the discussion in this sttbsection.'we will sssurne
`that the source is ntentoryless with a distribution corre-
`lpfll'ldl.n]l0l'.llBOGDWill't
`asndtltatthechso-
`no! is a list‘ with 1 BER given by P,. Let us stsppcte. T0!‘
`the time being, tit.s.tthe BCC ietoiseseleoted ft'otnepIe~
`scribed fsorily of ECC'e. We will spectly this fsrniltr in
`the next subsection and provide Jtsstllicstlon for this
`cl-tolcu.
`'
`For the given source and channel, consider a (UTQ.
`HC) psir (as selected in Section IV) with an aven|I= W
`tttteofr. renewed by so act: tvitlt r,snd Ietd(r,. r.:-o.
`P.) denote the MSE incurred in encoding and tret1stttis-
`sion of the source. Since the analytical cttrnputstiort of3
`is it'ttp0eIt'ble.- we have resorted to stmntsdon" to deter-
`tttltttt its value for selected clsotlcu of r,, r,. at. Ind P,.
`ttmtoeamtttecmgueaoodtng ma-rt gitranbyr - r./re
`Nonr considers aired encoding rate r. Anton: the strait-
`sble pairs of {r,. r,). there may be severe! that result in
`tlteencodl
`rster-.Letusdenoteby(r,‘. .r,'Jthepeirt.bst
`rttlnirnizes
`(r,, r,; a, P3: denote this minimum distor-
`tion by d.(r: tr. P,}. in miles ttoltll.
`5.0‘. or. P.) -
`min
`50.. r.; or. P.)-
`tIt.nl:1sht--r
`The fitnctton d.(r. at. P,) determines the distortion-rare
`pcrforrnance of the ¢.|'l£0CllI'l[ scheme used for a source
`with pesdmeter is and e BSC with BER P" after the ep-
`pttsptiate selection of the (UFO. HC. ECC) triple is ttutde.
`Notice that. for a hired encoding rsre r. identifying the
`"As before. Ill olneln the MSE we have lt|'I:I'I|ed our tlrnulstion mull:
`but ill nuts.
`
`(73
`
`it]
`‘
`-
`Fig. 9. Reconstructed "LE.NA” at citaeesl IE1 at’ In".
`(II System AII
`“H5 h/It. 10.19 net: to) Strum B runs his. 11.33 til}: (ct two to.
`tarp. 21.29 eat.
`a
`
`rtel-optimized quentinttion is developed in which source
`coding accuracy is traded for reduced sensitivity to ct-ml.
`nel noise.
`
`In this paper. we will consider an approach similar to
`'
`thttr of [lo] nnd [lT].. in our subhsnd codingeysterns. sn
`
`Page 268 of 437
`
`Page 268 of 437
`
`

`
`IE2! J-I-}UlNAl. ON SELECTIII AIIA3 IN CO|r|MIiNiCA‘f|iONI. VOL. I0. MCI. 5. JUNE I99!
`TAILB VI
`PSNP. Prnroumzcc ltssul.-r; rm dB] lul “£_.E.NA"
`
`
`Sysle
`l:clO"I at lD"l K to"rxro-*1 x in-*1 :rlll"1x tll“‘i:: to-'rxto"1x In": ><t0"Ix ID"
` IBIJI
`
`Mrl'E-PSNR
`Ell
`I-(.1-I
`2J.2£
`30.64
`1.-we
`IL]?
`15.?!
`31.39
`7.43
`|2.lJ
`23.91
`34.59
`9 jun‘ KAI-PSNI
`I039
`I633
`11.99
`31.00
`8.27
`l!.l6
`!4.H
`JSJ6
`3.61
`l6.'l'1
`36.57
`13.53
`’
`MIN-PSN'|l
`9. I1
`|I.I2
`I6.“
`20.5!
`_6.9'.l
`lfl.l9
`III?
`31.3?
`6.65
`9.7‘!
`I7-I I
`10.29
`51'!)-PSNI
`0.40
`Lm
`3.0!
`3.02
`0.11
`I. I6
`3.4!
`4.3]
`0.34
`J.“ .
`‘.45
`I36
`
`AVE-PSNR
`I431
`ILI2
`Zl.-IO
`JL54
`£3.96
`' 10.33
`l9.ll
`54.71‘
`_
`fl.fl3
`HA5
`51.0]
`31.49
`Sylllnri MAX-PSNR
`. I140
`14.07
`51.93
`JLI9
`1.4.94
`14.56
`35.94
`35.31 _
`15.52
`13.51 . _35.'ll
`JI.53
`[4 X 4] MIN-PSNII
`_
`I3.-II
`IIJ2
`23.55
`24.53
`I312
`I333
`23.51
`I-IJI
`I103
`IIJ9
`23.2}
`21'."
`STD-UNI
`0.54
`L50
`3.49
`L57
`CH5
`1.61
`1.91
`' l.IIl
`D.!l
`1.43
`J.l1!.
`LII
`
`AVE-RH!
`11.9’!
`1161
`2l.54
`“.54
`210!
`H12
`29.???
`29.95
`21.92
`19.“ -
`33.33
`33.94
`MAX-PSNR
`24.09
`2l.|'l.I
`2l.6.1
`IE6!
`14.3!
`3.0?
`19.94
`2194
`13.?!
`SLDI.
`33.94
`3-4.0l
`“Lo
`MIN-HR!
`3l.l-6
`1‘l.ID
`IIJO
`tl.$d
`1o.l.I
`17.3!
`39.51
`29.?!
`10.16
`10.14
`52.“
`33.I1
`
`0.51 0.22 0.06 |l.D4 0.50 IL} 0.03 0.04 0.71 0.6! 0.3!STD-PSNI 0J7
`
`
`
`
`
`
`
`
`
`
`
`
`ii. Simulation Results over Noisy Channels
`We Issuzrtc that the channel
`is a rncrnoryless binary
`Sjlmmfltfir.‘ channel (ESE) with a bi! en'or rate (BER) of
`P,. For our simulations in this section. we have consid-
`ered P, - 10'’. I0". 10".. and 10". To make certain
`tlaatour results uenrcaningntl. foreacir encoding sclieme.
`bit rate. sud channel BER. we have repeated our simula-
`tions 50 times son
`the average rsrut (AVE-
`PSNR). maximum PSNR (MAX-PSNR). tnlnimum PSNR
`[MIN-PSNR]. _ and standard deviation of the FSNR
`(STD-PSNR). Simulations are carried out for"l.ctrs" en-
`coded by Systems A and B and the W—O scheme" at de-
`sign bit rates of 0.25. 0.5. and l b/p. The simulation
`results are surnrrurlaed in Table Vi’. A few important ob-
`servations about rims results see in order.
`1) 535!!!“ A ll Ill-Irllncly sensitive to channel errors.
`Also. the STD-PSNR of System A is fslriy largo (espe-
`eialiy for low BER'a) implying thus, siren at low-channel
`_ BER‘: these is a possibility of severe porforrnarscc deg-
`redation (e.:.. -14 as cliffetceoe between AVE-PSNR
`and MIN-PSNII forsystem A II I up with P, - to").
`2) system B is also very sensitive to channel erross.
`However. it performs considerably better than System A.
`in all cases considered. die MIN-PSNR of System B was
`significantly larger (4-E II!) than that of System A:
`the
`AVE-PSNR of System B.wa.I also larger than that or Sys-
`tem A. especially for lesser values of the channel BER.
`Finally.-lire STD-FSNR of System I! is smaller than that
`of System A.
`3) The W-0 scheme elrhlbits the highest degree or ro-
`bustness in the presence of clI|.nI'tcI'noi.Ie. In most cases.
`the effect of channel noise is negligible for P, < 10".
`Also. contrary to our observation for Systems A and B.
`the STD-PSNR in this case is -my small. In almost utl
`cuts. the W-0 Intern performs better thsn System B
`
`"in all or our llllnllallou for noisy cilaallels. the oven‘! puclet league
`is I026 bits. This is not an optimized length rm. we feel. shoultl provide
`on appropriate rredeoll between the channel arm cllerll and the increase
`or’ side informaliorl.
`
`witli the exception of l fewgssas where rite channel noise
`is my small (9, - to").
`lni-'ig. 9,snonrnpleol'reconstruoled Images frornslre
`three systems is presented foran encoflrrg rate or0.5 b/p
`and P, - I0"; these images correspond to those cases in
`our simulation which result in minimum PSNR. Clearly,
`the subjective perforrosnoe of rise three Iysl.e.n'I.I closely
`follows the lllenri suggested by the PSNR results of Table
`Vi.
`The results of Table Vi (aim stlpportod by Fig. 9) sug-
`gest that systems A and 3, despite their superior perfor-
`mance for noiseless channels, exhibit an unacceptable
`level of sensitivity to channel errors and hence should not
`be used over noisy channels (at least over the range of
`channel BER’: eortsidetul here). In the next section. we
`will describe a combined souroelclrannel coding method-
`ology to reduce this more sensitivity to channel noise.
`VI. Common Souncelctlsmnsr. Coomo
`Systems A and 3 exhibit a high degree ofsensitivity to
`channel noise because they Ilsve been designed to mini-
`mize the source coding distortion sssurning a noiseless
`channel. It It a well-known fact that. ill general. the more
`clllcient the source coding scheme it. the more sensitive
`it will be to channel noise unless some corrective mea-
`sures are taken. Specifically. it is shown in [15] for zero-
`merrrory qtrlntloers and in [I6] and [17] F0!’ plldiclive
`coding and transient: oodles of Irnsges that. in the pres-
`ence of channel noise. increasing the accuracy ofl In-lime
`encoder could result in an overall performance degrada-
`tion.
`.
`one possible method ofmitigssing the channel error ef-
`fects is use of error control coding. in this manner. of all
`bits used for encoding the image. some will be used in
`source coding while the test will be kept to provide pro-
`tection against channel noise.
`in H6! and [17]. an ap-
`proach in which specific source encoders and channel en-
`coders are combined is considered: in this approach. the
`. roles oi the source code and channel code are adjusted so
`as to minimize the MSE. in [15]. anapprosch for chan-
`
`Page 269 of 437
`
`Page 269 of 437
`
`

`
`
`
`IEEB JOURNAL ON SELECTED Alla! IN’ C|3HIt|UH|CA‘l‘I6Pl$. VDL Ifl.
`
`1. JUN! I991
`
`‘Ill
`
`on
`
`4-
`
`
`
`AvorlgoEll.Rik[bllsfnnnplg]
`
`an G
`
`.90!
`
`DIN
`
`-
`
`.DI.
`
`.03
`
`.1
`
`.3
`
`'
`
`1
`
`Fig. la.
`
`use r U‘-L0‘)
`l.ass-distortion performance oi the selected set of IUTQ. HG.
`ECC.‘tIrt1I|es:a I 0.6.
`‘
`
`peir (r,'. r,'J is equivalent to detennining theaptimsl hat-
`a once between the source coding scctlncy and the channel
`error protection.
`Having detemtined the J(r,. 1-,; or. P,) functions by
`simulation. We here computed the functions d,tr: ct. P,]
`for values of a II in Section tv. P, - iii", to". and
`I0" and a finite number of values of r." ‘An example of
`the function a‘,[r: or. P,) is provided in Fig. 10 for or I
`0.6 and three dlllerent values of P,. to this figure. ditTer-
`ent symbols are used to determine the I'll: of the optimum
`channel code used. Also, for cornperison purposes. the
`distortion-rate perfornrsttoe of rise (UTQ. I-{C} pairs of
`Section IV obtsined tori noiseless channel is also in-
`cluded In this figure (dotted curve).
`'l'he deviation be-
`tween these performsoce curves and the one for the noise-
`less chsnnel
`is merely "the result of the chttnnei noise.
`Obviously, the devlstien is wider for more noisy chsn-.
`ncis.
`Once the channel-optimised distortion-rote perfor-
`mances are deterrnlneii. the bit allocation procedure of
`Section IV cut be used in a sirniisr runner to obtain the
`optimum bit sliocstion men; the sobhends.
`Before we present the slmultstion results for this com-
`bined sottrceichennei coding scheme. in what follows we
`will ducribe the due of ECC's we have used in our sys-
`terns.
`
`3. Error Correction Coding School:
`The EEC used in our system is s specific form of con-
`voltttionsl codes known as the rots"-crurtnoribie punctured
`canwiuriortai (RCPC) code. TIte_RCPC code was intro-
`duced by Hsgenauerl I B] as on extension of the puncntred
`oonvolutlonsl codewhich was O‘l'i[illl1I)‘
`introduced by
`Cain er i. [I9] nniniy for theptu-pose or obtaining sim-
`pler Vitcrbi doooding for me K/i'r‘(K sl 1) codes. The
`main advantage of the IICPC codes is that its rate (end.
`hence.
`the error correction npobiiitjr) can be easily
`changed by relying the number of punctured bits in the
`P|Ifl€tllI'lll[
`lltllfili-lhflllfolit With the some ltnrdwsre. a
`variety of channel oodinj rem can be obllilied. This is a
`desirable chsrsctotiatio in our system us we wish to my
`the ‘rite of the ECC for each subbcnd so es to obtain the
`best balance between the source coding rate and the citnn~
`nei coding rate. We slsottid mention the: this idea was flrst
`used in subbsnd coding of speech [20] for adopting the
`degree of en-or protection to the error sensitivity oi‘ dif-
`ferent coder bit streams.
`The RCPC code is defined by a generator rap matrix
`of a convolutionsl code with the constraint length L,:
`«Lu
`T
`:‘~rI
`‘'11-: must coerpuurien or the cur; e. at fonclhn ll .I:;t.n,« eirremt
`it-urn till above. Because there is only I llllle number of r.'s Ind r,‘s util-
`sble. we hut: uutlsllly considered the BI olsil possible points trim. r.: e.,
`-“.1. r_.r'r,] in the distortion-rsis olsne Ind selected time rim ii: an Ihl
`lower boundary nrrtiis utofpolm.
`.
`
`I34!)
`
`r- 1.2.
`
`1
`at!) =- N.
`1
`
`which generates the mother code of use I /N,'. arid also
`by puncturing riser:-it-es with the purtcruritsg period .P..
`an fl‘ -0
`(ans).
`
`.tN. — IJP.
`(lib)
`which determine the patterns of punctured bits. 111: nom-
`imtl sure otthe RCPC codes is given by:
`(9)
`s.-P./cr.+op r- L2.
`.uv.-’nP.
`which covers the rsnge between UN, and P,/(P, + i}.
`In all of our studies, we have used the RCPC code shown
`in tablet in [In] with N, - 4, L, - 5, sndP. - 8." The
`generator tap trtetrix 3 end the puncturing matrices IIU)
`rarr- 1.2,
`.8ssesiIownlnFlp. llandl2.re-
`spectively. We have-restricted our mention to the BSC
`with itsrd-decision decoding; better peribrmsnce could be
`obtained on sdditive Cisusalsn noise channels with Infi-
`decision decoding.
`it should be noted that R. in (9) is not strictly equal to
`r, used in (1) as the rate of the convoluriostai code. This
`is becsuse L. - i dumn-tyi bits should be Iddcd to the end
`or the sotlrce encoder output to return the sine ofthc trel-
`Iis to the ell-seto state. Consequently. r, is given by:
`
`I
`re - “pk: "' use ‘
`it should also be noted that when the combined source!
`channel coding scheme is used. the number of Htttfnsan
`codewords per packet will be dllfetent from that in (6). In
`this case. the number of codewords in the psckct associ-
`
`""11: plrfnrtnsstoe Iirflisas ncrc cede wilt be improved with larger me
`still pnetiealieonstrairu lsrI|tiIa.u:r. 8 s I... 5 I0.
`_
`
`Page 270 of 437
`
`Page 270 of 437
`
`

`
`‘MNAII MI: Fnkvnsnin: susuuo mnol enema
`
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`continua
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`tiiitité
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`
`llllllll.
`ttititii
`'m' ouoooooo
`ootinoo
`
`tied with the iih itubbitnd is given by:
`
`(11)
`fle.t"' {Pei-lp/(l'a.t ' "til
`where r,__. and r,_,- are the source end clrlrtstel curling rntes
`selected from encoding the ith sitbhsnd and i'l.- is the stuns
`ss in (6).
`
`6'. Simulation illentirs
`In this section. we will psesent sirnuistlon results for
`|l'|uepel‘f0I'i'tLIltt:cnl'Sy'I1es'i'thlai'IIl Brno-diliedby theconv
`itined sottteeichsnnel coding approach. Eton-I now on the
`channel-optimized versions of System A and System B
`(with blocltsize 4 x 4) will he called System C Istd Sys-
`tent D. respectively. We have studied the perfnrrmnee of
`Systems C end D at design bit rates of 0.25. 0.5. and
`I b/p for chsnnel BER‘: of I0". 10''. end 10". In all
`cases. the sun-ie pecitetiution schertte W'l1h l, -I 1004 was
`used. All subsequent sirttuistion results at based on the
`5.12 x 512 "LENA" image.
`.
`To provide some insight into how the encoding rate is
`divided between the source coding. and elurtnei coding
`operations. in Titbie VII we hove included the average bit
`rate used for chsnnei coding fordifferent overs]! encoding
`rllel. Notice that the percentage of bit rate dedicated to
`' error control coding is larger for noisier channels. Is one
`should expect. Also. in this table we have included the
`
`us
`
`'
`
`
`PSNR results corresponding to the case that the system is
`designed for I. noisy channel but applied to s ttolei‘-[€55
`channel. Tlusso remit: provide sit upper bound on the—sys~
`tem PSNR over noisy clslniseis. The dilferenee between
`these upper bounds end the PSNR's of Table IV use due
`to Ilse lower rate used I01’ OWN! Hiding in Table VII.
`The perfotrnance of Systems C and D in ternts oi AVE-
`PSNR. MIN-PSNR. MAX-PSNR. Ind STD-PSNR ms
`summarized in Tsble VIII for dilferent chlstrte! BER’: and
`ericodins rates. 1'[1e_fo[|owiItg itrtpottsnt olnervstions can
`he made.
`.
`1) Both system: C and D provide drernstic immova-
`ments our systems A end B. The improvement of System
`C over System A is in the surge 7-27 :13 in AVE-PSNR.
`The improvernent of System D over System B varies be-
`tween 3 Ind 21 dB in AVE-PSNR. Typicnlly. ilsesc'lIh-
`pi-oven-tents Ire terse: at higher encoding me: and for
`noisier chsnnels.
`2) lnelicescs forbothsysietttscsstd D.lheliIIAX-
`PSNR coincides with the upper bottttd on PSNR listed in
`Table VII. Tliis menu that bit errors caused by the noisy
`channel ere sometimes perfectly eonected by the RCPC I
`codes.
`3) In almost all uses. System D perfarrns better than
`System C. Ftlnltemsorll. Syrians D eitltibiis I highs de-
`gree of robustness agpinss channel noise. Typically.
`diiferenee between MAX-PSNII and MIN-FSNR ll
`sttuiierirt System D then In System C: the nine holds for
`STD-l‘SNR., Since in built symitts the some type ol'el'I.sii-
`nel code is used. this superiority olsystern D must be due
`to the inherent roltustness of!-D DCT against trsn.srni:-
`sion noise (similar to our observations in section V].
`4) Systems-C and D perform better llsstt
`the “I-0
`scheme in the ptuence ofclteitnel noise (see Table VI)-
`Wltet is perlssps most interesting is shut the perforrt-mice
`ofSys.tesnsC1ndDoversnoiIychettnelise1tenbetter
`ilmsthuoftliew-Oschetneitsthesbsenoe ofclunttel
`noise (with only one e:¢cep‘iltiII:'Syslem C. 0.25 it/p.and
`P, - 10"). Title lts.s.lteest ourjnltificetlon for not con-
`siderlng echsnttel-optimised version ofiha W-0 seltetne.
`InPlg|.l3e|sdI4,wepreseuIteconsuuc1ediIItIs¢6
`corresponding-to MI'l"l-PSNR end MAX-.PSNIl.obu.ined
`l'1'utnSysiemsCsndDfortitedesignn.teofo.5 is/pa:
`nwo stream velues ofcltsmel nan. llunely P. - to"
`and in". It is importemtomenilon tlul theavenge qusI~
`ity of the teconltnteied lrnsges in our simulations is usu-
`ally closer to the image enrrelpottditsg to MAX-PSNR
`rltliet l-lllil MIN-PSNR. This is especially true in Sys-
`tem D.
`'
`'
`
`D.
`
`(‘Ismael Mismatch
`In designing Systems C sud D. it is assumed met the
`channel BER. is known. In many precticei sltustinru, Ihl:
`esset value of the BS}! is not known or the BER varies
`with time. in such sitststiorts. it is important to know the
`amount of pet-fotrnsnoe loss eluted by channel misnunch.
`Lg|_ us denote by PSNR (Pu, PM) the AVE-PSNR caused
`
`Page 271 of 437
`
`Page 271 of 437
`
`

`
` '\
`
`'
`lull JOURNAL an IELILTIIJ nus IN cuflflufltctrrtous. mL.
`
`_
`to. no.1. JUN! I991
`
`.
`TABLE ytt
`Dtmtwmu mam Bewuu souncs comm an Gamma; {.‘enIue roe “L.ENA"
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`TABLE VITI
`BN1 PIIPBIHAHCI ltuuus (IN tun ml "L.ENA“ in ms Huucl or claims. Non:
`I.l}BPP
`
`
`Ix tn"
`-tan
`1:: ll!"
`t x ID"
`ta: to"
`ix to‘-'
`I x to"
`It II)“
`| x to-'
`
`sun
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`rue _
`29.50
`not
`30.74
`32.91
`use
`3.1.1.1
`34.3:
`5
`C mx-mm
`:9.ee
`30.9:
`':u.o.1
`32.49
`33.ee
`34.35
`33.19
`31:4
`31.5.5
`"“°"‘
`MIN-PSHI
`use
`30.40
`:rt.ts
`1t.sn
`15.59
`33.91
`14.31
`22.5:
`31.1:
`mm:
`3.:s
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`us
`1.9:
`0.0:
`2.32
`3.15
`a. I I
`
`AVE-Psmt
`19.96
`30.94
`31.49
`32.3:
`33.90
`34.40
`33.24
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`:7 S1
`3 mm D MAX-PIN!
`30.10
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`32.13
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`35.50
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`37 so
`3'
`um-rear:
`us:
`use
`32.52
`zs.39
`_:e.m
`n.-ts
`u.to
`sun
`31 t:
`st-ta-nmt
`0.11
`0.2:
`use
`a.sr.-
`0.1:
`M‘:
`n.sI
`Me
`0 In
`
` ‘\_'..--u.
`
`:3
`4
`.4.
`
`l
`
`1i
`
`M
`{E}
`ham Symtu D :1 ttesiyt on me al‘0.5
`. I-I. Rnnunnsntcned
`B D. I'll MAX-PSNR. -P. - IO" {It} MAX-PSNR. P, - I0". (:1 MIN-
`P8NI.P, - Io".¢s)mN-mar, - 19-1.
`
`. ll. lutnutntehl "I.8l'h|" fiwlylulu Cudniga hit aura;
`F!
`II- in MAI-PSNR. F. - In". ten MAJ:-rttmt. r, - in“. [ct MIN-
`I:
`Pstdn. .-, - to". (II MIN-Ie'N1t..I, . III".
`
`by at system designed for n chmnel with BER Pm. and
`Ipplied to a c-tunnel with BER. P”. The FSNR (P,_.. P.,.)
`results for different values of PM and PM for both sys-
`tems C and D are presented in Tsble IX. These results are
`for an encoding rate of 0.5 b/p. We have observed that
`the trend of performance lou is the mate for other bit
`rates.
`
`1) System D is much more robust with respect to chum
`net mismatch than System C.
`
`2} Practically in all ones. the AVE-PSNR of the mis-
`meldled case with P” -: Pm. coincides with lite MAX-
`PSNR of the marched cue {‘t.e.. when the system is de-
`signed and applied to 1 channel with BER 3.0- This im-
`plies that. in such cases. all channel eltnrs are corrected
`_ by the RCPC codes used in the system.
`3) To design the system. oyereslittlmlllz Ihe Channel
`BER is better than uttderestin-utin;
`it. For example -in
`
`Page 272 of 437
`
`Page 272 of 437
`
`

`
`4
`terms: AND FAIVAIIDIH: sussntro tit4os_:ooIt_R.'l_
`
`TABLE IX
`Crmtnlt. Mts‘mm:u Penpottmmca fiuuL11 4'7 0.! Info.
`
`
`
`
`
`I W.
`*
`
`‘
`
`I190
`18.75
`15.19
`31.38
`1.46
`9.32
`IL?)
`30.14
`Ava:-smt
`t4.94
`20.51
`11.31
`3131
`L21
`nu:
`sans
`32.:-1
`am-:.rsNn
`13.12
`I636
`12.17
`25.19
`6.91
`1.66
`tut
`21.60
`MIN-PSNR
`0.4:
`l.l'l'
`L3!
`0.9:
`0.3:
`on
`1.29
`1.-to
`lTDvPSNl.
`10.3:
`31.54
`use
`3:.-ts
`l3.I‘l'
`29.15
`mu
`32.49
`ave-rsmt
`I
`..
`tstam-suit
`32.49
`. use
`14.10
`tsu
`32.13
`sun
`34.49
`use
`" '°
`t.tm.t~amt
`32.49
`t.s.sv
`10.91
`um
`32.10
`:v.oo
`13.47
`11