Two-Dimensional Coding for Advanced Recording

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1 Two-Dimensional Coding fo Advanced Recoding N. Singla, J. A. O Sullivan, Y. Wu, and R. S. Indec Washington Univesity Saint Louis, Missoui s

2 Motivation: Aeal Density Pefomance: match medium, senso, pocessing Cuently use continuous films with discete gains ; exchange decoupled; ceate bits fom 000 gains; mae gains smalle To incease aeal bit density we need a medium that can sustain smalle, stable magnetic egions Potential solutions: - glue (via exchange) stuctue within egion; discete film; bit pe egion - couple magnetization within egion via exchange; smooth film; ion beam modification; ceate discete egions Want a manufactuable pocess!

3 Challenges with the Pattening of Media Fine featues (<20nm) Lage aea coveage (many cm s) High substate thoughput Complicated, non-ectangula iegula stuctues (tacs, secto, sevo)... conventional pocessing inadequate

4 Nanoimpinting fo pattening ecoding media

5 Teis: Hitachi Ion Beam Modification

6 Nanoimpinting/Ion Modification Small-scale featues (0 nm) Lage-scale extensibility Smooth topogaphy Suitable fo iegula pattens non-ectangula, secto and sevo...viable fo pattening ecoding media, memoy elements and sensos

7 Nanoimpinting 6 millionmillion bits/squae inch!

8 Pattened media Outstanding Issue: Two-Dimensional ISI intefeence fom neighbos in both diections Conventional magnetic stoage educe bit-aspect-atio inceases ITI Optical ecoding lase spot spead; page oiented optical memoies Pobe ecoding pobe s point spead function Existing schemes (Vitebi, BCJR) cannot deal with 2D ISI

9 Joint Equalization and Decoding Schemes fo 2D ISI Geneal 2D ISI using 2D MMSE equalization and decoding using novel message-passing algoithms that tae advantage of the 2D dependence Sepaable 2D ISI using tubo equalization Singla et al., Iteative decoding and equalization fo 2-D ecoding channels, IEEE Tans. Magn., Sept

10 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) Recoding Channel x(i,j) {+,-} Channel ISI is 2D and linea Noise assumed to be AWGN

11 2D 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 Includes guad band j i j i j i j i j i j i w x x x x,,,,,, = o 3x3

12 . MMSE Equalization a(i,j) LDPC Encode x(i,j) (i,j) MMSE Channel ISI Equalize x (i,j) LDPC Decode a (i,j) Channel w(i,j) Extinsic Infomation Equalize may o may not iteate with the LDPC decode Soft infomation, estimated mean of the codewod, passed fom LDPC decode to equalize

13 Pefomance Bloc length 0000 egula (3,6) LDPC code Iteative MMSE and decoding 0 Bit eo ate in log ISI-fee It Wiene_0 Wiene No Equalization SNR [db]

14 2a. Full Gaph Message-Passing Chec Nodes (z) Codewod Bit Nodes (x) The sy is falling! Measued Data Nodes () h = i, j = xi, j +.5xi, j + 0.5xi, j xi, j 0 + w i, j

15 Full Gaph x(i,j) x(i,j+) x(i,j+2) Fom Chec Nodes x(i+,j) (i,j) (i+,j) x(i+,j+) (i,j+) (i+,j+) x(i+,j+2) x(i+2,j) x(i+2,j+) x(i+2,j+2) Same as befoe just a diffeent epesentation

16 Pefomance Full Gaph Message Passing 0 Bit eo ate in log ISI-fee Full Gaph_50 It Wiene_0 Wiene SNR [db]

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

18 2b. 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, Dec. 994

19 Gouped ISI Gaph Labeling of data nodes into 4 subsets Fo each iteation use data nodes of one label only J. A. O Sullivan, and N. Singla, Odeed subsets message-passing, Int l Symp. Infom. Theoy, Yoohama, Japan 2003.

20 Pefomance Odeed Subsets Message Passing 0 Bit eo ate in log ISI-fee Odeed Subsets_200 Full Gaph_50 It Wiene_0 Wiene SNR [db]

21 3. A Sepaable 2D 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 2D ISI apply existing one-dimensional equalization methods educed detecto complexity Tüchle et al., Tubo equalization: pinciples and new esults, IEEE Tans. On Comm., May 2002.

22 Row-Column Decode Diagam (i, j) Column MAP Detecto Row MAP Detecto LDPC Decode Had Decision Extinsic Infomation Conventional One-Dimensional Iteative Detecto Inputs to column detecto ae not binay Wu et al., Iteative detection and decoding fo sepaable two-dimensional intesymbol intefeence IEEE Tans. Magn., July 2003.

23 Pefomance Row-Column Decode Bit eo ate,log Base ISI-fee Row-Column Decode Odeed Subsets_200 Full Gaph_ SNR [db]

24 Conclusions Advanced ecoding schemes may give ise to 2D ISI Use joint detection and decoding fo 2D ISI MMSE equalization and decoding good pefomance, modeate complexity Message passing algoithms full gaph algoithm pefomance deteioated due to shot cycles odeed subsets message-passing gives best pefomance fo geneal 2D ISI Sepaable ISI decoding best pefomance low complexity appoximate channel esponse by sepaable esponse

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