Hotog Tien Cdng m B j g Tip chl KHOA HOC & C
151(06): 131-134
: Sf,^^B^N^"=^^"*^'"=^^^
Hoiing Tilu Cong"', P h , m Xnan Nghia', Nguyln Anh T n i n ' tT.,.^ n L ... . 'llgc vien Ky thugt guan Su.
l^'msBg, hgc Cang nghe thdng en vdauyen thong-BHThdi Nguyin T6MTAT
kenh BEC khi xac sui. x 6 . ta™ tir o T l i n 0 3 thi J ^ ^ ^ f ^ f " '^'? °'° ^ "^ "'"' '^^'''?' ™ bao x i : suit l5i bit l i 10^. T ™ g te v i k ^ i BIWI^XA^-^- ^ ^ * " " "'^ ^' " " ^ do Ipi ma hoa l i 0.5 dB d ly l ^ S f i r i ™ ' ' ^ " ' " ^ • " ™ ^ " S « « 1 » 128 eho Tfr khoa: ilffipidn cm stf phdn cue kenh, md kinh, kenh BEC kinh B-AWGN
B ^ T V A N S f i
; Ma hoa phan cue la mot ky thuat moi dugc Arikan [ I ] phat minh cho truyin tin tren
• cac M n h B-DMC. Ky thuSt nay cho phep
; trujen d u lifu v « cac t6c dp g4n vdi dung I lugng doi xirng ciia cac k6nh do voi dp tin i cjy cao tuy y, sii dung cac thujt t o i n ma hoa va giai ma co dp phlic tap thSp. Khong gi6ng v6i c i c ma t m y i n t h i n g nhu LDPC hay Turbo, kha nang ctia m a Phan cue da dugc i chiing minh b i n g ly thuySt. Tuy nhien, cho 1 den nay v l n chua co mpt phuong phap hiiu qua de c i u t r i e m a Phan cue lien cac kenh khac ngosi trir kenh nhi phan xoa (BEC).
Phnong phdp tjo m a chung Si tao ma Phan eve tren c i c kenh khac B E C duoc sil dung la xSp xi Monte Carlo [ I ] . Arikan da d l xuil phuong phap don gian dung kenh B E C co dung lugng nrong duong de tjo ma Phan cue
•rong P ] . Gan day, mpt s6 phugng phap tao mS k h i c dugc d i xuit trong [3], [4]. Mori va O0ng svr da sii d\ing cong cu tiin hoa mjt dp (DE) de tao ma cho bat ky B-DMC Irong [4], song c6 dp ph4c tap cao. D i giam dp phiie tap cua phuong p h i p DE Tri&nov da d i xuat trong [3] phuong p h i p tao ma IrSn e g so s u dung xap xi Gauss.
M i l khac, tinh c h i t cua k&ih B-AWON thay d i i theo ty sa tin tren tap (SNR). D i co t h i i p dimg m i P h i n cue trtn kenh B-AWON lac
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g i i da sii dung phuong phap ciia Arikan dimg kenh B E C co dung lugng tugng dugng kenh B-AWGN tai mpt g i i tri SNR-thiit k i , sau do ta se xac djnh dugc mpt bp ma Phan cue sii dung tren mgt dai SNR.
Trong bai b i o n i y , dua h e n phuong phap cua Arikan c i c t i c gia liin hanh mo phong dinh gia p h i m chat ciia ma Phan cue trta kenh BEC va B-AWGN. Danh gia l i c dpng ciia dp dai ttr ma den pham c h i t ciia ma Phin cgc.
Phin con Iai ciia bai bao co b6 cue nhu sau:
Muc 2 gioi thi?u v i s u phan cue kenh, m i hoa v i giii m i h i y man tu. Muc 3 trinh bay phuong phap ma P h i n c^c tren kSnh B- AWGN. M o phong d i n h g i i k i t q u i dugc Irinh bay trong Muc 4, cuii cling l i k i t luan MA PHAN e y e
Str p b a n cue kenh
Ma phin cue dugc d i xuat dua tren hiSn tugng phan circ kenh [1]. Dinh 1^ phan cgc kenh phit bilu niiu sau, khi dp dai ma A'(Af = 2 " , n la so nguyen duong) tiin tgi vo Cling, thi mpt kinh bil cue hoa tro thanh kenh khong nhilu hoae la kenh thuin toy nhieu. Kenh khong nhieu c6 t(W). B i n g cich Iruyen c i c bit mang Ihong lm trSn c i c kenh khong nhieu va truyin c i c bit long bdng tren c i c kenh thuin toy nhiiu, vj tri va noi dung cua c i c bit idng bang dugc bp giai ma huy toin tg (SCD), nen c i c m i Phan cue co t h i dat tgi dung lupng doi xung c i c kenh bil
Hoarg Ti^n Cong ^ a Dig Tap chi KHOA HOC & CONG NGHE 151(06)- 131-134 Ma boa
Cho truac tap cac chi so / c i i a cac phan trr ciia mpt vector x, tac gia ky hieu vector con tuong irng la x, Tuong tu. khi / k y hieu la cac chi s6 cac cot ciia ma tran A , thi ma tran con tuong img la A^
Mot bo ma Phan cue duoc mieu ta bang bo cac tham s6 (N,K,A,u^, ) , trong do N la so bit ma, K la s6 bit thong tm dung de ma tao ra mot Etc ma, ^ la tap W - A" cac so nguyen tir {0, 1, . , A' - / } ung vai cac vi tri cac bit mang thong tin,
A'^ =[0.l,...,iv -\]\A\di tap cac chi so cac bit bit dong bang, va u , la vector chiia cac hit dong bdng (vi du u ^ - 0 ) ,
Dau vao ciia bp ma hoa Phan cue co tham so {N,K,A) la vector thong tin u do dai K nhu tren Hinh 1 Tu thong tin u , bo ma hoa tao thanh vector du lieu d theo quy tac d^, =u^, (cac bit dong bdng) va d ^ = u , trong do. Ty Ie ma la fi^ ^ / / V ' Ky hieu tich
= \og,{N)y
Kronecker n lan ma tran F Tir ma dirpc tao ra nhu trong cong thirc (1)- x - G , d
G = F " duoc goi la ma Iran sinh ciia ma phan cue
Giai ma
Bo giai ma hiiy tuan tu (SCD) la bo giai ma quyel dinh mem Dau vao ciia bo giai ma SCD la vector dau ra kenh y^ va bo tham s5 ma hoa [N,K..4,U^ ) Dku ra la vector tin ucrc krang u Bo giai ma SCD bao gdm N bo quyet dinh (DE), moi DE quySt dinh 1 bit thong lin u^ Cac DE hoat dong luSn tu tir 1 den ., Neu chi s6 i e .•!• , lhi bit thir (v,da bict iruac nen bp DE thir ; quy^t dinh il, = H \ a gui den ifu ca cac DE k^ Ii6p N6u . bo DF thir ; dai dC-n tdn khi ccior uac lirong da quyijl dinh nhan Jirac ^
" l "
theo
sau do tinh ty so hpp le ong thlic (2):
Va ra
", ^'
quyet dinh
0, 4'(/',.;r')>i.
1, z,';'(r:,.ir')<i
cue da (LRI
(3)
Cac LR duac tinh toan theo cong thiic 78, 79 trong [1].
Do do, viec tinh LR o do dai A'^giam xuong viec tinh 2 ty so LR o dp dai N/2. Thii lyc de quy tiep tuc cho den mirc N~\, cr miic nay cac ty so LR c6 the tinh tru'c tiep
Z.1'1 [y^) = W{y^ I 0) / lV{y 11) Do phlic tap ciia thuat toan giai ma \a 0(Nlog N) MA PHAN c u e TREN KENH B-AWGN Mo hinh kenh su dung trong bai bao la kenli B-AWGN, vai ky vpng bang khong va phuang sai la A^^ / 2 Tin hieu tren kenh sii dung dicu che nhi phan Mo hinh kenh diroc mo ta tren Hinh 1, Cac bit trong tir ma \ duijc dieu che thanh cac symbol xbang each sir duTig bp dicu che khoa dich pha nhi phan CBPSK) Bp dieu che BPSK thuc hien anhxa bil 0^-jRE^va l - > + ^ / ^ , trong do
£,, la nang luang de truyen moi bit thong tin Mo ta toan hoc kenh B-AWGN nhu sau-
Khong lam mat tinh tong qual, Irong toanb?
bai bao chiing toi chuan hoa phuong sai lap am bang 1 cho kenh B-AWGN Ap dung phuong phap ciia Arikan tinh loan cac tham so Z{W) theo cong thirc 4 lai SNR- I thiet ke va sir dung quy tac tao ma Phan cue dc xac dinh bp tham so ma Phan cue. Giasu tai gia tn SNR-thie! kc kenh B-AWGN co dung luong la C. thi kenh BEC co dm luang tuang duang se co xac suat xoa lj c- = l - C , Ky bicu 2 ( j f ; " ) . ; = l N la lham so Bhattacharyya cua kenh bil iKl" thu /
^ ^ ^ T i e a CSng vaDtg y^psU KHOA HOC & CbHG NGH$ 151(06): 131-134
^€{U)'
M l U a BPSK
Giii mi SC
TrSn cor s o so sanh cac g i i tri z/w^'M vai ' root mfic ngttong cho t m o c , ta chpn dugc cac '. kSnh chat Iirong t6t d e t r a y i n bit mang thong jlj tin \ ^ cac Irenh chat lugng xSu de tniy€n cac
^ bit dong bang, 4 K E T Q U A M O P H O N G
^ De fliay dugc kha nang ap dung ma phan cue ' Iren kfinh B-AWGN, chung toi thuc hien mo i phong va danh gia hifiu qua tang ich cua ma
% d^t duffc voi cac chigu dai ma tu 16 d i n 128.
. Gla tri SNR flieo fliiet k6 bJng -1.5917 dB } fimgvdigjdtri Z ( » ^ ' ) = 0 . 5 .
ffinh 1. hid Ilinh he thong mo phong
Irenh CO xac suSt xoa e = 0 . 3 , n i u giam ty le ma hoa tu 0.3 d&i 0.2 flii dak lugng he th6ag se tang Ien t u 10*^" dSn 1 0 ^ . Khi ch5t lugng kenh truy&i cang x l u thi d o lgi thu dugc do viec gjam toe d o truyen tin ciing giam di.
(3)
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^,
4., ^.
M
'-^A
s - ^y~~Tr—
ffinh 2. Slf phdn ofc kenh B-AWGN co dung lufrng C = 0.5 v&i N = 256 Hmh 2 cho fliSy dung lugng d6i xung tiem c^n toi 0 ung voi cac chi s6 kenh nho va tiem c | n 1 (ing voi cac chi s6 kenh Ion, hinh thanh 2 bo kenh c6 xu huong la kenh khong nhilu va kenh flman tiiy nhilu. T>o N = 256 hiru h?n nen y%sx co I so kech co dung lugng ddi xftng 6 muc Irung gian.
Ket q i u SiaAi gia chat lugng ciia ma Phan cvrc trgn kfinh BEC dugc th^ hi?n tren ffinh 3.
Tir kgt qua tren Hinh 3 cho fldy khi chit Iugng kenh khong doi neu giam t6c dp truyen tin Uli pham chat dugc cai thien dang kk. Vdi
ffinh 3. Pham chat cua mdphdn arc tren kenh BEC(0.5)vm N = \6 Ket qua danh gia chat lugng cQa ma Phan cue t e n kenh B-AWGN dugc thg hien tren H i n t 4. Ket qua tren ffinh 4 cho thiy p h i m chSt ciia ma Phan cue dugc tang Ien khi tang dp dai ma. De dat dugc muc ty le 16i bit (BER:
Bit Error Rate) la 1 0 ^ , n6u tang dp dai ma tir 64 len 128 thi tang ich ma thu dugc la 0.5 dB.
Khi chat lugng kenh cang t6t len thi cac duong BER co xu huong phan ky cang nhilu.
Do do, dp lgi thu dugc ngay cang tang.
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Hinh 4. Pham chat cua ma Phdn circ
;
KET LUAN
Tli ket qua n h t o dugc ciJa bai bao cho thiy ma Phan circ co dp phiic tap giam hon cac
H o a n g Tien C o n g I Dig Tap chi KHOA HOC & CONG NGHE 151(06), 131-lif loai ma kenh khac mot each dang ke Ben
canh do cung tha> rang, doi \ 6 i kenh BEC khi xac suJt xoa cang tang thi t>' le ma phai giam de dam bao chat luong cho truoc, con d6i \ai kenh B-AWGN thi cho thay rang khi do dai rir ma cang Ion cho chat lugng giai ma cang duac cai thien
T A I L I E U THAiM KHAO
! E Arikan, Channel polarizauon A meihod for LOiiilniciing capacily-achieving codes for iimmelric binaiy-input memon less channels.
IEEE Transactions on Information Theon-, VQ|
55,110 7. pp. 3051-3073. 2009.
2 E Arikan. A performance comparison ofpokr codes and reed-nniller codes. [J^E Communications Lcliers. \ o ! i2, no 6, pp. 44^
449.2008
3 P Triforov, Ef cienl design and decoding o/
polar codes, IEEE Trans Commun , \ol 60. no 11. pp. 3221-3227, Nov 2012
4, R Mori and T Tanaka. Peifonnance of polar codes with lhe coiislnic-lion using densin evolution, IEEE Communications Letters, \oI 13 no 7, July 2009
SUMMARY
STUDYING THE PERPORMANCE OF POLAR CODE IN B-AWGN CHANNEL Hoang Tien Cong''. Phai
• College ol Iiijonnation and €•
I Xuan Nghia', Nguyen Anh Tuan^
Le Oiiy Don Technical University, '1 Teihiiology- TNU This paper introduced the detmitions of Polar code and simulated to evaluated the performance of Polar code m BEC and B-AWGN channel Simulated results showed that the delenon probabilitj' mcreased Irom 0 2 to 0 3 so need to code rate reduced from 0 3 to 0 2 to guarantee BER was 10^ in BEC With the length of code words incieased from 64 lo 128, system performance prov idcd coding gam about 0 5 dB at BER= 10^ m B-AWGN channel
Keywords Pola, codes chaimel polanzalion. ciniiinel coding. BEC channel.;. B-AWGN chaimels
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