(
`
`Coding for Increased Distance
`With a d = 0 FDTS/DF Detector
`
`Barrett J. Brickner and Jay Moon
`May 25, 1995
`
`University of Minnesota
`CENTER FOR MICROMAGNETICS AND INFORMATION TECHNOLOGIES
`
`UMN EXHIBIT 2033
`LSI Corp. et al. v. Regents of Univ. of Minn.
`IPR2017-01068
`
`
`Page 1 of 6
`
`
`
`Coding for Increased Distance
`With a d = 0 FDTS/DF Detector
`
`Barrett J. Brickner and Jay Moon
`May 25, 1995
`
`University of Minnesota
`CENTER FOR MICROMAGNETICS AND INFORMATION TECHNOLOGIES
`
`UMN EXHIBIT 2033
`LSI Corp. et al. v. Regents of Univ. of Minn.
`IPR2017-01068
`
`
`Page 1 of 6
`
`
`
`Coding for Increased Distance ...
`
`1
`
`Summary
`
`Examination of the most likely error sequences for FDTS/DF with a d=0 code indicates that
`± ( ... , -2, + 2, -2, ... ) results from confusing the sequences separated by Bmin. This suggests that the use
`of a d = 0 code that suppresses sequences that could generate these errors would provide an increased
`signal margin. One of the sequences pairs that generates the minimum distance error must contain three
`or more consecutive transitions. Thus, the objective of the coding is to prevent tribit or longer transition
`runs.
`
`A convenient way of viewing the required code constraint is to apply a (d,k) = (0,2) constraint
`such that the output is assumed to be NRZI data rather than NRZ. A rate 4/5 block code that meets this
`constraint exists. However, codes with higher rates can be found to meet the (0,2) constraint.
`Simulations show that significant improvements result from the use of a 16/19 block code. A word of
`caution: the amount of improvement will depend on the particular pulse respon~e. but these codes will
`yield an improvement for densities of 2.5 or higher (assuming the ±(-2, +2,-2) sequence has minimum
`distance).
`
`An example of how a linear boundary may be implemented for a signal space detector (SSD)
`as previously presented is included for reference. Also, a detector using a signal dependent threshold
`is shown. This is unlikely to be useful for large tree depths (7), but may be of interest at a lower
`complexity.
`
`Barrett J . Brickner, Jay Moon
`
`University of Minnesota
`
`May 25, 1995
`
`
`Page 2 of 6
`
`
`
`Coding for Increased Distance ...
`
`2
`
`Description of Codes
`
`Figure 1 shows the state diagram for a
`(d,k) = (0,2) code with no constraint on the
`number of consecutive O's. The capacity of this
`code is C = 0.8791, which is less than 8/9.
`
`A 4/5 block code exists (shown in
`Figure 2) with the (0,2) constraint. This has a
`maximum of 8 consecutive O's, or a mmnnum
`transition spacing of 9T.
`
`To increase the code rate, a block code
`with rate 16/19 = 0.8421 exists. A state diagram
`for this code is given in Figure 3. This diagram
`yields a capacity of 0.8732.
`
`Table I. Detector Rate to Obtain 100 Mbit/sec
`
`Code
`
`Rate
`
`(0,4/4)
`
`(0,2)
`
`(0,2)
`
`(0,2)
`
`(1,7)
`
`8/9
`
`12/14
`
`16/19
`
`8/10
`
`2/3
`
`Detector
`Frequency
`
`113 MS/s
`
`117 MS/s
`
`119 MS/s
`
`125 MS/s
`
`150 MS/s
`
`Figure 1. (0,2) Code
`
`0000
`0001
`0010
`0011
`0100
`0101
`0110
`0111
`1000
`1001
`1010
`1011
`1100
`1101
`1110
`1111
`
`... 00001
`... 00010
`...
`00100
`... 00101
`...
`00110
`... 01000
`... 01001
`... 01010
`... 01100
`... 01101
`... 10000
`... 10001
`... 10010
`... 10100
`... 10101
`... 10110
`
`Figure 2. A Rate 4/5 (0,2) Block Code
`
`Figure 3. (0,2) Code, Max. 8T spacing for 1 's
`
`Barrett J. Brickner, Jay Moon
`
`University of Minnesota
`
`May 25, 1995
`
`
`Page 3 of 6
`
`
`
`Coding for Increased Distance ...
`
`3
`
`1E-01
`
`1[-02
`
`a:::
`·w
`ID
`
`1E-03
`
`lE-04
`
`1E- 05+---
`6
`
`-+----+---+----+---+---t--,f--+-'~"t-~---~
`10
`1 2
`13
`14
`15
`16
`17
`7
`11
`8
`9
`SNR (dB)
`
`Figure 4. Du=2.5: (d,k) = (0,4) Rate 8/9 Code
`
`------
`
`DFE
`-------+--
`,y= I
`
`-------
`
`,y =2
`----f3--
`
`,y=3 -,y= 4
`
`-----.-
`
`,y = 5
`
`--+-(cid:173)
`,y= I
`
`,y = 2
`--E3-(cid:173)
`
`----(cid:173)(cid:143) FE
`,y = 3 -,y =4
`
`----..:(cid:173)
`,y = 5
`
`1E-05-t---+---+----i-----+---t------1r---t-~>t-~-t----,--~
`10
`12
`13
`14 15
`16
`17
`7
`1 1
`6
`8
`9
`SNR (dB)
`
`Figure 5. Du=2.5: (d,k) = (0,8), NRZI (0,2), Rate 4/5 Block Code
`
`e'.J 1 E- 0 3 -...--1---+-----+-------i
`ID
`
`----(cid:173)(cid:143) FE
`
`---+--(cid:173)
`,y = I
`
`,y=2
`--E3-(cid:173)
`
`,y=3 -,y = 4
`
`,y= 5
`
`1E-05+---+---+--
`7
`8
`6
`
`-+---+-
`10
`9
`
`-+---t----'.'JliE-'-~+--+'--+--~
`11
`12
`13
`14 15
`16
`17
`SNR (dB)
`
`Figure 6. Du=2.5: (d,k) = (0,7), NRZI (0,2) Rate 16/19 Block Code
`
`Barrett J . Brickner, Jay Moon
`
`University of Minnesota
`
`May 25 , 1995
`
`
`Page 4 of 6
`
`
`
`Coding for Increased Distance ...
`
`4
`
`SSD Using Piecewise Linear Boundaries
`
`2~-~ -~ - -~ --
`
`- ~ - - -~
`
`(f0,f1)
`/
`
`..... C o , - - - - - - -----1- - -~~------1
`
`----
`
`~
`
`-1
`
`(g0,g1)
`
`- 2 - - - - -- -~ - --~ - - -~
`-2
`-1
`0
`x(k)
`
`2
`
`Figure 7. Separating Two Points in Space
`
`'T
`
`i=O
`
`'T
`
`i=O
`
`D---__,
`
`2(f0-g0)
`
`2(f1 -g1)
`
`go2- t<f + g12 -ff
`
`Figure 8. Boundary Using an FIR Filter
`
`Barrett J. Brickner, Jay Moon
`
`University of Minnesota
`
`May 25, 1995
`
`
`Page 5 of 6
`
`
`
`Coding for Increased Distance ...
`
`5
`
`A Signal-Dependent Threshold Implementation
`
`2 r--- - - -~- - - - - , -- - -----.----~
`
`---I
`
`~ Or----~----=...+-=' - -~ --
`'--'
`~
`
`X
`
`-
`
`~
`
`-1
`
`0
`
`- 2 ' - - -- - - - - - - ' - --------'----------'-"------"--
`- 2
`-1
`0
`x(k)
`
`--.J
`2
`
`Figure 9. Two-Dimensional Signal Space
`
`M
`-U
`X
`
`-b 1
`+b 1
`
`Xk
`- - - - - r - - -........ D +---..... I
`
`ROM
`
`Figure 10. Variable Threshold Using a ROM
`
`D
`
`....
`ak-1
`
`Barrett J. Brickner, Jay Moon
`
`University of Minnesota
`
`May 25, 1995
`
`
`Page 6 of 6
`
`
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