Use of snake-in-the-box codes for reliable identification of tracks in servo fields of a disk drive

• US 20020126407A1
• Filed: 01/05/2001
• Published: 09/12/2002
• Est. Priority Date: 01/05/2001
• Status: Active Grant

• Current Assignee: Intovoice Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Etzion, Tuvi, Blaum, Mario
• Granted Patent: US 6,496,312 B2
• Time in Patent Office: Days
• US Class Current: 360/49
• CPC Class Codes: G11B 20/12 Formatting, e.g. arrangement of data block or words on the record carriers within interface between computers and data recorders G06F3/06
• CPC Class Codes: G11B 20/18 Error detection or correction; Testing , e.g. of drop-outs
• CPC Class Codes: G11B 2220/20 Disc-shaped record carriers
• CPC Class Codes: G11B 27/3027 used signal is digitally coded
• CPC Class Codes: G11B 5/59633 Servo formatting G11B5/59627, G11B5/59677, G11B5/59683, G11B5/59688 take precedence

Abstract

A “snake-in-the-box” (SITB) code is used to encode a track identifier (TID) in a servo sector of a disk drive to identify a particular track on the disk surface. The SITB code describes the longest possible vector that can fit into a finite space, and comprises a type of difference-preserving code. When an SITB code is used for the TID, any single bit error in the TID will be detected. The Hamming distance for TIDs of adjacent tracks is 1 with a SITB code, as with a Gray code. However, for TIDs of tracks that are not adjacent, the Hamming distance is at least 2 with a SITB code.

Claims

1. A method for encoding a track identifier for servo control in a data storage device, comprising:

(a) encoding the track identifier as a snake-in-the-box code; and

(b) storing the encoded track identifier as servo information on the data storage device.

2. The method of claim 1, wherein the encoded track identifier contains bits identifying a track position, as well as bits for error detection.

3. The method of claim 2, wherein the snake-in-the-box code allows for detection of one or more errors in the encoded track identifier.

4. The method of claim 1, wherein adjacent ones of the encoded track identifiers are at a distance of exactly 1 and non-adjacent ones of the encoded track identifiers are at a distance of at least 2.

5. The method of claim 1, further comprising mapping k bits of the track identifier into n bits of a track identifier field in a logically efficient way, such that a result is the snake-in-the-box code.

6. The method of claim 5, wherein an input to the encoding step is given by a k-bit vector (I[1], I[2], . . . , I[k]) that represents the track identifier and an output from the encoding step is an n-bit vector (ENC[1], ENC[2], . . . , ENC[n]) that represents the track identifier field.

7. The method of claim 6, wherein k=15 and n=19.

8. The method of claim 7, wherein the encoding step comprises the steps of:

(1) computing SLAST according to the following;

SLAST←

{overscore (I[13])}I[14]I[15]

(2) computing SENC[9, 2, 3, 4, 10] according to the following;

SENC[9]←

I[9]

SENC[2]←

I[9]I[10]

SENC[3]←

I[10]⊕

I[11]

SENC[4]←

I[11]⊕

I[12]

SENC[10]←

I[12]⊕

SLAST

(3) computing SR[1-5] according to the following;

SR[1]←

0

SR[2]←

({overscore (I[13])}⊕

I[14]⊕

I[15]){overscore (I[14]I[15])}

SR[3]←

I[13]⊕

I[14]

SR[4]←

I[13]

SR[5]←

{overscore (I[13])}{overscore (I[14]I[15])}

(4) computing ST[1-4] according to the following;

ST[1]←

I[10]I[11]I[12]

ST[2]←

{overscore (I[10])}I[11]I[12]

ST[3]←

{overscore (I[11])}I[12]

ST[4]←

{overscore (I[12])}

(5) computing SP[1-5] according to the following;

SP[1]←

(ST[1]SR[4])({overscore (ST[1])}SR[1])

SP[2]←

(ST[2]SR[4])({overscore (ST[2])}SR[2])

SP[3]←

(ST[3]SR[4])({overscore (ST[3])}SR[3])

SP[4]←

(ST[1]SR[1])(ST[2]SR[2])(ST[3]SR[3])(ST[4]SR[4])

SP[5]←

SR[5]

(6) computing SENC[6, 7, 8, 2, 5] according to the following;

SENC[6]←

(SLAST(SP[1]⊕

SENC[9]))({overscore (SLAST)}SENC[9])

SENC[7]←

(SLAST(SP[2]⊕

SENC[2]))({overscore (SLAST)}SENC[2])

SENC[8]←

(SLAST(SP[3]⊕

SENC[3]))({overscore (SLAST)}SENC[3])

SENC[1]←

(SLAST(SP[4]⊕

SENC[4]))({overscore (SLAST)}SENC[4])

SENC[5]←

(SLAST(SP[5]⊕

SENC[10]))({overscore (SLAST)}SENC[10])

(7) computing LAST according to the following;

LAST←

I[9]I[10]1[11]I[12]I[13]I[14]I[15]

(8) computing ENC[1-9] according to the following;

ENC[1]←

I[1]

ENC[2]←

I[1]⊕

I[2]

ENC[3]←

I[2]⊕

I[3]

ENC[4]←

I[3]⊕

I[4]

ENC[5]←

I[4]⊕

I[5]

ENC[6]←

I[5]⊕

I[6]

ENC[7]←

I[6]⊕

I[7]

ENC[8]←

I[7]⊕

I[8]

ENC[9]←

I[8]⊕

LAST

(9) computing T[1-8] according to the following;

T[1]←

I[2]I[3]I[4]I[5]I[6]I[7]I[8]

T[2]←

{overscore (I[2])}I[3]I[4]I[5]I[6]I[7]I[8]

T[3]←

{overscore (I[3])}I[4]I[5]I[6]I[7]I[8]

T[4]←

{overscore (I[4])}I[5]I[6]I[7]I[8]

T[5]←

{overscore (I[5])}I[6]I[7]I[8]

T[6]←

{overscore (I[6])}I[7]I[8]

T[7]←

{overscore (I[7])}I[8]

T[8]←

{overscore (I[8])}

(10) computing P[1-10] according to the following;

P[1]←

(T[1]SENC[9])({overscore (T[1])}SENC[1])

P[2]←

(T[2]SENC[9])({overscore (T[2])}SENC[2])

P[3]←

(T[3]SENC[9])({overscore (T[3])}SENC[3])

P[4]←

(T[4]SENC[9])({overscore (T[4])}SENC[4])

P[5]←

(T[5]SENC[9])({overscore (T[5])}SENC[5])

P[6]←

(T[6]SENC[9])({overscore (T[6])}SENC[6])

P[7]←

(T[7]SENC[9])({overscore (T[7])}SENC[7])

P[8]←

(T[8]SENC[9])({overscore (T[7])}SENC[8])

P[9]←

SENC[10]

P[10]←

(T[1]SENC[1])(T[2]SENC[2])(T[3]SENC[3])(T[4]SENC[4])(T[5]SENC[5])(T[6]SENC[6])(T[7]SENC[7])(T[8]SENC[8])

(11) computing ENC[10-19] according to the following;

ENC[10]←

(LAST(P[1]⊕

ENC[1]))({overscore (LAST)}ENC[1])

ENC[11]←

(LAST(P[2]⊕

ENC[2]))({overscore (LAST)}ENC[2])

ENC[12]←

(LAST(P[3]⊕

ENC[3]))({overscore (LAST)}ENC[3])

ENC[13]←

(LAST(P[4]⊕

ENC[4]))({overscore (LAST)}ENC[4])

ENC[14]←

(LAST(P[5]⊕

ENC[5]))({overscore (LAST)}ENC[5])

ENC[15]←

(LAST(P[6]⊕

ENC[6]))({overscore (LAST)}ENC[6])

ENC[16]←

(LAST(P[7]⊕

ENC[7]))({overscore (LAST)}ENC[7])

ENC[17]←

(LAST(P[8]⊕

ENC[8]))({overscore (LAST)}ENC[8])

ENC[18]←

(LAST(P[9]⊕

ENC[9]))({overscore (LAST)}ENC[9])

ENC[19]←

LASTP[10]

(12) wherein the symbol “

←

”

stores a result, the symbol “

”

is a Boolean OR operation, the symbol “

”

is a Boolean AND operation, the symbol “

⊕

”

is a Boolean XOR operation, the overline “

⁻

”

indicates bit negation, the brackets “

[ ]”

indicate a bit position, and the parentheses indicate a precedence order.

9. A method for decoding a track identifier for servo control in a data storage device, comprising:

(a) accessing an encoded track identifier stored as servo information on the data storage device; and

(b) decoding the track identifier as a snake-in-the-box code.

10. The method of claim 9, wherein the encoded track identifier contains bits identifying a track position, as well as bits for error detection.

11. The method of claim 9, wherein the snake-in-the-box code allows for detection of one or more errors in the encoded track identifier.

12. The method of claim 9, wherein adjacent ones of the encoded track identifiers are at a distance of exactly 1 and non-adjacent ones of the encoded track identifiers are at a distance of at least 2.

13. The method of claim 9, wherein the decoding step further comprises mapping n bits of a track identifier field into k bits of the encoded track identifier in a logically efficient way, such that a result is the track identifier.

14. The method of claim 13, wherein an input to the decoding step is given by a n-bit vector (B[1], B[2], . . . , B[n]) that represents the track identifier field and an output from the decoding step is given by a k-bit vector (I[1], I[2], . . . , I[k]) that represents the track identifier.

15. The method of claim 14, wherein n=19 and k=15.

16. The method of claim 15, wherein the decoding step comprises the steps of:

(1) computing I[1-8] and LASTF according to the following;

I[1]←

B[1]

I[2]←

I[1]⊕

B[2]

I[3]←

I[2]⊕

B[3]

I[4]←

I[3]⊕

B[4]

I[5]←

I[4]⊕

B[5]

I[6]←

I[5]⊕

B[6]

1[7]←

I[6]⊕

B[7]

I[8]←

I[7]⊕

B[8]

LASTF←

I[8]⊕

B[9]

(2) computing P[1-9] according to the following;

P[l]←

B[1]⊕

B[10]

P[2]←

B[2]⊕

B[11]

P[3]←

B[3]⊕

B[12]

P[4]←

B[4]⊕

B[13]

P[5]←

B[5]⊕

B[14]

P[6]←

B[6]⊕

B[15]

P[7]←

B[7]⊕

B[16]

P[8]←

B[8]⊕

B[17]

P[9]←

B[9]⊕

B[18]

(3) computing T[1-8] according to the following;

T[l]←

I[2]I[3]I[4]I[5]I[6]I[7]I[8]

T[2]←

{overscore (I[2])}I[3]I[4]I[5]I[6]I[7]I[8]

T[3]←

{overscore (I[3])}I[4]I[5]I[6]I[7]I[8]

T[4]←

{overscore (I[4])}I[5]I[6]I[7]I[8]

T[5]←

{overscore (I[5])}I[6]I[7]1[8]

T[6]←

{overscore (I[6])}I[7]I[8]

T[7]←

{overscore (I[7])}I[8]

T[8]←

{overscore (I[8])}

(4) computing R[1-10] according to the following;

R[1]←

(P[1]T[1])(P[2]T[2])(P[3]T[3])(P[4]T[4])(P[5]T[5])(P[6]T[6])(P[7]T[7])(P[8]T[8])

R[2]←

(P[2]{overscore (T[2])})(P[10]T[2])

R[3]←

(P[3]{overscore (T[3])})(P[10]T[3])

R[4]←

(P[4]{overscore (T[4])})(P[10]T[4])

R[5]←

P[9]

R[6]←

(P[6]{overscore (T[6])})(P[10]T[6])

R[7]←

(P[7]{overscore (T[7])})(P[10]T[7])

R[8]←

(P[8]{overscore (T[8])})(P[10]T[8])

R[9]←

(P[1]{overscore (T[1])})(P[10]T[1])

R[10]←

(P[5]{overscore (T[5])})(P[10]T[5])

(5) computing 1[9-12] and SLAST according to the following;

I[9]←

LASTR[1]

I[10]←

LAST(I[9]⊕

R[2])

I[11]←

LAST(I[10]⊕

R[3])

I[12]←

LAST(I[11t]⊕

R[4])

SLAST←

I[12]⊕

R[5]

(6) computing SP[1-5] according to the following;

SP[1]←

R[1]⊕

R[6]

SP[2]←

R[2]⊕

R[7]

SP[3]←

R[3]⊕

R[8]

SP[4]←

R[4]⊕

R[9]

SP[5]←

R[5]⊕

R[10]

(7) computing ST[1-4] according to the following;

ST[1]←

I[10]I[11]I[12]

ST[2]←

{overscore (I[10])}I[11]I[12]

ST[3]←

{overscore (I[11])}I[12]

ST[4]←

{overscore (I[12])}

(8) computing SR[1-4] according to the following;

SR[1]←

(SP[2]{overscore (ST[2])})(SP[4]ST[2])

SR[2]←

(SP[3]{overscore (ST[3])})(SP[4]ST[3])

SR[3]←

(SP[1]ST[1])(SP[2]ST[2])(SP [3]ST[3])(SP[4]ST[4])

SR[4]←

SP[5]

(9) computing I[13-15] according to the following;

I[13]←

LASTSLASTSR[3]

I[14]←

LASTSLAST(SR[2]⊕

SR[3])

I[15]←

LASTSLAST(SR[1]⊕

SR[2]⊕

SR[3]⊕

SR[4])

(10) wherein the symbol “

←

”

stores a result, the symbol “

”

is a Boolean OR operation, the symbol “

”

is a Boolean AND operation, the symbol “

⊕

”

is a Boolean XOR operation, the overline “

⁻

”

indicates bit negation, the brackets “

[ ]”

indicate a bit position, and the parentheses indicate a precedence order.

18. The apparatus of claim 17, wherein the encoded track identifier contains bits identifying a track position, as well as bits for error detection.

19. The apparatus of claim 18, wherein the snake-in-the-box code allows for detection of one or more errors in the encoded track identifier.

20. The apparatus of claim 17, wherein adjacent ones of the encoded track identifiers are at a distance of exactly 1 and non-adjacent ones of the encoded track identifiers are at a distance of at least 2.

21. The apparatus of claim 17, further comprising means for mapping k bits of the track identifier into n bits of a track identifier field in a logically efficient way, such that a result is the snake-in-the-box code.

22. The apparatus of claim 21, wherein an input to the means for encoding is given by a k-bit vector (I[1], I[2], . . . , I[k]) that represents the track identifier and an output from the means for encoding is an n-bit vector (ENC[1], ENC[2], . . . , ENC[n]) that represents the track identifier field.

23. The apparatus of claim 22, wherein k=15 and n=19.

24. The apparatus of claim 23, wherein the means for encoding comprises:

(1) means for computing SLAST according to the following;

SLAST←

{overscore (I[13])}I[14]I[15]

(2) means for computing SENC[9, 2, 3, 4, 10] according to the following;

SENC[9]←

I[9]

SENC[2]←

I[9]I[10]

SENC[3]←

I[10]⊕

I[11]

SENC[4]←

I[11]⊕

1[12]

SENC[10]←

I[12]⊕

SLAST

(3) means for computing SR[1-5] according to the following;

SR[1]←

0

SR[2]←

({overscore (I[13])}⊕

I[14]⊕

I[15]){overscore (I[14]I[15])}

SR[3]←

I[13]⊕

I[14]

SR[4]←

I[13]

SR[5]←

{overscore (I[13])}{overscore (I[14]I[15])}

(4) means for computing ST[1-4] according to the following;

ST[1]←

I[10]I[11]I[12]

ST[2]←

{overscore (I[10])}I[11]I[12]

ST[3]←

{overscore (I[11])}I[12]

ST[4]←

{overscore (I[12])}

(5) means for computing SP[1-5] according to the following;

SP[1]←

(ST[1]SR[4])({overscore (ST[1])}SR[1])

SP[2]←

(ST[2]SR[4])({overscore (ST[2])}SR[2])

SP[3]←

(ST[3]SR[4])({overscore (ST[3])}SR[3])

SP[4]←

(ST[1]SR[1])(ST[2]SR[2])(ST[3]SR[3])(ST[4]SR[4])

SP[5]←

SR[5]

(6) means for computing SENC[6, 7, 8, 2, 5] according to the following;

SENC[6]←

(SLAST(SP[1]⊕

SENC[9]))({overscore (SLAST)}SENC[9])

SENC[7]←

(SLAST(SP[2]⊕

SENC[2]))({overscore (SLAST)}SENC[2])

SENC[8]←

(SLAST(SP[3]⊕

SENC[3]))({overscore (SLAST)}SENC[3]) (7)

SENC[1]←

(SLAST(SP[4]⊕

SENC[4]))({overscore (SLAST)}SENC[4])

SENC[5]←

(SLAST(SP[5]⊕

SENC[10]))({overscore (SLAST)}SENC[10])

(7) means for computing LAST according to the following;

LAST←

I[9]I[10]1[11]I[12]I[13]I[14]I[15]

(8) means for computing ENC[1-9] according to the following;

ENC[1]←

I[1]

ENC[2]←

I[1]⊕

I[2]

ENC[3]←

I[2]⊕

I[3]

ENC[4]←

I[3]⊕

I[4]

ENC[5]←

I[4]⊕

I[5]

ENC[6]←

I[5]⊕

I[6]

ENC[7]←

I[6]⊕

I[7]

ENC[8]←

I[7]⊕

I[8]

ENC[9]←

I[8]⊕

LAST

(9) means for computing T[1-8] according to the following;

T[1]←

I[2]I[3]I[4]I[5]I[6]I[7]I[8]

T[2]←

{overscore (I[2])}I[3]I[4]I[5]I[6]I[7]I[8]

T[3]←

{overscore (I[3])}I[4]I[5]I[6]I[7]I[8]

T[4]←

{overscore (I[4])}I[5]I[6]I[7]I[8]

T[5]←

{overscore (I[5])}I[6]I[7]I[8]

T[6]←

{overscore (I[6])}I[7]I[8]

T[7]←

{overscore (I[7])}I[8]

T[8]←

{overscore (I[8])}

(10) means for computing P[1-10] according to the following;

P[1]←

(T[1]SENC[9])({overscore (T[1])}SENC[1])

P[2]←

(T[2]SENC[9])({overscore (T[2])}SENC[2])

P[3]←

(T[3]SENC[9])({overscore (T[3])}SENC[3])

P[4]←

(T[4]SENC[9])({overscore (T[4])}SENC[4])

P[5]←

(T[5]SENC[9])({overscore (T[5])}SENC[5])

P[6]←

(T[6]SENC[9])({overscore (T[6])}SENC[6])

P[7]←

(T[7]SENC[9])({overscore (T[7])}SENC[7])

P[8]←

(T[8]SENC[9])({overscore (T[8])}SENC[8])

P[9]←

SENC[10]

P[10]←

(T[1]SENC[1])(T[2]SENC[2])(T[3]SENC[3])(T[4]SENC[4])(T[5]SENC[5])(T[6]SENC[6])(T[7]SENC[7])(T[8]SENC[8])

(11) means for computing ENC[10-19] according to the following;

ENC[10]←

(LAST(P[1]⊕

ENC[1]))({overscore (LAST)}ENC[1])

ENC[11]←

(LAST(P[2]⊕

ENC[2]))({overscore (LAST)}ENC[2])

ENC[12]←

(LAST(P[3]⊕

ENC[3]))({overscore (LAST)}ENC[3])

ENC[13]←

(LAST(P[4]⊕

ENC[4]))({overscore (LAST)}ENC[4])

ENC[14]←

(LAST(P[5]⊕

ENC[5]))({overscore (LAST)}ENC[5])

ENC[15]←

(LAST(P[6]⊕

ENC[6]))({overscore (LAST)}ENC[6])

ENC[16]←

(LAST(P[7]⊕

ENC[7]))({overscore (LAST)}ENC[7])

ENC[17]←

(LAST(P[8]⊕

ENC[8]))({overscore (LAST)}ENC[8])

ENC[18]←

(LAST(P[9]⊕

ENC[9]))({overscore (LAST)}ENC[9])

ENC[19]←

LASTP[10]

(12) wherein the symbol “

←

”

stores a result, the symbol “

”

is a Boolean OR operation, the symbol “

”

is a Boolean AND operation, the symbol “

⊕

”

is a Boolean XOR operation, the overline “

⁻

”

indicates bit negation, the brackets “

[ ]”

indicate a bit position, and the parentheses indicate a precedence order.

26. The apparatus of claim 25, wherein the encoded track identifier contains its identifying a track position, as well as bits for error detection.

27. The apparatus of claim 25, wherein the snake-in-the-box code allows for detection of one or more errors in the encoded track identifier.

28. The apparatus of claim 25, wherein adjacent ones of the encoded track identifiers are at a distance of exactly 1 and non-adjacent ones of the encoded track identifiers are at a distance of at least 2.

29. The apparatus of claim 25, wherein the means for decoding further comprises means for mapping n bits of a track identifier field into k bits of the encoded track identifier in a logically efficient way, such that a result is the track identifier.

30. The apparatus of claim 29, wherein an input to the means for decoding is given by a n-bit vector (B[1], B[2], . . . , B[n]) that represents the track identifier field and an output from the means for decoding is given by a k-bit vector (I[1], I[2], . . . , I[k]) that represents the track identifier.

31. The apparatus of claim 30, wherein n=19 and k=15.

32. The apparatus of claim 31, wherein the means for decoding comprises:

(1) means for computing I[1-8] and LASTF according to the following;

I[1]←

B[1]

I[2]←

I[1]⊕

B[2]

I[3]←

I[2]⊕

B[3]

I[4]←

I[3]⊕

B[4]

I[5]←

I[4]⊕

B[5]

I[6]←

I[5]⊕

B[6]

I[7]←

I[6]⊕

B[7]

I[8]←

I[7]⊕

B[8]

LASTF←

I[8]⊕

B[9]

(2) means for computing P[1-9] according to the following;

P[1]←

B[l]⊕

B[10]

P[2]←

B[2]⊕

B[11]

P[3]←

B[3]⊕

B[12]

P[4]←

B[4]⊕

B[13]

P[5]←

B[5]⊕

B[14]

P[6]←

B[6]⊕

B[15]

P[7]←

B[7]⊕

B[16]

P[8]←

B[8]⊕

B[17]

P[9]←

B[9]⊕

B[18]

(3) means for computing T[1-8] according to the following;

T[1]←

I[2]I[3]I[4]I[5]I[6]I[7]I[8]

T[2]←

{overscore (I[2])}I[3]I[4]I[5]I[6]I[7]I[8]

T[3]←

{overscore (I[3])}I[4]I[5]I[6]I[7]I[8]

T[4]←

{overscore (I[4])}I[5]I[6]I[7]I[8]

T[5]←

{overscore (I[5])}I[6]I[7]I[8]

T[6]←

{overscore (I[6])}I[7]I[8]

T[7]←

{overscore (I[7])}I[8]

T[8]←

{overscore (I[8])}

(4) means for computing R[1-10] according to the following;

R[1]←

(P[1]T[1])(P[2]T[2])(P[3]T[3])(P[4]T[4])(P[5]T[5])(P[6]T[6])(P[7]T[7])(P[8]T[8])

R[2]←

(P[2]{overscore (T[2])})(P[10]T[2])

R[3]←

(P[3]{overscore (T[3])})(P[10]T[3])

R[4]←

(P[4]{overscore (T[4])})(P[10]T[4])

R[5]←

P[9]

R[6]←

(P[6]{overscore (T[6])})(P[10]T[6])

R[7]←

(P[7]{overscore (T[7])})(P[10]T[7])

R[8]←

(P[8]{overscore (T[8])})(P[10]T[8])

R[9]←

(P[1]{overscore (T[1])})(P[10]T[1])

R[10]←

(P[5]{overscore (T[5])})(P[10]T[5])

(5) means for computing I[9-12] and SLAST according to the following;

I[9]←

LASTR[1]

I[10]←

LAST(I[9]⊕

R[2])

I[11]←

LAST(I[10]⊕

R[3])

I[12]←

LAST(I[11]⊕

R[4])

SLAST←

I[12]⊕

R[5]

(6) means for computing SP[1-5] according to the following;

SP[1]←

R[1]⊕

R[6]

SP[2]←

R[2]⊕

R[7]

SP[3]←

R[3]⊕

R[8]

SP[4]←

R[4]⊕

R[9]

SP[5]←

R[5]⊕

R[10]

(7) means for computing ST[1-4] according to the following;

ST[1]←

I[10]I[11]I[12]

ST[2]←

{overscore (I[10])}I[11]I[12]

ST[3]←

{overscore (I[11])}I[12]

ST[4]←

{overscore (I[12])}

(8) means for computing SR[1-4] according to the following;

SR[1]←

(SP[2]{overscore (ST[2])})(SP[4]ST[2])

SR[2]←

(SP[3]{overscore (ST[3])})(SP[4]ST[3])

SR[3]←

(SP[1]ST[1])(SP[2]ST[2])(SP [3]ST[3])(SP[4]ST[4])

SR[4]←

SP[5]

(9) means for computing I[13-15] according to the following;

I[13]←

LASTSLASTSR[3]

I[14]←

LASTSLAST(SR[2]⊕

SR[3])

I[15]←

LASTSLAST(SR[1]⊕

SR[2]⊕

SR[3]⊕

SR[4])

(10) wherein the symbol “

←

”

stores a result, the symbol “

”

is a Boolean OR operation, the symbol “

”

is a Boolean AND operation, the symbol “

⊕

”

is a Boolean XOR operation, the overline “

⁻

”

indicates bit negation, the brackets “

[ ]”

indicate a bit position, and the parentheses indicate a precedence order.

17. An apparatus for encoding a track identifier for servo control in a data storage device, comprising:

(a) means for encoding the track identifier as a snake-in-the-box code; and

(b) means for storing the encoded track identifier as servo information on the data storage device.

25. An apparatus for decoding a track identifier for servo control in a data storage device, comprising:

(a) means for accessing an encoded track identifier stored as servo information on the data storage device; and

(b) means for decoding the track identifier as a snake-in-the-box code.

33. An article of manufacture embodying logic for encoding a track identifier for servo control in a data storage device, the logic comprising:

(a) encoding the track identifier as a snake-in-the-box code; and

(b) storing the encoded track identifier as servo information on the data storage device.

34. The article of manufacture of claim 33, wherein the encoded track identifier contains bits identifying a track position, as well as bits for error detection.

35. The article of manufacture of claim 34, wherein the snake-in-the-box code allows for detection of one or more errors in the encoded track identifier.

36. The article of manufacture of claim 33, wherein adjacent ones of the encoded track identifiers are at a distance of exactly 1 and non-adjacent ones of the encoded track identifiers are at a distance of at least 2.

37. The article of manufacture of claim 33, the logic further comprising mapping k bits of the track identifier into n bits of a track identifier field in a logically efficient way, such that a result is the snake-in-the-box code.

38. The article of manufacture of claim 37, wherein an input to the encoding logic is given by a k-bit vector (I[1], I[2], . . . , I[k]) that represents the track identifier and an output from the encoding logic is an n-bit vector (ENC[1], ENC[2], . . . , ENC[n]) that represents the track identifier field.

39. The article of manufacture of claim 38, wherein k=15 and n=19.

40. The article of manufacture of claim 39, wherein the encoding logic comprises the logic of:

(1) computing SLAST according to the following;

SLAST←

{overscore (I[13])}I[14]I[15]

(2) computing SENC[9, 2, 3, 4, 10] according to the following;

SENC[9]←

I[9]

SENC[2]←

I[9]1[10]

SENC[3]←

I[10]⊕

I[11]

SENC[4]←

I[11]⊕

I[12]

SENC[10]←

I[12]⊕

SLAST

(3) computing SR[1-5] according to the following;

SR[1]←

0

SR[2]←

({overscore (I[13])}⊕

I[14]⊕

I[15]){overscore (I[14]I[15])}

SR[3]←

I[13]⊕

I[14]

SR[4]←

I[13]

SR[5]←

{overscore (I[13])}{overscore (I[14]I[15])}

(4) computing ST[1-4] according to the following;

ST[1]←

I[10]I[11]I[12]

ST[2]←

{overscore (I[10])}I[11]I[12]

ST[3]←

{overscore (I[11])}I[12]

ST[4]←

{overscore (I[12])}

(5) computing SP[1-5] according to the following;

SP[1]←

(ST[1]SR[4])({overscore (ST[1])}SR[1])

SP[2]←

(ST[2]SR[4])({overscore (ST[2])}SR[2])

SP[3]←

(ST[3]SR[4])({overscore (ST[3])}SR[3])

SP[4]←

(ST[1]SR[1])(ST[2]SR[2])(ST[3]SR[3])(ST[4]SR[4])

SP[5]←

SR[5]

(6) computing SENC[6, 7, 8, 2, 5] according to the following;

SENC[6]←

(SLAST(SP[1]⊕

SENC[9]))({overscore (SLAST)}SENC[9])

SENC[7]←

(SLAST(SP[2]⊕

SENC[2]))({overscore (SLAST)}SENC[2])

SENC[8]←

(SLAST(SP[3]⊕

SENC[3]))({overscore (SLAST)}SENC[3]) (7)

SENC[1]←

(SLAST(SP[4]⊕

SENC[4]))({overscore (SLAST)}SENC[4])

SENC[5]←

(SLAST(SP[5]⊕

SENC[10]))({overscore (SLAST)}SENC[10])

(7) computing LAST according to the following;

LAST←

I[9]I[10]1[11]I[12]I[13]I[14]I[15]

(8) computing ENC[1-9] according to the following;

ENC[1]←

I[1]

ENC[2]←

I[1]⊕

I[2]

ENC[3]←

I[2]⊕

I[3]

ENC[4]←

I[3]⊕

I[4]

ENC[5]←

I[4]⊕

I[5]

ENC[6]←

I[5]⊕

I[6]

ENC[7]←

I[6]⊕

I[7]

ENC[8]←

I[7]⊕

I[8]

ENC[9]←

1[8]⊕

LAST

(9) computing T[1-8] according to the following;

T[1]←

I[2]I[3]I[4]I[5]I[6]I[7]I[8]

T[2]←

{overscore (I[2])}I[3]I[4]I[5]I[6]I[7]I[8]

T[3]←

{overscore (I[3])}I[4]I[5]I[6]I[7]I[8]

T[4]←

{overscore (I[4])}I[5]I[6]I[7]I[8]

T[5]←

{overscore (I[5])}I[6]I[7]I[8]

T[6]←

{overscore (I[6])}I[7]I[8]

T[7]←

{overscore (I[7])}I[8]

T[8]←

{overscore (I[8])}

(10) computing P[1-10] according to the following;

P[1]←

(T[1]SENC[9])({overscore (T[1])}SENC[1])

P[2]←

(T[2]SENC[9])({overscore (T[2])}SENC[2])

P[3]←

(T[3]SENC[9])({overscore (T[3])}SENC[3])

P[4]←

(T[4]SENC[9])({overscore (T[4])}SENC[4])

P[5]←

(T[5]SENC[9])({overscore (T[5])}SENC[5])

P[6]←

(T[6]SENC[9])({overscore (T[6])}SENC[6])

P[7]←

(T[7]SENC[9])({overscore (T[7])}SENC[7])

P[8]←

(T[8]SENC[9])({overscore (T[8])}SENC[8])

P[9]←

SENC[10]

P[10]←

(T[1]SENC[1])(T[2]SENC[2])(T[3]SENC[3])(T[4]SENC[4])(T[5]SENC[5])(T[6]SENC[6])(T[7]SENC[7])(T[8]SENC[8])

(11) computing ENC[10-19] according to the following;

ENC[10]←

(LAST(P[1]⊕

ENC[1]))({overscore (LAST)}ENC[1])

ENC[11]←

(LAST(P[2]⊕

ENC[2]))({overscore (LAST)}ENC[2])

ENC[12]←

(LAST(P[3]⊕

ENC[3]))({overscore (LAST)}ENC[3])

ENC[13]←

(LAST(P[4]⊕

ENC[4]))({overscore (LAST)}ENC[4])

ENC[14]←

(LAST(P[5]⊕

ENC[5]))({overscore (LAST)}ENC[5])

ENC[15]←

(LAST(P[6]⊕

ENC[6]))({overscore (LAST)}ENC[6])

ENC[16]←

(LAST(P[7]⊕

ENC[7]))({overscore (LAST)}ENC[7])

ENC[17]←

(LAST(P[8]⊕

ENC[8]))({overscore (LAST)}ENC[8])

ENC[18]←

(LAST(P[9]⊕

ENC[9]))({overscore (LAST)}ENC[9])

ENC[19]←

LASTP[10]

(12) wherein the symbol “

←

”

stores a result, the symbol “

”

is a Boolean OR operation, the symbol “

”

is a Boolean AND operation, the symbol “

⊕

”

is a Boolean XOR operation, the overline “

⁻

”

indicates bit negation, the brackets “

[ ]”

indicate a bit position, and the parentheses indicate a precedence order.

41. An article of manufacture embodying logic for decoding a track identifier for servo control in a data storage device, the logic comprising:

(a) accessing an encoded track identifier stored as servo information on the data storage device; and

(b) decoding the track identifier as a snake-in-the-box code.

42. The article of manufacture of claim 41, wherein the encoded track identifier contains bits identifying a track position, as well as bits for error detection.

43. The article of manufacture of claim 41, wherein the snake-in-the-box code allows for detection of one or more errors in the encoded track identifier.

44. The article of manufacture of claim 41, wherein adjacent ones of the encoded track identifiers are at a distance of exactly 1 and non-adjacent ones of the encoded track identifiers are at a distance of at least 2.

45. The article of manufacture of claim 41, wherein the decoding logic further comprises mapping n bits of a track identifier field into k bits of the encoded track identifier in a logically efficient way, such that a result is the track identifier.

46. The article of manufacture of claim 45, wherein an input to the decoding logic is given by a n-bit vector (B[1], B[2], . . . , B[n]) that represents the track identifier field and an output from the decoding logic is given by a k-bit vector (I[1], I[2], . . . , I[k]) that represents the track identifier.

47. The article of manufacture of claim 46, wherein n=19 and k=15.

48. The article of manufacture of claim 47, wherein the decoding logic comprises the logic of:

(1) computing I[1-8] and LASTF according to the following;

I[1]←

B[1]

I[2]←

I[1]⊕

B[2]

I[3]←

I[2]⊕

B[3]

I[4]←

I[3]⊕

B[4]

I[5]←

I[4]⊕

B[5]

I[6]←

I[5]⊕

B[6]

I[7]←

I[6]⊕

B[7]

I[8]←

I[7]⊕

B[8]

LASTF←

I[8]⊕

B[9]

(2) computing P[1-9] according to the following;

P[1]←

B[1]⊕

B[10]

P[2]←

B[2]⊕

B[11]

P[3]←

B[3]⊕

B[12]

P[4]←

B[4]⊕

B[13]

P[5]←

B[5]⊕

B[14]

P[6]←

B[6]⊕

B[15]

P[7]←

B[7]⊕

B[16]

P[8]←

B[8]⊕

B[17]

P[9]←

B[9]⊕

B[18]

(3) computing T[1-8] according to the following;

T[1]←

I[2]I[3]I[4]I[5]I[6]I[7]I[8]

T[2]←

{overscore (I[2])}I[3]I[4]I[5]I[6]I[7]I[8]

T[3]←

{overscore (I[3])}I[4]I[5]I[6]I[7]I[8]

T[4]←

{overscore (I[4])}I[5]I[6]I[7]I[8]

T[5]←

{overscore (I[5])}I[6]I[7]I[8]

T[6]←

{overscore (I[6])}I[7]I[8]

T[7]←

{overscore (I[7])}I[8]

T[8]←

{overscore (I[8])}

(4) computing R[1-10] according to the following;

R[1]←

(P[1]T[1])(P[2]T[2])(P[3]T[3])(P[4]T[4])(P[5]T[5])(P[6]T[6])(P[7]T[7])(P[8]T[8])

R[2]←

(P[2]{overscore (T[2])})(P[10]T[2])

R[3]←

(P[3]{overscore (T[3])})(P[10]T[3])

R[4]←

(P[4]{overscore (T[4])})(P[10]T[4])

R[5]←

P[9]

R[6]←

(P[6]{overscore (T[6])})(P[10]T[6])

R[7]←

(P[7]{overscore (T[7])})(P[10]T[7])

R[8]←

(P[8]{overscore (T[8])})(P[10]T[8])

R[9]←

(P[1]{overscore (T[l])})(P[10]T[1])

R[10]←

(P[5]{overscore (T[5])})(P[10]T[5])

(5) computing I[9-12] and SLAST according to the following;

I[9]3 LASTR[1]

I[10]←

LAST(I[9]⊕

R[2])

I[11]←

LAST(I[10]⊕

R[3])

I[12]←

LAST(I[11]⊕

R[4])

SLAST←

I[12]⊕

R[5]

(6) computing SP[1-5] according to the following;

SP[1]←

R[1]⊕

R[6]

SP[2]←

R[2]⊕

R[7]

SP[3]←

R[3]⊕

R[8]

SP[4]←

R[4]⊕

R[9]

SP[5]←

R[5]⊕

R[10]

(7) computing ST[1-4] according to the following;

ST[1]←

I[10]I[11]I[12]

ST[2]←

{overscore (I[10])}I[l1]I[12]

ST[3]←

{overscore (I[11])}I[12]

ST[4]←

{overscore (I[12])}

(8) computing SR[1-4] according to the following;

SR[1]←

(SP[2]{overscore (ST[2])})(SP[4]ST[2])

SR[2]←

(SP[3]{overscore (ST[3])})(SP[4]ST[3])

SR[3]←

(SP[1]ST[1])(SP[2]ST[2])(SP [3]ST[3])(SP[4]ST[4])

SR[4]←

SP[5]

(9) computing I[13-15] according to the following;

I[13]←

LASTSLASTSR[3]

I[14]←

LASTSLAST(SR[2]⊕

SR[3])

I[15]←

LASTSLAST(SR[1]⊕

SR[2]⊕

SR[3]⊕

SR[4])

(10) wherein the symbol “

←

”

stores a result, the symbol “

”

is a Boolean OR operation, the symbol “

”

is a Boolean AND operation, the symbol “

⊕

”

is a Boolean XOR operation, the overline “

⁻

”

indicates bit negation, the brackets “

[ ]”

indicate a bit position, and the parentheses indicate a precedence order.