Joint Iterative Equalization and Decoding for 2-D ISI Channels

Transcription

1 Joint Iteative Equalization and Decoding fo 2-D ISI Channels Joseph A. O Sullivan, Naveen Singla, Yunxiang Wu, Ronald S. Indec Electonic Systems and Signals Reseach Laboatoy (ESSRL) Magnetics and Infomation Science Cente (MISC) Depatment of Electical Engineeing Washington Univesity in St. Louis 7/2/02

2 Outline Poblem desciption Joint equalization and decoding schemes fo: Geneal 2-D ISI Using 2-D MMSE equalization and decoding Using novel message passing algoithms that tae advantage of the 2-D dependence Sepaable 2-D ISI Using tubo equalization Conclusions 7/2/02 2

3 Poblem Desciption Reliable data etieval fom channels having 2-D ISI As bit aspect atio educes inte-tac intefeence becomes significant Optical memoies Futue stoage media: 2-D pattened media 7/2/02 3

4 Channel Model a(i,j) LDPC Encode x(i,j) Channel ISI (i,j) Equalize x (i,j) LDPC Decode a (i,j) w(i,j) Channel x(i,j) {,-} Channel ISI is 2-D and linea Noise assumed to be AWGN 7/2/02 4

5 7/2/ D Intesymbol Intefeence Μ Ο Μ Μ Ο x x x x x x x Μ Ο Μ Μ Μ Ο Μ w(i,j) = h GUARD BAND j i j i j i j i j i j i w x x x x,,,,,, =

6 Pefomance Bloc length 0000 egula (3,6) LDPC code 0 Ignoing ISI Bit eo ate in log ISI-fee ISI ignoed SNR [db] 7/2/02 6

7 MMSE Equalization a(i,j) LDPC Encode x(i,j) Channel ISI (i,j) MMSE Equalize x (i,j) LDPC Decode a (i,j) w(i,j) Channel Equalize designed assuming inputs to be Gaussian 7/2/02 7

8 Pefomance MMSE equalization and decoding 0 Bit eo ate in log ISI-fee Wiene ISI ignoed SNR [db] 7/2/02 8

9 Iteative MMSE Equalization a(i,j) LDPC Encode x(i,j) (i,j) MMSE Channel ISI Equalize x (i,j) LDPC Decode a (i,j) w(i,j) Extinsic Infomation Channel Soft infomation, estimated mean of the codewod, passed fom LDPC decode to equalize E[ x] x = = P( x E[ x] = ) P( x W **[ = ) h ** E[ x]] 7/2/02 9

10 Pefomance Iteative MMSE and decoding 0 Bit eo ate in log ISI-fee It Wiene_0 Wiene SNR [db] 7/2/02 0

11 Full Gaph Message Passing Chec Nodes Codewod Bit Nodes Data Nodes i, j = xi, j.5xi, j 0.5xi, j 0. 25xi, j 0 w i, j 7/2/02

12 Full Gaph x(i,j) x(i,j) x(i,j2) Fom Chec Nodes x(i,j) (i,j) (i,j) x(i,j) (i,j) (i,j) x(i,j2) x(i2,j) x(i2,j) x(i2,j2) 7/2/02 2

13 Pefomance Full Gaph Message Passing 0 Bit eo ate in log ISI-fee Full Gaph_50 It Wiene_0 Wiene SNR [db] 7/2/02 3

14 Full Gaph Analysis Length 4 cycles pesent which degade pefomance of message passing algoithm x(i,j) x(i,j) x(i,j2) Fom Chec Nodes x(i,j) (i,j) (i,j) x(i,j) (i,j) (i,j) x(i,j2) x(i2,j) x(i2,j) x(i2,j2) Kschischang et al., Facto gaphs and the sum-poduct algoithm, IEEE Tans. Infom. Theoy, 47(2), , Feb. 200.

15 Odeed Subsets Message Passing Fom Imaging Data set is gouped into subsets to incease ate of convegence Fo Decoding Obseved data is gouped into subsets to eliminate shot length cycles in the Channel ISI gaph H. M. Hudson, and R. S. Lain, Acceleated image econstuction using odeed subsets of pojection data, IEEE Tans. Medical Imaging, 3(4), , Dec. 994

16 Gouped ISI Gaph Labeling of data nodes into 4 subsets Fo each iteation use data nodes of one label only 7/2/02 6

17 Pefomance Odeed Subsets Message Passing 0 Bit eo ate in log ISI-fee Odeed Subsets_00 Full Gaph_50 It Wiene_0 Wiene SNR [db] 7/2/02 7

18 Outline Poblem desciption Joint equalization and decoding schemes fo: Geneal 2-D ISI Using MMSE equalization and decoding Using novel message passing algoithms that tae advantage of the 2-D dependence Sepaable 2-D ISI Using tubo equalization 7/2/02 8

19 A Sepaable 2-D ISI x(i, j) Row ISI y(i, j) Column ISI (i, j) Channel Detecto Sepaable Channel Response w(i,j) h = = ( 0.5) Advantages of Sepaable 2-D ISI Reduced Detecto Complexity Apply existing one-dimensional equalization methods Tüchle et al., Tubo equalization: pinciples and new esults, IEEE Tans. On Comm., 50(5), May 2002.

20 Iteative Decode Diagam I (i, j) Column Equalization MAP Detecto LDPC Decode Had Decision Extinsic Infomation Conventional One-Dimensional Iteative Decode Row-by-Row Decode MMSE and Zeo-focing citeia used fo Equalization 7/2/02 20

21 Pefomance 0 - Row-by-Row Decode ISI-fee Row-by-Row: M M SE_ite0 Row-by-Row: ZF_ite3 Bit-Eo-Rate In log SNR [db] 7/2/02 2

22 Iteative Decode Diagam II (i, j) Column MAP Detecto Row MAP Detecto LDPC Decode Had Decision Extinsic Infomation Conventional One-Dimensional Iteative Detecto Full Row-and-Column Decode Inputs to column detecto ae not binay 7/2/02 22

23 Pefomance Bit-Eo-Rate in log Full Row-and-Column Decode ISI_fee Ite_Subite2 Ite4_Subite2 Ite0_Subite2 Row-by-Row: M M SE_ite0 Row-by-Row: ZF_ite SNR [db] 7/2/02 23

24 Conclusions MMSE Equalization and Decoding Good Pefomance with Iteative Equalization Low Complexity FIR Implementation Message Passing Algoithms Full Gaph algoithm pefomance deteioated due to shot cycles Odeed Subsets Message Passing gives best pefomance fo geneal 2-D ISI Sepaable ISI Decoding Best Pefomance fo Sepaable 2-D ISI Low Complexity Equalize geneal 2-D ISI to neaby sepaable channel esponse 7/2/02 24

25 Refeences Chen et al., Nea-optimal paallel distibuted data detection fo pageoiented optical memoies, IEEE Jounal of selected Topics in Quantum Electonics, 4(5), , Sept./Oct W. Wees IV, Full suface data stoage, Ph.D. thesis, Univesity of Illinois at Ubana Champaign, Hagenau et al., Sepaable MAP Filtes fo decoding of poduct and concatenated codes, Poc. of Int. Conf on Comm., , Aug Kavčić et al., Binay intesymbol intefeence channels: Gallage codes, density evolution and code pefomance bounds, submitted to IEEE Tans. Infom. Theoy. 7/2/02 25