CCSDS Coding&Synchronization Working Group March Washington DC, USA SLS-C&S_08-CNES02

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1 CCSDS Coding&Synchonization Woking Goup Mach Washington DC, USA DVB-S2 like fame constuction and LDPC codes ate o/and size extension fo use of Vaiable Coding & Modulation suitable fo X and Ka bands High Rate TeleMety needs SLS-C&S_08-CNES02 Guy Lesthievent & Xavie Deplancq (CNES), Xavie Giaud (cabinet Novacom) 1. Intoduction The concept of Vaiable Coding & Modulation (VCM) is of paticula inteest fo LEO-Eath Exploation Satellites Sevices using High Data Rate TeleMety links. The vaiable elevation in eception due to the LEO satellite movement is going fom 5 up to 50 (even nea 90 fo some passes) fo most of the passes. And the need of a magin even at low elevations combined with the use of on boad high gain antennas (gimbaled o electonically pointed) fo effective EIRP leads to impotant magin on the est of the pass that should be used fo tansmission data ate incease (see ef /1/). So thee is a need to have at CCSDS a family of codes and modulations to cope with both a bette use of X band magin and fo an optimal use of Ka band possibilities and impaiments (atmospheic and ains popagation effects). Simultaneously, the is also a need to ethink about the constitution of the CCSDS tansmission fame in ode to allow to wok bothwith low magin, low Signal to Noise Ratio (SNR) and vaiable sets of channel codes and modulations. This wok which deals with those both topics has been mainly pefomed by cabinet NOVACOM (Pais) and CNES in the context of a CNES R&D.

2 2 2. Constuction of channel codes families Fom the CCSDS pesent Oange Books (see ef /2/, /3/ and /4/), two families ae aleady constituted fo VCM concept application, the one fom ESA poposal (ef /2/) with Seially Concatenated Tubo Codes and the one fom CNES poposal (ef /4/) based on the shot fames and a subset of the DVB-S2 standad (ef /5/). Only the NASA LDPC poposal doesn t look like a eal family. But the constuction ules ae well pesented and it is quite obvious to extend the ate o even the dimension of the LDPC codes (C2 and AR4JA). By the way of the geneic LDPC encode (and also the geneic LDPC decode) pesented in ef /5/, it is then possible to exploe on AR4JA and C2 extensions and compae with DVB-S2 equivalent solution. Consideing a code, the main paametes ae its length N and its dimension K. The minimum distance is also a vey impotant paamete but it s not always possible to know it. As fa as all the poposed LDPC codes ae quasi-cyclic, a peiod P can be defined with N and K being multiple of P, i.e. N=P.N and K=P.K. All those codes ae also defined by thei paity matix H. By extending this paity matix with the same ules than C2 constuction o AR4JA constuction (see ef /2/), it is then possible to obtain a full set of paametes and intoduce then a eal family DVB-S2 family Peiod : P = 360 Dimension : K K P = and [ { 45,60,72,90,108,120,135,144,150,160,162} o { (9),(15),18,(20),27,30,33,35,37,40} K (nomal fame)] K (shot fame) Length : [ N = 180P (nomal fame)] o N = 45P (shot fame) Code ate : (1/4), (1/3), 2/5, (1/2), 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, (9/10) 2.2. CCSDS C2 family extension Peiod : P = 511 Dimension : K = 14P Length : N N P Code ate : 7/8, 7/9, 2/3 = and N { 16,18,21} 2.3. CCSDS AR4JA family extension Peiod : P = M / 4 and Dimension : K = 8( 1) P Length : N = 8P Code ate : t M 2 1 whee = 2,3,4,5,6,7, 8 = whee 7 t Codes combination with modulations All the ates obtained peviously can be combined with diffeent modulations such as SRC shaped QPSK, 8PSK and 16APSK. Fo those two last shaped modulations, a specific effot is to be done to convet the demodulato Log Likelihood Ratio (LLR) meteing the fiability of the eceived constellation symbol to the LLR of the bits demanded by the LDPC decode. In fact this poblem is not new and fo Gaussian channels (like the one fo High Data Rate TeleMety), it has been demonstated (see ef /6/) that a pagmatic appoach called Bit Inteleaved Coded Modulation (BICM)

3 3 behaves quite equally than the computation consuming appoach with full demapping fo high ode modulations (fom and above 8PSK). We popose then to follow the same pinciple and to inset an inteleave between the encode and the mappe/modulato so as to take advantage of the deinteleave in eception to deive easily the bits LLRs fom the constellation symbols LLRs. 3. Tansmission faming When using ultimate codes like the ones of the CCSDS Oange Books poposals (ef /2/, /3/, /4/), the impotance of tansmission faming is temendous fo pope demodulation in so fa as those codes ae aound 1 db o less fom the Shannon bound. In ode to cope with the vey low SNR, the demodulato must be helped by both obust tansmission heades and pilots. This ule has been followed by the DVB-S2 standad (see ef /4/ and /5/) and the SCC/MHOMS poposal (see ef /2/). But they diffe in the way that SCC/MHOMS uses a fixed physical fame size in numbe of symbols, whateve the modulation choice is, and DVB-S2 CCSDS poposal subset uses only 3 sizes due to the fixed length of the code family (16200 coded bits) combined with the 3 possible constellations (QPSK, 8PSK, 16APSK) Faming ules of DVB-S2 standad (and SCC poposal) All the tansmission fame have an Identifie (ID) of 7 bits potected by a Reed-Mülle code of length 64. Those 64 coded bits ae always associated to a obust π/2 BPSK modulation and the 64 coesponding constellation symbols ae foming the Physical Laye-Heade (PL-Heade). With the 7 bits of the ID, thee ae 128 possible fomats that can infom the eceive of : Length of channel code Rate of channel code Constellation Inteleave Use o not of pilots The pilots ae known constellations points (1,0) in Fesnel plan gouped by N p = 36 symbols evey N u = 16*90 = 1440 symbols fom the heade. With this ule, the last goup of symbols is sometime close than N u symbols fom the following PL-Heade but this ule don t tie the paametes altogethe and it is affecting vey lightly the fame efficiency of the tansmission Geneic poposed faming ules We conside that the chosen family between the possible LDPC codes depends on the spacecaft pointed by the eceiving antenna. This spacecaft is in fact known and thee is no need to infom about the family at the tansmission fame level. The paametes that must be contained in the heade shall be potected by a obust code and shall infom the eceive about: length of the channel code, ate of the code, constellation, inteleave type, use o not of pilots. As fa as the length, the ate and the constellation choice give between 9 (C2 extended family) to moe than 100 possibilities (AR4JA extended family), we suggest to keep in line with DVB-S2 and use then 6 bits fo this indexing. We show heeunde all the possible choices and estictions : DVB-S2 :

4 ate Dimension Constellation nomal (64k) shot (16k) QPSK 8PSK 16APSK 32APSK 1/ NA NA NA 1/ NA NA NA 2/ NA NA NA 1/ NA NA NA 3/ NA NA 2/ NA 3/ / NA 5/ / / NA (*) geen : possible conf. oange: CCSDS non chosen conf. ed : non authoized (std) conf. The global choice is 17 possibilities C2 extension : Length Dim ate 2/3 ate 7/9 ate 7/ with all constellations QPSK, 8PSK and 16APSK allowed It coesponds then to 9 possibilities AR4JA extension : M Rate 1/2 2/3 3/4 4/5 5/6 6/7 7/8 Leng. Dim. Leng. Dim. Leng. Dim. Leng. Dim. Leng. Dim. Leng. Dim. Leng. Dim xxx code too shot (dim <1024) o too long (length > 32768), xxx QPSK only, xxx Associated constellations to be defined, By applying this limitation we get 15 pue QPSK and 48 othes configuations by not using 16APSK 2/3 and 16 APSK 6/7 and 8PSK 4/5 and 8PSK&16APSK fo code ate 6/7 (too close in pefomances to 5/6 and 7/8). This allows to use a 6 bits index. The use o not of the pilots needs anothe index bit. Fo what concens the inteleave, thee ae many possibilities (non exhaustive list): Full andom S-andom Convolutional Row/column (ight o left) 4

5 Helical 5 As fa as the fist two types need a pseudo-andom numbe geneation that is moe tedious to chose popely (no fine and simple ule exists fo this choice), we have consideed only the 3 othes methods. The choice of the convolutional inteleave is in fact only memoy saving diven because it implies some specific pime decomposition in ode to wok popely, this pime decomposition being impossible with size of powe of 2 like in some cases fo the extended AR4JA family. We have then conside the simple ow/column inteleave, allowing eithe to wok ight sided o left sided in ode to find best mixing. It has been the choice fo DVB-S2 (see ef /4/ and /5/). The wok of those type of inteleave is known by CCSDS (ou inteleave fo concatenated codes is a ow/column) so we will not disgess about this. The helical inteleave is moe fancy and looks to be moe inteesting when the length N of the codewod has to be applied to a constellation of efficiency η that is not a diviso of N. Then it is nice to wok on a table T of N ows and η columns gouping η codewods and by witing the bits of the diffeent codewods helically especting : T(i,j)=CW((i-j)mod η )(j) We popose an example fo a 8PSK constellation heeunde, whee the codewods bits ae equi-distibuted in all the index positions of constellation symbol : CW(0)(0) CW(0)(1) CW(1)(2) CW(0)(3) CW(0)(4) CW(1)(5) CW(1)(0) CW(0)(1) CW(0)(2) CW(1)(3) CW(0)(0) CW(1)(1) CW(0)(2) CW(0)(3) CW(0)(4) CW(1)(4) CW(0)(5) CW(0)(5) Between each PL-Heade that is making the helical beginning, it is possible to put a numbe of codewods, multiple of η. The ID can then infom implicitly about the value. The paametes N u and N p fo the pilots need to be adjusted but as fa as the SNR is the main incentive fo the choice and as fa as thee is few diffeence with DVB-S2 standad codes pefomances, we can compute some bounds fo thee values. We know that we want to wok with at least 1 db magin with a minimum Es/No aound -0.5 db (ates 2/5 o 1/2 with QPSK) and as fa as the phase and symbol ate estimates fo those pilots zone has to be fine a pilot SNR pilot > 14 db is needed. As fa as we have : SNR pilot = Es/No + 10*log10(N p ) + magin We have then as esult : N p 32 symbols In fact thee is no need to high up this to much as we loose in effiency, so the maximum value fo N p can be the one fom DVB-S2, 36 symbols. If we want to cope with a dopple ate of aound -2 khz/s in X band and -6.5 khz/s in Ka band with ate up to 150 MBauds, we can expect in the bad case a full otation in 150M/6.5k coesponding to aound symbols. If we conside that the linea behavio of the estimato in between needs to get good phase points evey 22.5 maximum we get then a maximum value fo N p of 1442 symbols. And if we want to conside fame efficiency and if we put minimum limit at 0.97, we get then the minimum size fo N u of 1200 as fa as : ( )/1200 = 0.97

6 6 We can obseve that all the codes dimension can be divided in slices between 1200 up to 1536, with a mean aound All those elements comfot the DVB-S2 choice (36, 1440) by showing that it is well adapted fo ou High Rate Telemety needs. 4. Pefomances compaisons We popose some compaison ove all those codes by using the geneic achitectue fo both encode but also fo the decode. The citeia is the Fame Eo Rate (FER) vesus the Eb/No atio. The size of the fame has been adjusted to the maximum of the possible fo the codes simulated. Fo QPSK, the esults povided in the Oange Book (ef /1/) have been povided fo compaisons pupose. We place the satuation at sat = 3.0, we have quantized the banch metics at 6 bits (bmq=6), and the full metics at 10 bits (fmq=10). We have put the maximum iteations numbe at 100 so as to get the ultimate pefomance. Thee ae in fact compaison between low maximum iteations decoding with both AR4JA and C2 codes. Peliminay simulations show that the AR4JA family extension behaves the best with the helical inteleave but is quite sensitive to this numbe of maximum iteations. The loss is aound 0,1 db fom 200 (ultimate) down to 20 iteations maximum (unde 10-3 FER) and nea 0,08 db between 100 (close to ultimate) down to 50. But pefomances look still acceptable. Futhemoe, C2 code family seem moe obust to this paamete even if pefomances ae a bit less effective. The loss is aound 0,1 db when going fom 100 (ultimate) down to 12 iteations maximum. DVB-S2 family behaves in between those 2 cases. Duing all the simulations, moe than coded fames have been tansmitted with the pinciple of the PLheade descibed and poposed futhe. No heade has been false decoded showing then the obustness of the scheme.

7 7 1E+0 FER (16384 bits) CCSDS = p(eb/no in db) with sat = 3, bmq=6, fmq=10, 100 it max 1E-1 1E-2 1E-3 1E-4 1E-5 1E-6 AR4JA 7/8 14.3k DVB QPSK 8/9 GSFC C2 7/8 8k C2 7/8 8k OB DVB QPSK 4/5 AR4JA 4/5 16k 1E-7 AR4JA 4/5 16k OB GSFC C2 2/3 7k DVB QPSK 2/3 AR4JA 2/3 16k AR4JA 2/3 16k OB DVB QPSK 3/5 AR4JA 1/2 16k 50itm AR4JA 1/2 16k OB DVB QPSK 2/5 AR4JA 1/2 16k 100itm 1E-8 0,60 0,80 1,00 1,20 1,40 1,60 1,80 2,00 2,20 2,40 2,60 2,80 3,00 3,20 3,40 3,60 3,80 4,00 4,20 4,40

8 8 1E+0 FER (8k to 16k) CCSDS =f(eb/no in db) fo 8PSK & 16APSK with sat=3, bmq=6, fmq=10, helical inteleave, 200it max 1E-1 1E-2 1E-3 1E-4 1E-5 1E-6 8PSK DVBS2 2/3 8PSK AR4JA 2/3 8PSK DVBS2 3/4 8PSK DVBS2 5/6 8PSK DVBS2 8/9 16APSK DVBS2 3/4 1E-7 16APSK DVBS2 5/6 16APSK DVBS2 8/9 8PSK AR4JA 5/6 8PSK AR4JA 7/8 200itm 8PSK AR4JA 7/8 20itm 8PSK C2 7/8 100itm 8PSK C2 7/8 20itm 8PSK C2 7/8 12itm 16APSK AR4JA 3/4 ilcd 16APSK AR4JA 7/8 1E-8 3,6 3,9 4,2 4,5 4,8 5,1 5,4 5,7 6,0 6,3 6,6 6,9 7,2 7,5 7,8 8,1

9 5. Conclusion On the basis of the NASA Oange book (ef /3/), we have pesented an extension fo both AR4JA fom 1k up to 16k with ate between 1/2 up to 7/8 but also ate extension of the C2 code of 2/3 and 7/9 and we have poposed to synchonize those blocks with a fame constucted the same way as the DVB-S2 one with the use of a PLHeade containing an InDex (ID) fo ate and modulation choice. We have combined this with thee possible inteleaves (2 line/column and an oiginal helical one) so as to suppot modulations like 8PSK and 16APSK. Futhe wok can be done one the design and choice of the inteleave and on the extension in ode to optimize pefomances but esults ae still inteesting. We have given some pefomances of the diffeent families of codes obtained with those vaious modulation and make some compaison with DVB-S2 poposal pefomances showing that all those families behave quite similaly. We have also show that the stuctue is obust fo fame synchonisation and offes the VCM use (Vaiable Coding & Modulation) paticulaly inteesting fo EESS-LEO with X o Ka bands links. We have also made a poposal of fame constuction fo CCSDS physical laye that can suppot VCM and that allows to tansmit CCSDS fames o CADU with extended pefomance compaed to actual ASM Refeence papes Ref /1/ : «DVB-S2 : a vey open and attactive standad fo TMs» G. Lesthievent CNES, CCSDS SLS- RFM_04-08 pape, May 2004 Ref /2/ : CCSDS O-0.2 Flexible Seially Concatenated Convolutional Tubo Codes with Nea Shannon Bound Pefomance fo Telemety Applications, Oange Book, July 2007 Ref /3/ : CCSDS O-1.1a Low density paity check codes fo use in Nea-Eath and Deep Space applications, Oange Book, July 2007 Ref /4/ : CCSDS O-1d Use of DVB-S2 coding & modulation standad fo high data ate TM link, Daft Oange Book, June 2007 Ref /5/ : ETSI EN v1.1.1 DVB Second geneation faming stuctue, channel coding and modulation systems fo Boadcasting, Inteactive Sevices, News Gatheing and othe boadband satellite applications, ETSI standad, Januay 2004 Ref /6/ : Bit-inteleaved coded modulation, G. Caie, G. Taicco, and E. Bigliei, IEEE Tans. Infom. Theoy, vol. 44, pp , May 1998.