Ordered Subsets Message- Passing

Transcription

1 Odeed Subsets Message- Passing Joseph A. O Suivan, Naveen Singa Eectonic Systes and Signas Reseach aboatoy ESSR) Depatent of Eectica Engineeing Washington Univesity in St. ouis 7/3/2003

2 Intoduction Systes with 2-D ISI Joint equaiation and decoding fo 2-D ISI Fu gaph essage-passing Odeed subsets essage-passing Density evoution Concusions

3 Pobe Desciption Joint equaiation and decoding fo channes having 2-D ISI As bit aspect atio educes inte-tac intefeence becoes significant Optica eoies Futue stoage edia: Pattened edia

4 Syste Mode a i, j) i, j) i, j) i, j) i, j) ECC Encode Channe ISI Channe w i, j) Equaie DPC codes used fo eo-coection i,j) {,-} Channe ISI is 2-D and inea Noise assued to be AWGN ECC Decode a

5 2-D Intesybo Intefeence Μ Ο Μ Μ Ο Μ Ο Μ Μ Μ Ο Μ GUARD BAND j i j i j i j i j i j i w,,,,,, = W X h R = * * X R wi,j) = h

6 Fu Gaph Message-Passing Chec Nodes ) Codewod Bit Nodes ) Measued Data Nodes ) h = i, j = i, j.5i, j 0.5i, j 0. 25i, j 0 w i, j

7 Message-Passing Su-Poduct) Codewod bit nodes to chec nodes Chec nodes to codewod bit nodes = N N )\ ' ) ' ) ) ) = N )\ ' ) ' ) 2 tanh ) 2 tanh

8 Message-Passing Su-Poduct) Codewod bit nodes to easued data nodes Measued data nodes to codewod bit nodes = ) ) )\ ' ) ' ) N N }) ) \ ' : { ) ' ) N f =

9 Fu Gaph i,j) i,j) i,j2) Fo Chec Nodes i,j) i,j) i,j) i,j) i,j) i,j) i,j2) i2,j) i2,j) i2,j2) Singa et a., Iteative decoding and equaiation fo 2-D ecoding channes, IEEE Tans. Magn., Sept

10 Pefoance Boc ength 0000 egua 3,6) DPC code 0 Fu Gaph Message-Passing Bit Eo Rate, og Base h = ISI-fee Fu Gaph_ SNR [db]

11 Fu Gaph Anaysis ength 4 cyces pesent which degade pefoance of essage-passing agoith i,j) i,j) i,j2) Fo Chec Nodes i,j) i,j) i,j) i,j) i,j) i,j) i,j2) i2,j) i2,j) i2,j2) Kschischang et a., Facto gaphs and the su-poduct agoith, IEEE Tans. Info. Theoy, Feb. 200.

12 Odeed Subsets Message-Passing Fo Iaging Measued data is gouped into subsets to incease ate of convegence Fo Decoding Measued data is gouped into subsets to eiinate shot ength cyces in the channe ISI gaph H. M. Hudson and R. S. ain, Acceeated iage econstuction using odeed subsets of pojection data, IEEE Tans. Medica Iaging, Dec. 994.

13 abeed ISI Gaph h = abeing of easued data nodes into 4 subsets Fo each iteation use easued data nodes of one abe ony

14 Pefoance 0 Odeed Subsets Message-Passing Bit Eo Rate, og Base h = ISI-fee OSMP_00 Fu Gaph_ SNR [db]

15 Ma-Poduct Decoding Ma-Poduct Agoith Bit Eo Rate, og Base h = ISI-fee OSMP_00 Fu Gaph_50 ISI-fee_sp OSMP_00_sp Fu Gaph_50_sp SNR [db]

16 Density Evoution Codewod bit nodes to chec nodes ) ) = N ) ) ' ' N )\ CONVOUTION Chec nodes to codewod bit nodes tanh ) = ) tanh 2 2 ' N )\ ) ' OOKUP TABE S.-Y Chung et a., On the design of ow-density paity-chec codes within db of the Shannon iit, IEEE Co. ettes, 2002.

17 Density Evoution Codewod bit nodes to easued data nodes Measued data nodes to codewod bit nodes = ) ) )\ ' ) ' ) N N CONVOUTION }) ) \ ' : { ) ' ) N f = MONTE CARO SIMUATION

18 Density Evoution Resuts Code Paaetes d v,d c ) 3,4) Theshod OSMP σ o ).4 Theshod Fu Gaph σ f ).34 SNR Diffeence 20ogσ o / σ f ) ,6) ,30) h =

19 Pefoance Bit Eo Rate, og Base Su-Poduct OSMP and Fu Gaph Message-Passing 0.47 h = BIAWGN Capacity DPC No ISI OSMP_00 Fu gaph_50 OSMP Theshod Fu Gaph Theshod SNR [db]

20 Geneaied Beief Popagation in between essage-passing agoiths and statistica physics Using nowedge of statistica physics to odify essage-passing agoiths to achieve bette pefoance in oopy gaphs Is thee a in between the OSMP agoith and GBP? Yedidia et a., "Geneaied Beief Popagation", Advances in Neua Infoation Pocessing Systes NIPS), Dec

21 Concusions Odeed subsets essage-passing using the idea fo iaging Used fo joint equaiation and decoding fo 2-D: gives bette pefoance than fu gaph agoith Siia esuts fo a-poduct agoith Density evoution esuts cooboate siuation esuts

22 Refeences Kavčić et a., Binay intesybo intefeence channes: Gaage codes, density evoution and code pefoance bounds, IEEE Tans. Info. Theoy, Juy T. Richadson and R. Ubane, The capacity of ow-density paity-chec codes unde essage-passing decoding, IEEE Tans. Info. Theoy, Feb. 200.

23 Ma-Poduct Decoding Rea suation is epaced by a opeato Deteines which codewod has agest APP In the negative og-ieihood doain apoduct becoes in-su which is the we-nown Vitebi agoith N. Wibeg, Codes and decoding on genea gaphs, Ph. D. dissetation, inöping Univ., inöping, Sweden, 996.