Blind Estimation of Block Interleaver Parameters using Statistical Characteristics

Transcription

1 Advancd Scinc and Tchnology Lttrs Vol.139 (FGC 2016), pp Blind Estimation of Block Intrlavr Paramtrs using Statistical Charactristics Jinwoo Jong 1, Youngkyun Jon 1 and Dongwon Yoon 1 1 Dpt of Elctronic and Computr Enginring, Hanyang Univrsity Soul, Kora dwyoon@hanyang.ac.kr Abstract. In digital communications systms, intrlavrs ar usd to stir bits of channl codd data to robust against burst rror in noisy channl. Howvr, in non-cooprativ contxt such as signal intllignc systm(sigit) and spctrum survillanc systms, intrlavr may act as ncryptor to 3 rd party listnr who has no information about th intrlavr paramtrs usd in transmittr. Thrfor, blind stimation of intrlavr paramtr is ncssary in non-cooprativ contxt to rconstruct th original data squncs. In this papr, a blind stimation mthod is proposd which can blindly stimat intrlaving priod of block intrlavr from block codd and block intrlavd data squnc using statistical charactristics. Kywords: intrlavr, block cod, gauss limination, signal intllignc 1 Introduction Blind dtction involvs stimation of many transmission paramtrs, such as modulation, sourc cod, channl cod, intrlaving, and scrambling typs. This is a trmndous work, so in this lttr w focus only on th blind dtction of intrlaving. For a non-cooprativ contxt such as signal intllignc systm(sigit) and spctrum survillanc systms, intrlaving acts as an ncryption procss to a rcivr who lacks information about th paramtrs of th intrlavr [1], [2]. Such an intrlavd squnc can b rgardd as an unknown squnc, and to dcod it, th paramtrs of th intrlavr must b stimatd using a blind dtction mthod. Som prvious works providd a mthod for stimating th priod of block intrlavd squnc of block codd data, using Gaussian limination with th linar charactristic of block channl coding in th intrlavd squnc [3], [4]. Howvr, th mthods of [3] and [4] ar basd on th assumption that th numbr of rcivd data approachs infinity. In this papr, w propos a nw mthod which can stimat th priod of th block intrlavr with unknown block intrlavd squnc of th limitd lngth as an xtnsion of th prvious works [3] and [4]. In sction 2, brifly rviw th systm modl of th prvious works [3] and [4], and propos a nw blind stimation mthod with unknown block intrlavd squnc of th limitd lngth. In sction 3, vrify through computr simulation and conclud in sction 4. ISS: ASTL Copyright 2016 SERSC

2 Advancd Scinc and Tchnology Lttrs Vol.139 (FGC 2016) 2 Estimation of th Priod of a Block Intrlavr Block channl coding mthods such as Hamming, Rd-Solomon, Golay, BCH, and LDPC gnrat rdundant bits as linar combinations of mssag bits, and ths rdundant bits and mssag bits form a cod word. Aftr block channl coding, thr is linarity btwn rdundant bits and mssag bits in a cod word. Intrlaving rordrs all th bits of a cod word. Aftr intrlaving, howvr, all bits of th intrlavd cod words still rtain thir linarity and xist within an intrlaving priod bcaus th intrlaving priod is an intgr multipl of th lngth of th cod word [1], [5]. In addition, th bit location ordr of intrlavd bits is th sam for vry intrlaving priod. Ths charactristics ar usd as clus of stimating intrlaving priods [3], [4]. Assum a block intrlavr with intrlaving priod. To stimat, prvious rsarch usd th following mthod [3], [4]: First, mak th analytical matrix H(, M ), loading column by column with data blocks which ar th intrlavd squnc dividd by an arbitrary stimatd intrlaving priod, whr is an arbitrary stimatd intrlaving priod, and M is th numbr of columns. If is an intgr multipl of, rdundant bits and mssag bits ar alignd in th sam row in, rspctivly, and th linarity btwn th rows of rdundant bits H(, M ) and mssag bits can b sn in H(, M ), sinc th ordr of intrlavd data bits is th sam for vry intrlaving priod. Aftr that, apply Gaussian limination to H(, M ) and xamin th numbr of 1 bits. Th algorithms of [3] and [4] ar fficint for a vry larg valu of, sinc thy ar proposd with th assumption that approachs infinity. In actual non-cooprativ contxts, howvr, intrcpting an normous amount of signal data is impracticabl. To ovrcom this shortcoming, w propos a nw approach that can stimat th intrlaving priod with block intrlavd squnc of block codd data of th limitd lngth in noislss and noisy channls. First, mak th analytical matrix H(, 2 ) by loading data blocks column by column as shown in Fig. 1, whr shadd aras rprsnt rdundant bits and plain aras rprsnt mssag bits. ot that th numbr of columns of th analytical matrix is just doubl instad of approaching infinity. M M M (a) is an intgr multipl of (b) is not an intgr multipl of Fig. 1. Analytical Matrix H(,2 ) for th stimation of intrlaving priod. 52 Copyright 2016 SERSC

3 Advancd Scinc and Tchnology Lttrs Vol.139 (FGC 2016) As shown in Fig. 1 (a), if an arbitrary stimatd intrlaving priod is an intgr multipl of th original intrlaving priod, th rdundant bits and mssag bits ar alignd in th sam row of, rspctivly. On th othr H(,2 ) hand, as shown in Fig. 1 (b), if is not an intgr multipl of alignd rows. W thn apply Gaussian limination to th analytical matrix L(,2 ), thr ar no such H(,2 ). Fig. 2 dpicts a Gaussian liminatd analytical matrix in a noislss channl whn (16, 11) Hamming cod is assumd and th original intrlaving priod 48 as an xampl, whr dots rprsnt 1 bits, and blank spacs rprsnt 0 bits. (a) is an intgr multipl of (b) is not an intgr multipl of Fig. 2. Scattr diagram of 1 and 0 bits for Gaussian liminatd analytical matrix L(,2 ) As shown in Fig. 2 (a), if is an intgr multipl of th original intrlaving priod 48 (i.., band across th bottom third of th diagram). Othrwis, as shown in Fig. 2 (b), if is not an intgr multipl of th original =48), rows of rdundant bits ar liminatd (not th blank intrlaving priod 48 (in this cas =47), thr ar no liminatd rows bcaus th rdundant bits and mssag bits ar not alignd in th sam row in th analytical matrix H(, 2 ), rspctivly. To vrify whthr or not an arbitrary stimatd intrlaving priod is an intgr multipl of th original intrlaving priod, w count th 1 bits and 0 bits, and analyz th ratio of th 1 bits to 0 bits in th right-hand squar portion (dashd lin in Fig. 2) of L(,2 ). W dfin th ratio of 1 bits to 0 bits of th th right-hand squar portion as Copyright 2016 SERSC 53

4 Advancd Scinc and Tchnology Lttrs Vol.139 (FGC 2016) umbr of '1' bits in th right-hand squar umbr of '0' bits in th right-hand squar 1 Rank( H ) 2 1 { Rank( H )} Rank( H ) 2 Rank( H ) 2{ Rank( H )} Rank( H ) (1) Rank( H ) r 2 r whr is th numbr of row which is not liminatd by Gaussian limination and r is th cod rat. By obsrving, w can dcid whthr or not is an intgr multipl of. If is an intgr multipl of, th valu of intgr multipl of, th minimum valu of is not nar to 1. And if is not an is nar to 1 in a noislss channl, sinc probabilitis of 1 bits and 0 bits of th th right-hand squar portion ar qually 1/2 as Fig. 2 (b) For xampl: Th cod rat of a convolutional cod may typically b 1/2, 2/3, 3/4, 5/6, 7/8, tc., corrsponding to that on rdundant bit is insrtd aftr vry singl, scond, third, tc., bit. Thrfor, whn is an intgr multipl of, th valus ar from 0.33 to Th cod rat of th Rd Solomon block cod dnotd RS(204,188) is 188/204, corrsponding to that = 16 rdundant byts ar addd to ach block of 188 byts of usful information. So, th valu of is Simulation Rsults In this sction, w validat th proposd blind dintrlaving procss by showing simulation rsults in a noisy channl. W assum a binary symmtric channl and run 1,000 Mont Carlo simulations for ach BER. And channl cods from MIL-STD 110B ar usd, thrfor, w st 0.6 th as th thrshold for dtction. Channl cods for fixd-frquncy opration of MIL-STD 110B ar shown in Tabl Copyright 2016 SERSC

5 Advancd Scinc and Tchnology Lttrs Vol.139 (FGC 2016) Tabl 1. Channl cods, fixd frquncy opration Data rat (bps) Effctiv cod rat Mthod for achiving th cod rat 4800 (no coding) (no coding) /2 Rat 1/ /2 Rat 1/2 cod 600 1/2 Rat1/2 cod 300 1/4 Rat l/2 cod rpatd 2 tims 150 1/8 Rat 1/2 cod rpatd 4 tims 75 1/2 Rat 1/2 Fig. 3 shows dtction probabilitis of intrlavr paramtrs in a noisy channl, whr th dottd vrtical lin rprsnts th bordr of practical BER rang (BER of 10-3 ). ot that th BER of 10-3 is rasonabl, bcaus it dnots th uncodd cas bfor channl dcoding. Fig. 3. Dtction probabilitis of intrlavr paramtrs ( th 0.6 ). Fig. 3 dpicts th dtction probabilitis of intrlavr paramtrs for various cod rats. W adopt 1/2, 1/4, and 1/8 cod rats and standard block intrlavrs. As shown in Fig. 3, th proposd algorithm is mor robust in a noisy channl whn th channl cod rat is small. Through computr simulations, w know that th proposd algorithm can almost prfctly stimat th intrlavr paramtrs in practical communication systms having prformanc rquirmnts of BER blow Copyright 2016 SERSC 55

6 Advancd Scinc and Tchnology Lttrs Vol.139 (FGC 2016) 4 Conclusion In this papr, w prsntd a blind dintrlaving procss that can rconstruct unknown intrlavd squnc of block codd data. W first mad th analytical matrix with data of th limitd lngth in noislss and noisy channls. H(,2 ) W thn Gaussian liminatd th th analytical matrix Rank( H ) H(,2 ) and obsrvd th valu of. From and, th cod rat could also b stimatd. Through computr simulations, w prsntd dtction probabilitis for various channl cod rats and intrlavr typs, and found that, in a noisy channl, our mthod could almost prfctly stimat intrlaving priods ovr a practical BER rang. Our rsults can b applid to unknown signal rconstruction for various cass of practical intrst. Acknowldgmnt. This work was supportd by th rsarch fund of Signal Intllignc Rsarch Cntr suprvisd by Dfns Acquisition Program Administration and Agncy for Dfns Dvlopmnt of Kora. r Rfrncs 1. Ramsy, J. L.: Ralization of Optimum Intrlavrs, IEEE Trans. on Information Thory, May 1970, 16, (3), pp Garllo, R., Montorsi, G.., Bndtto, S., and Canlliri, G.: Intrlavr Proprtis and Thir Applications to th Trllis Complxity Analysis of Turbo Cods, IEEE Trans. on Communications, May 2001, 49, (5), pp Lu, L., Li, K. H., and Guan, Y. L.: Blind Dtction of Intrlavr Paramtrs for on- Binary Codd Data Strams, IEEE Intrnational Confrnc on Communications, Drsdn, Grmany, Jun Sicot, G., Houck, S., and Barbir, J.: Blind dtction of intrlavr paramtrs, Signal Procssing, April 2009, 89, pp Andrws, K., Hgard, C., and Kozn, D.: A thory of Intrlavrs (Tchnical Rport , Computr Scinc Dpartmnt, Cornll Univrsity, Jun 1997) 56 Copyright 2016 SERSC