CC BY
15Journal of Siberian Federal University. Engineering & Technologies, 2017, 10(3), 377-387
УДК 621.396
Application of Error - Correcting Coding in Hydroacoustic Communication Channels
Boris I. Filippov* and
Novosibirsk State Technical University 20 Karl Marx, Novosibirsk, 630073, Russia
Received 04.07.2016, received in revised form 09.10.2016, accepted 19.01.2017
The paper considers the possibility of using error-correcting coding in hydroacoustic communication channels (HACC).Comparison of test results shows that errors substantially packaged, resulting in increase of error probabilities with the large multiplicity and the likelihood of receiving a code word without error. Results of comparative statistical studies of these codes on a channel model with impulse hindranceare listed. As a result of theoretical and practical studies of various structures of error protection device (EPD) to improve the noise immunity of equipment sonar communication systems (HACC) was selected the algorithm of error correction, which is based on convolutional code R = 1/2 with block, the threshold, the iterative decoding. To ensure the independence of errors at the decoder input (decorrelation of error stream), the matrix interleaver are encouraged to use in the EPD.
Keywords: sonar communication channel, the transmission of digital information, error control coding, statistical characteristics of error stream.
Citation: Filippov B.I., Chernetskiy G.A. Application of error - correcting coding in hydroacoustic communication channels, J. Sib. Fed. Univ. Eng. technol., 2017, 10(3), 377-387 DOI: 10.17516/1999-494X-2017-10-3-377-387.
Gennady A. Chernetskiy
Применение помехоустойчивого кодирования в гидроакустических каналах связи
Б.И. Филиппов, Г.А. Чернецкий
Новосибирский государственный технический университет Россия, 630073, Новосибирск, пр. Карла Маркса, 20
В работе рассматриваются возможности использования помехоустойчивого кодирования в гидроакустических каналах связи (ГАКС). Для обоснования выбора параметров разрабатываемого устройства защиты от ошибок были исследованы статистические характеристики потока ошибок в ГАКС. Сравнение результатов тестирования показывает, что ошибки существенно пакетируются, следствием чего является увеличение вероятностей
© Siberian Federal University. All rights reserved Corresponding author E-mail address: [email protected]
*
ошибок большой кратности и вероятности приёма кодового слова без ошибок. Для выяснения характеристик пакетирования ошибок были рассчитаны распределения длин пакетов и длин интервалов между пакетами ошибок. Полученные результаты статистической обработки файлов с массивами ошибок в ГАСС дают основание считать, что в рассматриваемом случае имеет место дискретный канал связи с пакетированием ошибок, который может быть описан математической моделью дискретного канала связи (ДКС) с памятью. Показано, что в рабочей области значений вероятности ошибки на входе декодерарвх (менее 710-2) код (1218,609) уступает коду (404,202), который позволяет вместе с перемежением символов в канале обеспечить сравнительно лучшие условия исправления независимых ошибок. Кроме того, выбранный сверточный код (404,202) с перемежителем практически не уступает в отношении импульсных помех каскадным кодам на основе коротких свёрточных кодов и циклических кодов Рида-Соломона, обычно используемых в аппаратуре цифровой связи при более низкой вероятности ошибок в канале, чем в аппаратуре ГАСС. Приведены результаты сравнительных статистических исследований этих кодов на модели канала с импульсными помехами. В результате теоретических и практических исследований различных структур устройства защиты от ошибок (УЗО) для повышения помехоустойчивости аппаратуры гидроакустических систем связи (ГАСС) был выбран алгоритм исправления ошибок на основе свёрточного кода R=1/2 с блочным, пороговым, итерационным декодированием. Для обеспечения независимости ошибок на входе декодера (декорреляции потока ошибок) в УЗО предлагается использовать матричный перемежитель. Благодаря ему в канале связи символы кода считываются по столбцам матрицы изображения (256х192 четверичных символа), а запись в матрицу и считывание на входе декодера производится построчно.
Ключевые слова: гидроакустический канал связи, передача цифровой информации, помехоустойчивое кодирование, статистические характеристики потока ошибок.
1. Introduction
The most effective resource of ensuring high noise immunity complex communication system is the introduction of the redundancy, which is necessary to detect and correct errors, that occur during operation of the system and it's elements. The theoretical basis of effective usage of input redundancy is the theory of error-correcting coding.
As shown by experimental studies, the statistical characteristics of hydroacoustic communication channels (HACC) have their counterparts in the short-wave, FM and other radio channels with variable parameters [1]. Therefore, designed principles and protection methods for these channels from errors may be used also in communication systems employing HACC, of course, we should take into account the specific properties of spreading of the acoustic signal in the aqueous medium.
2. Causes of errors in digital hydroacoustic communication channel
Literature states, that statistical characteristics of sonar signals and noise have complex, often transient nature [2-5]. These parameters depend on ocean conditions: water temperature, salinity, depth, presence of currents, the weather at the surface, bottom structure, species composition and abundance of biological objects, vessel traffic, etc°
An orientation and extension of the alleged link between the source and receiver of acoustic signals are crucial. Depending on the space orientation of the connection lines distinguish three main classes of hydroacoustic communication channels:
- Horizontal, when the communication line, which is connecting the source and the receiver, is in an angular sector less than 100 relative to the horizontal;
- Inclined, when the communication line, which is connecting the source and the receiver, is in the 100-350 range of angles relative to the horizontal;
- Vertical, when the communication line, which isconnecting the source and the receiver, is in the angular sector 150-350 from the vertical.
The length of vertical channels does not exceed 10-12 km. They are characterized by a weak manifestation of refraction, i.e. propagation path of rays between the source and receiver of signals close to a straight line. Ray trajectories remain rectilinear at the largest mean value differences of sound velocity depth, if output angles of rays of the signal source does not exceed 800 degrees from vertical. Weak manifestation of multipath and fading are noted [2, 6]; it indicates, that propagate from source to receiver signals have not significant (10-15%) changes of amplitude and phase of the signal with ray paths, when they are located within a 250 degree angle from the vertical.
In accordance with the above classification of the analyzed channel closer to the class of hydroacoustic communication channels inclined orientation [2].
In the process of propagation in aqueous medium sonar signal in channels with inclined orientation is changing its structure, which can be separated into amplitude and phase. Speaking of amplitude changing, it should be understood, firstly, changes signal level occur with increasing distance from the source, secondly, signal level fluctuations occur due to multipath effects and random changes of water environment gain.
Level change with increasing distance from the signal source associated with the expansion of the front and different types losses. The nature of these losses is well understood and described in the literature [3-6]. Without dwelling on their examination, we note that the main causes of acoustic energy losses are relaxation processes, the shear friction layer of water and scattering. Accounting for these losses made during the calculation of the energy corresponding to the link [7].
Fluctuations of level and phase of hydroacoustic signals associated with the statistical heterogeneity of the aquatic environment and they are a consequence of random changes of gain in the environment and the influence of multipath. Often, these fluctuations are called signal fading and take them to interference.
Interference in the sonar lines due to their nature are divided into three main classes: additive, multiplicative (fading) and the Doppler frequency shift. In turn, the additive noise are classified according to the statistical structure and the nature of origin. According to the statistical structure of the additive noise is divided into three groups: the fluctuation, pulsed (time concentrated) and harmonic (centered over the spectrum) [1].
The origin of the additive noise is divided into natural and technical. Among the additive noise of natural origin distinguish:
- dynamic noise which occurrence due to the dynamic processes happening in the ocean - the thermal motion of molecules, surface waves, the noise of the surf, by the collapse of air bubbles formed in the upper layer at the surface of water, when they falling in the wave crests, the blows rain drops on the surface;
- noises ice origin, caused by wind, flowing around roughness of ice surface, cracking of the ice cover, hummocking ice fields, flowing around passages of irregularities at lower boundary;
- biological noise associated with its origin life of three major groups of animals: invertebrates, fish and mammals;
- seismic noise caused by tectonic processes in the Earth.
Interference technical origin is separated into its own; media noise; noises foreign vessels; offshore drilling rigs; pipelines; extraneous signals sonar systems (hydro lighthouses, echo sounders, sonars, sonar communication systems, etc.).
The noise in the ocean is a superposition of many individual fields of independent sources, and the propagation of sound from these sources to the measurement points are connected with a plurality of independent and random distortions. This makes it possible to characterize the noise of the ocean is often a normal (HACC) distribution.
Multiplicative interference (signal fading) occur in a random changing the amplitude A(t) and phase ^(t) of the sonar signal. From the viewpoint of reception fading signals, they are equivalent to an increase in noise power. They lead to a decrease in signal/noise ratio at the input of receiver. However, fading feature is that their impact, in contrast to the additive noise, can't be compensated for by increaiingthe power of the transmitted signih . Therefore , toassess therealnoise immunity of signal receibeon aby evaluation of tlie crpociey orgydro-acoustic tommuntcrrten egrrem It's decesseey to know ten laws of !he PisiriPution oeinsrantayeoge vahles of tie leonl ofd pdase cf the slтnai ot blue input oP reeciven
A laryc pumtaeref stutlies PS, u-T, 8, 1], ihwh1ehedllerimcytyfandtyeereDicoistgdh of fluetuations of the amhtttpgeanppneste>(r) a0 the of^alac) acourticslgneSs are performed, are known.
In most caset, Ifwen hoted,lha)vatueh of signal': umoiitudes are i^o^ip^al^^ distributer ar t^tr^^i1epteii by theiaws ofRr)yletgla Ronle1g1P■Riee )0. Moreouo r, Tdo parameteis oclli^t;r))tu^iovr gopenb atrppgly on the ittucture and eopdltiegs a0 t"orrtLntio:a uc bnk: o rlentuSdm wl respcci to )lte llУttom oud the surfтcel teg dirPaueo meOwm tic tinnae sourcs rgd tt)^ reoncuremcnt punno, pftlems of ante tth]is and othoes.
Dkturbauces memfe stalkm of tho g^onnl^r effect. are o ipoetfickmd of
interference . Ig the sonfreg stemD oppler effectauused by re lutlvemavement betweee the emitttny and reecinm.e albenda]; o^eratine. ll]Drisl_t^ vesse1 mo^])n, drifting) ahd censer the il]Lpaeronei: treyuenog of the received s1gl^:rl taem tie tranemitted Urequevoy, resnlDing in o r1^t.ft of tar entire rpectn)m el frepuenclee :,scc tPr vaiue )0at ^ttonde of tite spectral wklth tub l0h goratian ml lie eldnen SWlPum; o° the freтde^ch canbet^ien Into noeoudt lo ee^^^eis^g1l^i^creceivee UanPwldthby inepeatign
its vahietoU y,. Tho c^^r^^spoi^dihy cCongein ITt) lnstontudeoys frequepey end dunutkm of^he siunal due tn tpe e)aeot sue broctieD1 scrtemi at ^ii5it^ data transnrisskinnre c terpens ateg by elocv
system. Dp Dte earrect chnkr o] equdcment gurametrrS) mfluence a] Dhe Dappkr effects redheed tn decreasfnelte lmmun1Sh wf tie Decepiien 0., ihe lbtrehuetlen of sume cnuinoiaht noise cans edby t^he extension tPo re ocsiver li^nt^t^id^l^, nnglhe 00^,00 mzntlop system.
In [1] foilawilig asllcesment ofprobabiilty c1taroeteristifbynd porameternof s1gneSs and inlerfcrence are listeA
-A opet^in^ensionai devoity eunctioi) a0' [hii^ distribution of the noise level W(U), estimates for ithe exportation me and variance of the nolre up ;
- A on, idimcnnlonoi 1i^itc(.io^ oI1 usie ie-^^el uf tiie d1htrihbtiop Ueneity ol sha recelvedsinnai eonar W(U), roa]rlat1onff it s matУcmytiohleppcrtytian mE, dispersion ;
- A oneidimensionot density function of the distribution phase of the received acoustic signals WAp), evohtation oe tis mathematica1 edpcctotionmii) disperskcn d^;
- The normalized correlation function of the signal R(t) amplitude and the correlation interval To.
However, results characterize more properties of sonar channels with vertical orientation. But methods of measurement parameters of signals and interference, their statistical processing applicable to hydroacoustic communication channels inclined [2] and the horizontal direction.
3. The statistical characteristics of flow of errors in the equipment HACC
To justify the choice of parameters of the developed error protection device have been investigated statistical characteristics of errors in the stream of hydroacoustic communication channel. By comparing samples of sent and received image frames have been received arrays of errors in channel of sonar communication systems (HACC).To do this, pixels of received and transmitted images were converted to primary streams of binary symbols, and by combining these streams by modulo two, they formed an array of errors in the frame image. In the process of converting frames of images, lines in violation of synchronization are excluded from consideration.
Four files with error arrays was obtained: ereMass1.txt, errMass2.txt, errMass3.txt, errMass4. txt. Each contains about 3-105 binary symbols. These files were used to determine the statistical characteristics of the error stream in real hydroacoustic communication channel, as well as tests for statistical error protection device.
Following characteristics were determined by:
- The average probability of error pcp;
- Distribution of multiplicities of errors t in the code word with length n-Pn(t);
- Distribution of the lengths of the error packets P(tn);
- Distribution of lengths of the intervals between packages of errors P(tnt).
Results of statistical processing of error arrays are listed below.
In Tables 1-4 the distribution of multiplicities of errors for the various values of average probability in a communication channel, were shown, wherein the error arrays were divided into codewords of length n = 100 characters.
For comparison distribution of multiplicities of errors in communication channel with independent nature of errors was obtained on the assumption, that the probability of error is the average error probability errMass1.txt fifile(pcp=0,005). Results are shown in Table 5.
Comparison of results in Tables 1 and 5 shows that errors in file errMass1.txt (paverage=0,005) significantly packaged, resulting in an increase in the probabilities of errors with a large multiplicity
Table 1. Distribution of multiplicities of errors Pn(t) in errMassl file
Multiplicity 0 1 2 3 4
0 0,84691 0,02135 0,04468 0,04895 0,01018
5 0,00558 0,01051 0,00361 0,00099 0,00230
10 0,00131 0,00033 0,00164 0,00066 0,00033
15 0,00000 0,00033 0,00033 0,00000 0,00000
p«verlge=0,005; n=100 characters.
Table 2. Distribution of multiplicities of errors Pn(t) in errMass2 file
Multiplicity 0 1 2 3 4
0 0,91524 0,03909 0,02825 0,00723 0,00296
5 0,00230 0,00131 0,00033 0,00033 0,00000
10 0,00099 0,00033 0,00033 0,00066 0,00033
15 0,00033 0,00000 0,00000 0,00000 0,00000
paverage=0,0019; «=100 characters.
Table 3. Distribution of multiplicities of errors Pn(t) in errMass3 file
Multiplicity 0 1 2 3 4
0 0,77957 0,08574 0,05486 0,03351 0,00591
5 0,00591 0,00887 0,00361 0,00197 0,00526
10 0,00131 0,00164 0,00033 0,00230 0,00066
15 0,00033 0,00066 0,00000 0,00033 0,00000
paverage=0,0061; «=100 characters.
Table 4. Distribution of multiplicities of errors Pn(t) in errMass4 file
Multiplicity 0 1 2 3 4
0 0,19054 0,06110 0,06932 0,07454 0,05683
5 0,04796 0,05552 0,04468 0,04763 0,04369
10 0,03318 0,02825 0,02562 0,02070 0,01938
15 0,02168 0,01643 0,01610 0,01577 0,01183
20 0,01347 0,00788 0,01150 0,00657 0,00591
25 0,00460 0,00263 0,00361 0,00230 0,00131
30 0,00197 0,00197 0,00033 0,00066 0,00033
paverage=0,073; «=100 characters.
Table 5. Distribution of multiplicities of errors Pn(t) in channel with independent errors
Multiplicity 0 1 2 3 4
0 0,60354 0,30511 0,07672 0,01279 0,00161
5 0,00020 0,00003 0,00000 0,00000 0,00000
paverage=0,005; «=100 characters.
and the probability of receiving code's word without errors. A similar pattern has error streams in other files: errMass2.txt, errMass3.txt, errMass4.txt. By the nature of errors on analyzed images we can assume, that causes of errors packaging are:
Boris ] Oüippoa ani( Gennody A. 0aernets0iy. tarlillication of itrror — РоггссПп0 d)oding 1п Hycfroacoustic Communication...
nuaderslatement ue ^ha recenTd ánfl kvcl ducto hnmpmp, rhintboard fndmantfestation of multipath propagation affacts as a rasult of raflaction from tha tnhomoganatttas of tha aquatic
- inremercgcd witKr jruCfe ctirrocfer Cpossibly cr(om Cfst drouctier servtn0 oessel), hhich is etpecéoiiy cfaracteristia for crrMaacSt.Oo^ errMoca^no/mpsonouncaO if ricdlcinPerfaranca with an intcn0 öl0 agosit O.1 грсоМоО.
Uo daScsmiop ^l^^i^^ceeo^^t ícs cuparl^^g arrorspacOat langth distribution and langth of сп]орьр1г bdOwgen oreora poekoncсwdrecokiulalcd.
Пгсшг t slews t-e vvt гаю. kngih of lt>urst; arrors m onO rho overage tcngth of tloa Inihival batwaan bursts oO triors tift from tha basa At (distança batwaan naighboring symbols of binary arrors in tha packet) Рог aroMasc] MIp^^.=0,0051.
Antral oveoaga leggth op iiurot error and avaraga langth of intarval batwaan pacOats ara dafinad bu Rg. i asvmpps, tfat ano соггеорош1^ to tha aqutty basa At and tha avaraga langth of burst arror lid thés са.е15 Ше polnl correcoondCngto Д1П m = 750 binary symbols, wharain tha maan intacval beSsooe n pockodc tif] =é800).
Similarly errMauug.txt file lpaverage =0,006é), tha avaraga burst arror langth is raducad to 480 charactars, and tha avaraga distança batwaan tha pacOats of arrors to 945 charactars. In errMtuu4. txtfile lpaverage =0,073) only condansatton of arrors can bu idantifiad with a partod of about 350 binary digits.
Rasults of tha statistical fila procassing arror arrays HACC, giva raasonto assuma that in this casa thara is a discrata communication channal bundling arrors, which can bo dascrtbad by a mathamattcal modalDKSmamory[e0].
By sotting tha avaraga duration of a burst arror can bo datarmtnad Q, which charactartzas tha pacOatizing and arror mamory in discrata communication channal and has tha following valuas:
0= I = 0.00125 for errors in the array errMassX.txt file.
Q = 0,0021for errors in the array errMass3.txt file.
4. Selection of error-correcting code to implement the EPD
The developed EPD should be built in sonar communication system and provides increased reliability of digital image transmission is not less than 100 times (the probability of errors in the received message should be reduced from 10-2to 10-4). In the future, we will consider the codes to detect andcorrecterrorsdueto it'sownredundancy.
Preliminary tests of a number of cyclic codecs and convolutional codes in conditions where error statistics correspond to the real error streams recorded in the files: errMassX.txt, errMass2.txt, errMass3.txt (Fig. 1) showed that to correct errors in the existing channel HACC, taking into account the errors packaging needed noise-proof code, which speed R < 1/2.
As correcting code errors in the EPD, cyclic BCH code with parameters (n, k) = (204,96) may be used, correcting errors of multiplicity tu < 14, which is at Pinput = 6-10~3 (memory Q = 0,002 communication channel) provides the probability of decoding errors Pd ~ 540 4. Convolution code (404.202) with a threshold iterative decoder in the same conditions provides Pd ~ 240-4.
To combat errors in the stacking EPD must be entered symbol of interleaver, which is known, allows to bring the channel to the channel characteristics with characteristics independent errors.
When setting the communication channel symbol interleaver and a cyclic code (204.96), and convolutional code (404.202) provide the required qualityindioators (Pd < 10v), whilefpe
Pd ~ 5-10-6 cyclic code, and convolutional code P ~ 2-10-7.
Based on these results, for thepraatioql imptementatian oo the EPDaqpqratusHAqC s^olehted convolution!! code (404.202) with a threshold iterative decoder block type used in conjunction with theinterleaverliqk characters.
Following featuresshould be in mind,whenweuse t0iscode:
- Convolutional code decoder with iterative block type threshold unlike cyclic code allows the use of arbitrary length codeword n > n0 • max[deg g (x)]. This allows for encoding information message use code words corresponding roh^e longA of the scri^ 256xa = lp24or0he kngtt of a column 192*4 = 768 onbinaeysymbuls;
- The computational complexity of docedipaoatqecenuetutlun sode in1ese thanl0n ^ tiiton r^ cyclic code with a decodenbyfhe algorism Bytlikeme>p-Mta sifof bmatyuodes ;
- The quality of decoding the coenoiutioníd wide defodeowi0h i^^^o^i^tive Uho)sMd^ smnewMt better than that of the cyciin ccde, wh^w ex+)ninl effect inherent continuous convolutionalooder;
- The lack of convolutional codes a! continuous, is the need to transfer at the end ueeaoh frama "liner" in a random codeword to the decoder outputs the last information word. Otherwise, wr have to put up with the faci shat ^]^sworf. lsinthememoryopihe decoder an0ir buU ^ven co the recipient, or will be forcedto read withoulesrhryorreetion
The selected convolutional code (404.102) tl;^t^h din gfnoeasmg pdlyuom;lal b1u) u) .f^ + dl7 -u + n76 + o113 + n137 + o155 + o156 + o1li^-u^h) auq tiee codl ratf R = K is one of the best canonical self-
orthogonalco des, which have an orthogonrd 10 checks and enables iterative decoding threshold. This medium-length codememoryregisterslengthdgcoder 202 in the cell.
Cnmoerative teses oftteedeered convohitional code have beef carried coit s404.202) on the same convo1utionaicodcR = f /2i^:td<^l^e hate (lvt8.6d9) having;yeei[degg (it^e] = 609.Teot seselts are sho—n in Fig.m
hie evidcnti^ intte workaren/>ln(ttva1ues (less than 7-10-2) eoee (1218.609) eoneeSes to eoee (404.20—, wMch klowochdraeeers wiïh ehdhneПnterleaeing toprchidr a retetivefy i)etter eoneitions correctm indep ehnecederoto.Mdreodeo, the odir ctedcenvolutiooal code —04.2°2) withan interleaver a1mo—equolrehardi—gimpulse noioe -dncatenaOencodes o^^esL onshort cndvorutloda1 toSes and cyc1icReed-Sntomon cgeeo, whioli typichUy ereucod m the apparatus of a digital communication —ith a lo—er likehhood of errorc inthe ehanne(teaninanapp—ralus HACC.Tabk 6 aM Fm l sho— results of comparative 7tatistk;al studies of Sltese codes on a chaneelmoSelwith im^^u^^^eoée.
In the houree ol I^O^coo inve ^a^ie cn mputgol) was iecumeS ehd else euration of a single
pulse ny(seio appooximatelreqnnl toOlloiengrh mOOO biIlatydigits; cnd ^probab^y of error by the action of puloedarterfereIlceisO ,5e whide thv duratidy of imputee ncise epproximaiely corresponds to the euration of the periodic error packets in files: errMass3.txt, errMass4.txt.
10"1 10"!
10"1 10"2 10"3 10"4 10"5 10"6 10"7 10"8 Pd
Fig. 2. Dedeeeeece of tie probability of eecoeieo error drogagi1itr of Pd errorsptaput eecoeer input
Table 6. Tie eedeeeeece of tie probability of error eecoeieo Pd and drogagi1itr occurreece of impulse noise Pi
1: coneolutional cod) (404.202), the threshold dfcodfr, 5 iteration, the intfrlfaefr; 2 and 3: cascading codr: Internal cod) convolution R = 1/2, a Vitrrbi dfcodfr, external - cod) Rend - Straw (255,239); 3: internal - the samr codr Rend-Solomon codr with intfrlfaefr; p = 0,0007 probability of independent errors.
Pi 0,1 0,05 0,025 0,01 0,005 0,0025 0,001 0,0005
1: Pd 1,7•10"a 1,810-3 6,040-4 7,4 •10-5 1,240-5 1,910-7 9,9-10-9
2: Pd 5,8•10"a 1,1•10"a 5,040-3 1,640-3 1,110-3 4.040-4 1,240-4 7,0 •10-5
3: Pd 4,4•10"a 1,7•10"a 7,0 •10-3 5,2-10-3 2,840-6 1,240-7 2,H0-9
0.1 0.025 0.005 0.001
Fig. 3. Dependence of the decoding error probability and the probability of occurrence of impulse noise: (1 -convolutional code (404.202) with an interleaver, the decoder, 5 iteration threshold; 2 and 3 - concatenated code: internal convolution code is R = 1/2, a Viterbi decoder, appearance - a Reed-Solomon code (255,239) in inner Embodiment3 - thesame code Reed-Solomoninterleaver)
It can be seen that the convolution code (404.202) from the interleaver in the range of operating values H ACC systemfailure probability is noUnferior tothe с ascade code, andtaki ngintoaccountthe complexity and concatenated codedecoding sate convolutional code with iterative decoding threshold is more preferable.
Giveo sesuitscoktirmthevalidCty of tite clmicd у! oconvolutюnat coda (fOh.202) with the interleaver of symbols, because, as noted, the cause of almost periodic interference HACC system can be precisely transients.
Conciusions
Asa шиПсУ tWeorotieaiand dractical atudsesof harюtкstrucSnter od Ше EPD to Che
noiyeimmunity afekшpment it[ wab ceieetedeп•ar еогуесЛюп algorithm, wЫsh isbmsekon comha[utioncl coda Rd lS2Ыotk, thethrerhold, the iterative decoding. The block size is chosen to be the length of a column of the matrix picture 192-4 = 768 binary symbol. It is shown that in a channel with independent errors, this algorithm provides increased reliability more than two orders: the probability of the symbol error decreases with 3-10-2 discrete communication channel to 10-4 at the ou^j^^t. of the^cader.
koensure the independsnoeaf отосп at the decoder input (de-correlation error stream), in the E2D are rncouraged to use the matriu interleaver. Thanks to it in the communication channel code symbols are read by columns of the image array (256u192 quaternary symbol) and the entry into the matriu, and reading is performed at the decoder input line.
References
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