2D Coding for Future Perpendicular and Probe Recording

Transcription

1 2D Coding fo Futue Pependicula and Pobe Recoding Joseph A. O Sullivan Naveen Singla Ronald S. Indec Washington Univesity Saint Louis, Missoui s

2 Outline: 2D Coding fo 2D ISI Motivation: 2D Intesymbol Intefeence (ISIITI) 2D Pattened/Self-Oganized Media Iteative Equalization and Decoding LDPC Codes Pefomance Results Etensions Pefomance Pedictions thesholds fom density evolution Conclusions

3 Outstanding Issue: Two-Dimensional ISI Pattened media intefeence fom neighbos in 2D Conventional magnetic stoage educe bit-aspect-atio inceases ITI Pobe ecoding pobe s point spead function Optical ecoding lase spot spead; page oiented optical memoies nonlinea ISI Eisting schemes (Vitebi, BCJR) do not diectly etend to 2D ISI

4 Outline: 2D Coding fo 2D ISI Motivation: 2D Intesymbol Intefeence (ISIITI) 2D Pattened/Self-Oganized Media Iteative Equalization and Decoding LDPC Codes Pefomance Results Etensions Pefomance Pedictions thesholds fom density evolution Conclusions

5 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. 22.

6 Joint Equalization and Decoding Schemes fo 2D ISI Pefomance can be impoved by combining eo contol coding with equalization Base on eisting equalization schemes Jointly model channel ISI and paity chec mati fo eo contol code thee level gaph Employ novel message-passing algoithms that tae advantage of the 2D dependence Sepaable ISI: Reduced Compleity Tubo Equalization Singla et al., Iteative decoding and equalization fo 2-D ecoding channels, IEEE Tans. Magn., Sept. 22.

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

8 2D Linea Intesymbol Intefeence Μ Ο Μ Μ Ο 2 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,,,,,, =

9 2D Linea Intesymbol Intefeence Μ Ο Μ Μ Ο 2 Μ Ο Μ Μ Μ Ο Μ GUARD BAND ), ( ), ( ), ( ), ( 2, j w i m n h n j m i j i m n = = ), ( j w i = c b c b a b c b c h

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

11 Pefomance Bit eo ate in log Bloc length egula (3,6) LDPC code Iteative MMSE and decoding ISI-fee It Wiene_ Wiene No Equalization h = SNR [db] % ISI enegy

12 Pefomance Bit Eo Rate, Log Base Iteative MMSE Equalization and Decoding h.22 = BIAWGN Capacity LDPC No ISI Itw iene_ Wiene 33% ISI enegy SNR (db)

13 Full Gaph Message-Passing Chec Nodes (z) Codewod Bit Nodes () Measued Data Nodes () h = i, j = i, j.5i, j.5i, j. 25i, j w i, j

14 Pefomance - Full Gaph Message Passing.5 h = % ISI enegy Bit eo ate in log ISI-fee Full Gaph_5 It Wiene_ Wiene SNR [db]

15 Pefomance Bit Eo Rate, Log Base Full Gaph Message-Passing h.22 = BIAWGN Capacity LDPC No ISI Full gaph_5 Itw iene_ Wiene % ISI enegy SNR (db)

16 Motivation: Outline: 2D Coding 2D Pattened Media 2D Intesymbol Intefeence Iteative Equalization and Decoding LDPC Codes Pefomance Results Etensions Pefomance Pedictions thesholds fom density evolution Conclusions

17 Full Gaph (i,j) (i,j) (i,j2) Fom Chec Nodes (i,j) (i,j) (i,j) (i,j) (i,j) (i,j) (i,j2) (i2,j) (i2,j) (i2,j2) Same as befoe just a diffeent epesentation

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

19 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

20 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 23.

21 Pefomance - Odeed Subsets Message Passing.5 h = % ISI enegy Bit eo ate in log ISI-fee Odeed Subsets_2 Full Gaph_5 It Wiene_ Wiene SNR [db]

22 Pefomance Bit Eo Rate, Log Base Odeed Subsets Message-Passing h.22 = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 33% ISI enegy SNR (db)

23 Pefomance Bit Eo Rate, Log Base Joint Equalization and Decoding Schemes h = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 5% ISI enegy SNR (db)

24 A Sepaable 2D ISI (i, j) Row ISI y(i, j) Column ISI (i, j) Channel Detecto Sepaable Channel Response w(i,j) h =.5.5 =.25.5 (.5) Advantages of sepaable 2D ISI apply eisting one-dimensional equalization methods educed detecto compleity Tüchle et al., Tubo equalization: pinciples and new esults, IEEE Tans. On Comm., May 22.

25 Row-Column Decode Diagam (i, j) Column MAP Detecto Row MAP Detecto LDPC Decode Had Decision Etinsic 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 23.

26 Pefomance Bit eo ate,log Base Row-Column Decode.5 h = % ISI enegy ISI-fee Row-Column Decode Odeed Subsets_2 Full Gaph_ SNR [db]

27 Outline: 2D Coding fo 2D ISI Motivation: 2D Intesymbol Intefeence (ISIITI) 2D Pattened/Self-Oganized Media Iteative Equalization and Decoding LDPC Codes Pefomance Results Etensions Pefomance Pedictions thesholds fom density evolution Conclusions

28 Pefomance Pediction by Analysis Pedict Thesholds Avoid Simulations Basis fo Design Thesholds Depend on Code Family ISI Odeed Subsets Message Passing Equalization and Decoding Scheme Appoach: Pass Density Functions as Messages Density Evolution Bit eo ate in log ISI-fee Odeed Subsets_2 Full Gaph_5 It Wiene_ Wiene SNR [db] T. Richadson and R. Ubane, Capacity of low-density paity-chec Codes unde messagepassing decoding, IEEE Tans. Infom. Theoy, Feb. 2

29 Density Evolution Results Thesholds fo Full gaph algoithms Code Paametes (d v,d c ) Rate Theshold SNR [db] Full Gaph Theshold SNR [db] Modified Full Gaph (3,4) (3,6) (3,3)

30 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 compleity 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 compleity appoimate channel esponse by sepaable esponse

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32 Iteative MMSE Equalization and Decoding a ( i, j) ( i, j) ( i, j) ( i, j) ( i, j) LDPC Encode Channel ISI Equalize LDPC Decode a w( i, j) Etinsic Infomation Soft infomation, estimated mean of the codewod, passed fom LDPC decode to equalize E[ ] = = E[ ] P( = ) P( = ) W **[ h** E[ ]]

33 Pefomance Bit Eo Rate, Log Base Joint Equalization and Decoding Schemes h = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 4% ISI enegy SNR (db)

34 Pefomance Bit Eo Rate, Log Base Joint Equalization and Decoding Schemes h = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 5% ISI enegy SNR (db)

35 Pefomance Bit Eo Rate, Log Base Joint Equalization and Decoding Schemes h = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 4% ISI enegy SNR (db)

36 Pefomance Bit Eo Rate, Log Base Joint Equalization and Decoding Schemes h = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 4% ISI enegy SNR (db)

37 Pefomance Bit Eo Rate, Log Base Joint Equalization and Decoding Schemes h = BIAWGN Capacity LDPC No ISI Od Subsets_ Full gaph_5 Itw iene_ Wiene 4% ISI enegy SNR (db)

38 Pefomance Pediction by Density Evolution Assume messages ae i.i.d. andom vaiables Evolve message densities though the message maps If densities convege to desied density, then eo-fee tansmission possible othewise not Gives lowe bound on pefomance of message-passing scheme T. Richadson and R. Ubane, Capacity of low-density paity-chec Codes unde messagepassing decoding, IEEE Tans. Infom. Theoy, Feb. 2

39 Density Evolution fo Full Gaph Message-Passing Codewod bit nodes to chec nodes L ( l) ( l ) z = Lm m N ( ) ( l ) z' z' N ( )\ z Chec nodes to codewod bit nodes L CONVOLUTION tanh ( l) L z z L = ( ) tanh 2 2 ' N ( z)\ ( l ) ' z LOOKUP TABLE

40 Density Evolution Codewod bit nodes to measued data nodes Measued data nodes to codewod bit nodes = ) ( ) ( )\ ( ' ) ( ' ) ( N z l z m N m l m l m L L L CONVOLUTION }) ) \ ( ' : ({ ) ( ' ) ( m N L f L l m l m = MONTE CARLO SIMULATION