Robust and redundant physical block identification scheme for data storage devices

Claim 1

A method for storing unique data groups on a hard disk comprising the steps of: a. supplying a data group having associated with it unique identification fields; b. providing a plurality of integer moduli which are relative prime in pairs; c. encoding radial position information corresponding to a track on which the data group resides on the medium by: producing a radial physical block identification word comprising the integer remainders resulting from dividing the radial position information by each integer moduli; storing the physical block identification word in a unique identification field associated with the data group; d. encoding sector position information corresponding to the sector on the track on which the data group resides by: producing a sector physical block identification word comprising the integer remainders resulting from dividing the sector position information by each integer moduli; storing the sector physical block identification word in another unique identification field associated with the data group; and e. storing the unique identification fields and the data group on the disk.

Claim 2

A method for storing unique data groups on a hard disk comprising the steps of: a. supplying a data group having associated with it unique identification fields; b. providing a plurality of integer moduli which are relative prime in pairs; c. encoding radial position information corresponding to a track on which the data group resides on the medium by: producing a radial physical block identification word comprising the integer remainders resulting from dividing the radial position information by each integer moduli; storing the physical block identification word in a unique identification field associated with the data group; d. encoding sector position information corresponding to the sector on the track on which the data group resides by: producing a sector physical block identification word comprising the integer remainders resulting from dividing the sector position information by each integer moduli; storing the sector physical block identification word in another unique identification field associated with the data group; and e. storing the unique identification fields and the data group on the disk.

Claim 3

A method for storing unique data blocks on a hard disk comprising the steps of: a. supplying a data block including unique identification fields; b. providing a plurality of integer moduli which are relative prime in pairs; c. encoding radial position information corresponding to a track on which the block resides on the medium by: producing a radial physical block identification word comprising the integer remainders resulting from dividing the radial position information by each integer moduli; storing the physical block identification word in a unique identification field of the block; d. encoding sector position information corresponding to the sector on the track on which the block resides by: producing a sector physical block identification word comprising the integer remainders resulting from dividing the sector position information by each integer moduli; storing the sector physical block identification word in another unique identification field of the block; and e. storing the block on the disk.

Claim 4

A method for storing unique data blocks on a hard disk comprising the steps of: a. supplying a data block including unique identification fields; b. providing a plurality of integer moduli which are relative prime in pairs; c. encoding radial position information corresponding to a track on which the block resides on the medium by: producing a radial physical block identification word comprising the integer remainders resulting from dividing the radial position information by each integer moduli; storing the physical block identification word in a unique identification field of the block; d. encoding sector position information corresponding to the sector on the track on which the block resides by: producing a sector physical block identification word comprising the integer remainders resulting from dividing the sector position information by each integer moduli; storing the sector physical block identification word in another unique identification field of the block; and e. storing the block on the disk.

Claim 5

A method for storing unique data groups on a data medium comprising the steps of: a. encoding information M representing a unique characteristic of a data group wherein the data group has associated with it a unique identification field by: providing a plurality of integer moduli [A(0),A(1), . . . ,A(L-1)], the integer moduli being relatively prime in pairs: producing a physical block identification word comprising remainders [R(0),R(1), . . . ,R(L-1)], wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1); b. storing the physical block identification word in the unique identification field associated with the data group; and wherein the step of producing a physical block identification word comprises the steps of: for each A(i), selecting j<A(i); M'=information M; repeating until q'=0: find q' and r' such that M'=q'*[A(i)+j]+r', with r'<A(i)+j; M'=r'+j*q'; when q'=0, then if r'≧A(i) then R(i)=r'-A(i); if r'<A(i) then R(i)=r'.

Claim 6

A method for storing unique data groups on a data medium comprising the steps of: a. encoding information M representing a unique characteristic of a data group wherein the data group has associated with it a unique identification field by: providing a plurality of integer moduli [A(0),A(1), . . . ,A(L-1)], the integer moduli being relatively prime in pairs: producing a physical block identification word comprising remainders [R(0),R(1), . . . ,R(L-1)], wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1); b. storing the physical block identification word in the unique identification field associated with the data group; and wherein the step of producing a physical block identification word comprises the steps of: for each A(i), selecting j<A(i); M'=information M; repeating until q'=0: find q' and r' such that M'=q'*[A(i)+j]+r', with r'<A(i)+j; M'=r'+j*q'; when q'=0, then if r'≧A(i) then R(i)=r'-A(i); if r'<A(i) then R(i)=r'.

Claim 7

A method for storing unique data groups on a data medium comprising the steps of: a. encoding information M representing a unique characteristic of a data group wherein the data groups has associated with it a unique identification field by: providing a plurality of integer moduli [A(0),A(1), . . . ,A(L-1)], the integer moduli being relatively prime in pairs: producing a physical block identification word comprising remainders [R(0),R(1), . . . ,R(L-1)], wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1); b. storing the physical block identification word in the unique identification field associated with the data group: and wherein the step of producing a physical block identification word comprises the steps of: for each A(i), selecting the smallest k such that A(i)≧2 k ; j=2 k -A(i); M'=a binary representation of information M of s bits; repeating until q'=0: r'=the least significant k bits of M'; q'=the the most significant s-k bits of M'; M'=r'+j*q'; when q'=0, then if r'≧A(i) then R(i)=r'-A(i); if r'<A(i) then R(i)=r'.

Claim 8

A method for storing unique data groups on a data medium comprising the steps of: a. encoding information M representing a unique characteristic of a data group wherein the data groups has associated with it a unique identification field by: providing a plurality of integer moduli [A(0),A(1), . . . ,A(L-1)], the integer moduli being relatively prime in pairs: producing a physical block identification word comprising remainders [R(0),R(1), . . . ,R(L-1)], wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1); b. storing the physical block identification word in the unique identification field associated with the data group: and wherein the step of producing a physical block identification word comprises the steps of: for each A(i), selecting the smallest k such that A(i)≧2 k ; j=2 k -A(i); M'=a binary representation of information M of s bits; repeating until q'=0: r'=the least significant k bits of M'; q'=the the most significant s-k bits of M'; M'=r'+j*q'; when q'=0, then if r'≧A(i) then R(i)=r'-A(i); if r'<A(i) then R(i)=r'.

Claim 9

A method of identifying unique data groups within a data stream comprising the steps of: choosing information M representing a unique characteristic of a data group to be identified; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1), [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; comparing the expected physical block identification word [R(0),R(1), . . . ,R(L-1)] to a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] associated with a data group in the data stream; declaring the data group associated with the physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the data group to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the data group associated with the physical block identification word R' as not being the data group to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 10

A method of identifying unique data groups within a data stream comprising the steps of: choosing information M representing a unique characteristic of a data group to be identified; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1), [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; comparing the expected physical block identification word [R(0),R(1), . . . ,R(L-1)] to a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] associated with a data group in the data stream; declaring the data group associated with the physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the data group to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the data group associated with the physical block identification word R' as not being the data group to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 18

A method of identifying unique data groups within a data stream comprising the steps of: choosing information M representing a unique characteristic of a data group to be identified; providing information Mp representing a unique characteristic of a presently identified data group having associated with it a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; determining the difference E in location between the presently identified data group and the data group to be identified by subtracting the physical position information Mp from the physical position information M; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with the presently identified data group the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with presently identified data group the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the data group to be identified, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≧Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≦A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); comparing the remainders in the expected physical block identification word [R(1),R(2), . . . ,R(L-1)] to the remainders [R'(1),R'(2), . . . ,R'(L-1)] of a physical block identification word associated with a data group in the data stream; declaring the data group associated with the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as the data group to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the data group associated with the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as not being the data group to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 19

A method of identifying unique data groups within a data stream comprising the steps of: choosing information M representing a unique characteristic of a data group to be identified; providing information Mp representing a unique characteristic of a presently identified data group having associated with it a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; determining the difference E in location between the presently identified data group and the data group to be identified by subtracting the physical position information Mp from the physical position information M; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with the presently identified data group the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with presently identified data group the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the data group to be identified, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≧Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≦A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); comparing the remainders in the expected physical block identification word [R(1),R(2), . . . ,R(L-1)] to the remainders [R'(1),R'(2), . . . ,R'(L-1)] of a physical block identification word associated with a data group in the data stream; declaring the data group associated with the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as the data group to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the data group associated with the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as not being the data group to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 23

A method of locating data groups on a data medium comprising the steps of: choosing a physical address M of a data group to be located wherein the data group to be located has associated with it a unique identification field; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; reading from the medium a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] from the unique identification field associated with the data group to be located; comparing the remainders [R'(0),R'(1), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(0),R(1), . . . ,R(L-1)] in the expected physical block identification word; identifying the data group associated with the physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the data group to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and identifying the data group associated with physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as not being the data group to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 24

A method of locating data groups on a data medium comprising the steps of: choosing a physical address M of a data group to be located wherein the data group to be located has associated with it a unique identification field; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; reading from the medium a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] from the unique identification field associated with the data group to be located; comparing the remainders [R'(0),R'(1), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(0),R(1), . . . ,R(L-1)] in the expected physical block identification word; identifying the data group associated with the physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the data group to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and identifying the data group associated with physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as not being the data group to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 34

A method of locating data groups on a data medium comprising the steps of: a. choosing a physical address M of a data group to be located, the data group to be located having associated with it a unique identification field, the data group to be located being spaced on the medium from a present data group, the present data group having a physical address Mp and being associated with a unique identification field including a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; b. producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs, the step of producing an expected physical block identification word comprising the steps of: determining the difference E in location between the present data group and the data group to be located by subtracting the physical address Mp of the present data group from the physical address M of the data group to be located; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with the present data group the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with the present data group the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the data group to be located, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≦Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≧A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); c. reading from the medium a physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] from the unique identification field associated with the data group to be located; d. comparing the remainders [R'(1),R'(2), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(1),R(2), . . . ,R(L-1)] in the expected physical block identification word; e. identifying the data group associated with physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as the data group to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and f. identifying the data group associated with physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as not being the data group to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 35

A method of locating data groups on a data medium comprising the steps of: a. choosing a physical address M of a data group to be located, the data group to be located having associated with it a unique identification field, the data group to be located being spaced on the medium from a present data group, the present data group having a physical address Mp and being associated with a unique identification field including a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; b. producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs, the step of producing an expected physical block identification word comprising the steps of: determining the difference E in location between the present data group and the data group to be located by subtracting the physical address Mp of the present data group from the physical address M of the data group to be located; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with the present data group the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word associated with the present data group the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the data group to be located, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≦Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≧A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); c. reading from the medium a physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] from the unique identification field associated with the data group to be located; d. comparing the remainders [R'(1),R'(2), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(1),R(2), . . . ,R(L-1)] in the expected physical block identification word; e. identifying the data group associated with physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as the data group to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and f. identifying the data group associated with physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as not being the data group to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 42

A method of identifying unique data blocks within a data stream comprising the steps of: choosing information M representing a unique characteristic of a block to be identified; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1), [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; comparing the expected physical block identification word [R(0),R(1), . . . ,R(L-1)] to a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] stored in a unique identification field of a block in the data stream; declaring the block containing physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the block to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the block containing physical block identification word R' as not being the block to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 43

A method of identifying unique data blocks within a data stream comprising the steps of: choosing information M representing a unique characteristic of a block to be identified; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=(0,1, . . . ,L-1), [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; comparing the expected physical block identification word [R(0),R(1), . . . ,R(L-1)] to a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] stored in a unique identification field of a block in the data stream; declaring the block containing physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the block to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the block containing physical block identification word R' as not being the block to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 49

A method of identifying unique data blocks within a data stream comprising the steps of: choosing information M corresponding to a unique characteristic of a block to be identified; providing information Mp corresponding to a unique characteristic of a presently identified block having a unique identification field including a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; determining the difference E in location between the presently identified block and the block to be identified by subtracting the physical position information Mp from the physical position information M; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the block to be identified, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≦Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≧A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); comparing the remainders in the expected physical block identification word [R(1),R(2), . . . ,R(L-1)] to the remainders [R'(1),R'(2), . . . ,R'(L-1)] of a physical block identification word stored in the unique identification field of a block in the data stream; declaring the block containing the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as the block to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the block containing the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as not being the block to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 50

A method of identifying unique data blocks within a data stream comprising the steps of: choosing information M corresponding to a unique characteristic of a block to be identified; providing information Mp corresponding to a unique characteristic of a presently identified block having a unique identification field including a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; determining the difference E in location between the presently identified block and the block to be identified by subtracting the physical position information Mp from the physical position information M; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the block to be identified, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≦Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≧A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); comparing the remainders in the expected physical block identification word [R(1),R(2), . . . ,R(L-1)] to the remainders [R'(1),R'(2), . . . ,R'(L-1)] of a physical block identification word stored in the unique identification field of a block in the data stream; declaring the block containing the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as the block to be identified if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and declaring the block containing the remainders [R'(1),R'(1), . . . ,R'(L-1)] of the physical block identification word in the data stream as not being the block to be identified if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 52

A method of locating data blocks on a data medium, said data blocks including a unique identification field and a data field, comprising, for each block, the steps of: choosing a physical address M of a block to be located; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; reading from the medium a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] for the block to be located; comparing the remainders [R'(0),R'(1), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(0),R(1), . . . ,R(L-1)] in the expected physical block identification word; identifying the block having physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the block to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and identifying the block having physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as not being the block to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 53

A method of locating data blocks on a data medium, said data blocks including a unique identification field and a data field, comprising, for each block, the steps of: choosing a physical address M of a block to be located; producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs; reading from the medium a physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] for the block to be located; comparing the remainders [R'(0),R'(1), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(0),R(1), . . . ,R(L-1)] in the expected physical block identification word; identifying the block having physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as the block to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and identifying the block having physical block identification word [R'(0),R'(1), . . . ,R'(L-1)] as not being the block to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 61

A method of locating data blocks on a data medium comprising the steps of: a. choosing a physical address M of a block to be located, the block to be located being spaced on the medium from a present block having a physical address Mp and a unique identification field including a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; b. producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs, the step of producing an expected physical block identification word comprising the steps of: determining the difference E in location between the present block and the block to be located by subtracting the physical address Mp of the present block from the physical address M of the block to be located; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1), Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the block to be located, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≦Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≧A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); c. reading from the medium a physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] for the block to be located; d. comparing the remainders [R'(1),R'(2), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(1),R(2), . . . ,R(L-1)] in the expected physical block identification word; e. identifying the block having physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as the block to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and f. identifying the block having physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as not being the block to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.

Claim 62

A method of locating data blocks on a data medium comprising the steps of: a. choosing a physical address M of a block to be located, the block to be located being spaced on the medium from a present block having a physical address Mp and a unique identification field including a physical block identification word [Rp(0),Rp(1), . . . ,Rp(L-1)]; b. producing an expected physical block identification word comprising the remainders [R(0),R(1), . . . ,R(L-1)] wherein R(i)=M MOD A(i) for i=0,1, . . . ,L-1, [A(0),A(1), . . . ,A(L-1)] being integer moduli which are relative prime in pairs, the step of producing an expected physical block identification word comprising the steps of: determining the difference E in location between the present block and the block to be located by subtracting the physical address Mp of the present block from the physical address M of the block to be located; for all moduli A(i)=A(0),A(1), . . . ,A(L-1), letting A(0) be the smallest moduli for all A(i), verifying that the absolute value of the difference E is less than A(0) times the smallest moduli A(i) for i=1, . . . ,L-1; if the difference E is negative, producing temporary remainders [Rt(1),Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E and the corresponding moduli A(i) for i=1,2, . . . ,L-1; if the difference E is positive, producing temporary remainders [Rt(1), Rt(2), . . . ,Rt(L-1)] by adding to each of the remainders Rp(i) of the physical block identification word of the present block the difference E for i=1,2, . . . ,L-1; and producing a physical block identification word [R(1),R(2), . . . ,R(L-1)] for the block to be located, wherein for i=1,2, . . . ,L-1: R(i)=Rt(i)+A(i) if Rt(i)<0; R(i)=Rt(i) if 0≦Rt(i)<A(i); R(i)=Rt(i)-A(i) if Rt(i)≧A(i), wherein this step is repeated up to A(0) times until Rt(i) is less than A(i); c. reading from the medium a physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] for the block to be located; d. comparing the remainders [R'(1),R'(2), . . . ,R'(L-1)] in the physical block identification word read to the remainders [R(1),R(2), . . . ,R(L-1)] in the expected physical block identification word; e. identifying the block having physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as the block to be located if the comparison results in a number of remainders which differ by less than or equal to a threshold number of remainders; and f. identifying the block having physical block identification word [R'(1),R'(2), . . . ,R'(L-1)] as not being the block to be located if the comparison results in a number of remainders which differ by more than a threshold number of remainders.