Abstract:
A control module includes an encoder module, a detector module, a mapping module, and a difference module. The encoder module receives data, and based on the data, generates a first code word for drives. The drives are associated with a storage system. The detector module detects an addition of a second drive. The encoder module generates a second code word for the second drive. The mapping module: maps physical locations of the data in the drives to logical locations of the first code word; assigns a predetermined value to a logical location corresponding to an unused logical location; and based on the predetermined value, assigns the unused logical location to the second drive. The difference module generates a third code word based on each of the first and second code words. The encoder module, based on the first and third code words, generates a fourth code word for all drives.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. Ser. No. 13/454,831, filed Apr. 24, 2012 (now U.S. Pat. No. 8,386,889), which is a continuation of U.S. Ser. No. 11/805,344, filed May 23, 2007 (now U.S. Pat. No. 8,166,370), which is a continuation of U.S. Ser. No. 11/736,386, filed Apr. 17, 2007 (now U.S. Pat. No. 7,661,058), which application claims the benefit of U.S. Provisional Application No. 60/797,516, filed on May 4, 2006 and U.S. Provisional Application No. 60/792,492, filed on Apr. 17, 2006. The disclosures of the above applications are incorporated herein by reference in their entirety. 
    
    
     FIELD 
     The present disclosure relates generally to a redundant array of inexpensive disks (RAID) system, and more particularly to systems and methods for efficiently adding and removing drives in a RAID system. 
     BACKGROUND 
     The Background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present disclosure. 
     Performance in microprocessor and semiconductor memory technology continues to increase at a rapid pace. Drive storage technology has typically not kept pace. Redundant arrays of inexpensive disks (RAID) have been used to improve the data transfer rate and data input/output (I/O) rate over other types of disk access. RAID systems also provide greater data reliability at a low cost. 
     A RAID system distributes storage over multiple drives. When one of the drives fails, a RAID controller performs data recovery. It may also be desirable to add or remove a drive from the RAID system. The RAID system typically uses one or more parity drives to store error-correcting parity information and a plurality of data drives that store user information. If a data drive fails, the contents of the failed drive can be reconstructed using the information from the remaining data drives and the parity drive(s). 
     Each drive in a RAID system may generate its own Error Correction Code (ECC) and cyclic redundancy code (CRC). In addition, another layer of ECC may be added across the drives in the RAID system to handle drive failures. 
     Referring now to  FIGS. 1 and 2 , the structure of RAID system is shown in further detail. In  FIG. 1 , a storage system  10  includes data drives  12  d 1 -d k  and parity drives  14  p 1 -p r . The number of data drives k may be different than the number of parity drives r. The data drives  12  and parity drives  14  communicate via a bus  16 . The bus  16  may also communicate with a RAID control module  18 . 
     The RAID control module  18  may include a RAID ECC encoder  20  and a RAID ECC decoder  22 . The RAID control module  18  communicates with a system  24  such as a computer or a network of computers. The data storage system  10  stores and retrieves user information on the data drives  12 . The RAID control module  18  generates ECC redundancy that is stored on the parity drives  14 . The RAID control module  18  may use a cyclic code such as Reed Solomon (RS) ECC. 
     Let s i (j) be the user data corresponding to the Logical Block Address (LBA) j on the i th  data drive in the RAID system. The data bits in s i (j) may be grouped into symbols if a non-binary ECC is used. A RAID ECC code word is formed by associating corresponding symbols across all of the data drives, i.e. w(j,l)=(s 0 (j,l), s 1 (j,l), . . . , s k-1 (j,l), where l=0,1, . . . L−1 enumerates RAID ECC symbols within s i (j). 
     To recover one sector on a failed drive, the RAID control module  18  carries out L ECC decoding operations (one for each symbol). For example, if individual drives forming a RAID system have 0.5K byte sector format, and RAID ECC operates on a byte level (e.g. RAID ECC is RS ECC over GF(2^8)), then there are 512 RAID RS ECC codewords per each sector of a fixed component drive. 
     One simple example is a RAID system including two drives, where RAID ECC utilizes (2,1) repetition code. Consequently, both drives contain the same information. If the first drive (data drive) fails, then the second drive (parity drive) can be used to restore lost information. 
     Another exemplary of RAID system can employ Single Parity Bit Code-based ECC. For example, a RAID system may include k user drives and 1 parity drive (e.g. k=10). Let s i (j) denote the sector from i-th drive corresponding to LBA=j. The RAID ECC encoder ensures that s 0 (j)+s 1 (j)+ . . . +s 10 (j)=0 for all possible LBA values j (here “+” refers to bitwise XOR operation, and 0 represents a sector long zero vector). If only one out of 11 drives fails, for example drive 0, then the lost data can be reconstructed from the other drives via s 0 (j)=s 1 (j)+ . . . +s 10 (j) for all valid LBA values j. 
     Referring now to  FIG. 3 , exemplary logical and physical locations of a RAID system  50  including twelve drives is illustrated. The RAID system may include four parity drives. Let s i (j,l) represent the I-th symbol of a sector with LBA=j written on the i-th drive. Then s 0 (j,l), s 1 (j,l), . . . , s 11 (j,l) form the RS ECC codeword for all values of j and k. 
     The physical location of the drives within a RAID system  56  is illustrated with numerals 0-11. Arrows  58  illustrate the mapping between physical drive locations 0-11 and logical drive locations  52   0 - 52   11 , where logical drive location corresponds to an index of RS ECC codeword. 
     For example, the drive with physical location  10  stores a 1 st  symbol of each RAID RS ECC codeword. More locations may be added or removed when the requirements of the RAID system change. It is desirable to allow the RAID system to expand (add new data or parity drives) or contract (remove data or parity drives) without having to take the system offline for prolonged periods of time to perform maintenance. 
     Referring now to  FIG. 4 , when one of the drives is removed, the code length is changed. In this approach, the physical-to-logical map is changed. In step  100 , the physical-to-logical map for a particular group of drives is determined. The order of logical locations does not necessarily correspond to the order of physical locations of each of the drives. In step  102 , the code words are generated and saved to the drives in stripes. Code words for both the data and parity drives are generated. In step  104 , the code words are stored on the data and parity drives. 
     In step  110 , the system determines whether a data drive needs to be removed. This may or may not be due to drive errors. In step  112 , logical locations of the data that are greater than the logical location of the removed drive are mapped toward lower-degree logical positions to remove a gap. By shifting the logical locations, a second map (physical-to-logical) is created. The logical locations in the second map have consecutive low-degree positions occupied. In step  114 , the data drives are read and the code words for the data drives are generated. In step  116 , the parity part of second code word is written to the parity drive(s). 
     When drives are later added to the RAID system, they are assigned a highest degree logical position. All of the drives are read and the parity drives are written. 
     Using the approach described above requires a read operation on all of the data drives and a write of the parity drives when adding, removing or modifying drives. This can reduce the amount of uptime of the RAID system. 
     SUMMARY 
     A control module is provided and includes an encoder module, a detector module, a mapping module, and a difference module. The encoder module is configured to (i) receive data, and (ii) based on the data, generate a first code word for first drives. The first drives are associated with a storage system. The detector module is configured to detect an addition of a second drive added to the storage system. The encoder module is configured to generate a second code word for the second drive added to the storage system. The mapping module is configured to (i) map physical locations of the data in the first drives to logical locations of the first code word, (ii) assign a predetermined value to a logical location corresponding to an unused logical location of the logical locations, and (iii) based on the predetermined value, assign the unused logical location to the second drive added to the storage system. The difference module is configured to generate a third code word based on each of the first code word and the second code word. The encoder module is configured to, based on the first code word and the third code word, generate a fourth code word for all drives associated with the storage system. All drives associated with the storage system include the first drives and the second drive. 
     A method is provided and includes receiving data and based on the data, generating a first code word for first drives. The first drives are associated with a storage system. An addition of a second drive added to the storage system is detected. A second code word for the second drive added to the storage system is generated. Physical locations of the data in the first drives are mapped to logical locations of the first code word. The second drive added to the storage system is mapped to an unused logical location of the logical locations including: assigning a predetermined value to a logical location corresponding to a logical location of the logical locations; and based on the predetermined value, assigning the unused logical location to the second drive added to the storage system. A third code word is generated based on each of the first code word and the second code word. Based on the first code word and the third code word, a fourth code word is generated for all drives associated with the storage system. All drives associated with the storage system include the first drives and the second drive. 
     A control module is provided and includes an encoder module configured to (i) receive data, and (ii) based on the data, generate a first code word for multiple drives. A detector module is configured to, in response to detecting an error in a first drive of the multiple drives subsequent to generation of the first code word, initiate replacement of the first drive with a second drive. The encoder module is configured to generate a second code word for the second drive. A mapping module is configured to (i) map physical locations of the data in the multiple drives to logical locations of the first code word, (ii) assign a predetermined value to one of the logical locations corresponding to the first drive to identify an unused one of the logical locations, and (iii) assign the unused one of the logical locations to the second drive based on the predetermined value. A difference module is configured to generate a third code word based on each of the first code word and the second code word. The encoder module is configured to generate an updated code word for the multiple drives based on the first code word and the third code word. 
     In other features, a method is provided and includes receiving data at a control module. Based on the data, a first code word is generated for multiple drives. In response to detecting an error in a first drive of the multiple drives subsequent to generation of the first code word. The method further includes: initiating replacement of the first drive with a second drive; generating a second code word for the second drive; and mapping physical locations of the data in the multiple drives to logical locations of the first code word. A predetermined value is assigned to one of the logical locations corresponding to the first drive to identify an unused one of the logical locations. The unused one of the logical locations is assigned to the second drive based on the predetermined value. A third code word is generated based on each of the first code word and the second code word. An updated code word is generated for the multiple drives based on each of the first code word and the third code word. 
     In other features, a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes a RAID error correction code (ECC) encoder module that receives data for storage and that generates code words for data drives and one or more parity drives, which have physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to index positions in the cyclic code generator polynomial. A mapping module generates a map of the physical locations of the data and parity drives to the logical locations. When one of the data drives is removed, the mapping and RAID ECC encoder modules do not modify the map. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The RAID ECC encoder module is configured in erasure decoding mode. Before one of the data drives is removed, the RAID ECC encoder module reads the one of the data drives. A difference generating module generates a difference code word based on the removed data drive. The RAID ECC encoder adds the difference code word to an original code word generated before the removed data drive is removed. When the removed data drive is removed, the RAID ECC encoder module assigns a zero to a logical location in the code word corresponding to the removed data drive, modifies the parity drives and does not read other ones of the data drives. 
     In other features, a RAID system is provided and includes the RAID controller. K data drives each include an ECC/cyclic redundancy check (CRC) module that performs ECC and CRC, where K is an integer greater than one. R parity drives each include an ECC/CRC module that performs ECC and CRC, where R is an integer greater than zero. The mapping module maps the parity drives to lowest positions in the index. 
     In other features, the RAID ECC encoder module is configured to handle a maximum number of data drives k_max and to have a maximum correction power t_max. A RAID ECC decoder module decodes the code words. 
     In other features, a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes RAID error correction code (ECC) encoder means for receiving data for storage and for generating code words for data drives and one or more parity drives, which have corresponding physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. Mapping means generates a map of the physical locations of the data and parity drives to the logical locations. When one of the data drives is removed, the mapping and RAID ECC encoder means do not modify the map. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The RAID ECC encoder means is configured in erasure decoding mode. Before one of the data drives is removed, the RAID ECC encoder means reads the one of the data drives. Difference generating means generates a difference code word based on the removed data drive. The RAID ECC encoding means adds the difference code word to an original code word generated before the removed drive is removed. When the removed drive is removed, the RAID ECC encoder means assigns a zero to a logical location in the code word corresponding to the removed data drive, modifies the parity drives and does not read other ones of the data drives. 
     In other features, a RAID system is provided and includes the RAID controller. K data drives each include ECC/cyclic redundancy check (CRC) means for performing ECC and CRC, where K is an integer greater than one. R parity drives each include ECC/CRC means for performing ECC and CRC, where R is an integer greater than zero. The mapping means maps the parity drives to lowest positions in the index. The RAID ECC encoder means is configured to handle a maximum number of data drives k_max and to have a maximum correction power t_max. RAID ECC decoding means decodes the code words. 
     In other features, a method for operating Redundant Array of Inexpensive Disks (RAID) controller is provided and includes receiving data for storage and generating code words for data drives and one or more parity drives, which have corresponding physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. A map of the physical locations of the data and parity drives to the logical locations is generated. The index of the logical locations in the cyclic code generator polynomial are left unmodified when one of the data drives is removed. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The Reed Solomon coding is performed in erasure decoding mode. The method includes reading one of the data drives before the one of the data drives is removed. The method includes generating a difference code word based on the removed data drive. The method includes adding the difference code word to an original code word generated before the removed data drive is removed. When the removed drive is removed, the method includes assigning a zero to a logical location in the code word corresponding to the removed data drive; modifying the parity drives; and not reading other ones of the data drives. The method includes performing ECC and CRC on the data and parity drives. The method includes mapping the parity drives to lowest positions in the index. 
     In other features, a computer method stored on a medium for use by a processor for operating Redundant Array of Inexpensive Disks (RAID) controller is provided and includes receiving data for storage and generating code words for data drives and one or more parity drives, which have corresponding physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. A map of the physical locations of the data and parity drives to the logical locations is generated. The index of the logical locations in the cyclic code generator polynomial is left unmodified when one of the data drives is removed. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The Reed Solomon coding is performed in erasure decoding mode. The computer method includes reading one of the data drives before the one of the data drives is removed. The computer method includes generating a difference code word based on the removed data drive. The computer method includes adding the difference code word to an original code word generated before the removed data drive is removed. When the removed drive is removed, the computer method includes assigning a zero to a logical location in the code word corresponding to the removed data drive; modifying the parity drives; and not reading other ones of the data drives. The computer method includes performing ECC and CRC on the data and parity drives. The computer method includes mapping the parity drives to lowest positions in the index. 
     In other features, a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes a RAID error correction code (ECC) encoder module that receives data for storage and that generates code words stored by data drives and one or more parity drives, which have physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. A mapping module generates a map of the physical locations of the data and parity drives to the logical locations. A difference generating module generates a difference code word when data on one of the data drives is modified. The RAID ECC encoder module encodes the difference code word and adds the encoded difference code word to an original code word generated before the modification. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The RAID ECC encoder module is configured in an erasure decoding mode. A RAID system includes the RAID controller, K data drives each including an ECC/cyclic redundancy check (CRC) module that performs ECC and CRC, where K is an integer greater than one, and R parity drives each including an ECC/CRC module that performs ECC and CRC, where R is an integer greater than zero. 
     In other features, the mapping module maps the parity drives to lowest ones of the index. The RAID ECC encoder module is configured to handle a maximum number of data drives k_max. The RAID ECC encoder module is configured to have a maximum correction power t_max. A RAID ECC decoder module decodes the code words. 
     In other features, a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes RAID error correction code (ECC) encoder means for receiving data for storage and for generating code words for data drives and one or more parity drives, which have physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. Mapping mean maps the physical locations of the data and parity drives to the logical locations. Difference generating means generates a difference code word when data on one of the data drives is modified. The RAID ECC encoder means encodes the difference code word and adds the encoded difference code word to an original code word before the modification. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The RAID ECC encoder means is configured in an erasure decoding mode. A RAID system includes the RAID controller, K data drives each including ECC/cyclic redundancy check (CRC) means for performing ECC and CRC, where K is an integer greater than one, and R parity drives each including ECC/CRC means for performing ECC and CRC, where R is an integer greater than zero. 
     In other features, the mapping means maps the parity drives to lowest positions in the index. The RAID ECC encoder means is configured to handle a maximum number of data drives k_max and to have a maximum correction power t_max. RAID ECC decoding means decodes the code words. 
     In other features, a method for operating a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes: receiving data for storage; generating code words for data drives and one or more parity drives, which have physical locations; and generating the code words based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. The physical locations of the data and parity drives are mapped to the logical locations. A difference code word is generated when data on one of the data drives is modified. The difference code word is encoded and the encoded difference code word is added to an original code word before the modification. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The Reed Solomon code is configured in erasure decoding mode. The method includes mapping the parity drives to lowest positions in the index. The method includes configuring the RAID controller to handle a maximum number of data drives k_max and to have a maximum correction power t_max. The method includes decoding the code words. 
     In other features, a computer method stored on a medium for use by a processor for operating a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes: receiving data for storage; generating code words for data drives and one or more parity drives, which have physical locations; and generating the code words based on the data and a cyclic code generator polynomial. Logical locations correspond to an index of the cyclic code generator polynomial. The physical locations of the data and parity drives are mapped to the logical locations. A difference code word is generated when data on one of the data drives is modified. The difference code word is encoded and the encoded difference code word is added to an original code word before the modification. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The Reed Solomon code is configured in erasure decoding mode. The computer method includes mapping the parity drives to lowest positions in the index. The computer method includes configuring the RAID controller to handle a maximum number of data drives k_max and to have a maximum correction power t_max. The computer method includes decoding the code words. 
     In other features, a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes a RAID error correction code (ECC) encoder module that receives data for storage and that generates code words for data drives and one or more parity drives, which have physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to index positions in the cyclic code generator polynomial. A mapping module maps the physical locations of the data and parity drives to the logical locations. The mapping module adds a new data drive to an unused one of said logical locations. A difference generating module generates a difference code word based on the new data drive. The RAID ECC encoder module encodes the difference code word and adds the encoded difference code word to an original code word generated before the new data drive is added. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The RAID ECC encoder module is configured in an erasure decoding mode. A RAID system includes the RAID controller, K data drives each including an ECC/cyclic redundancy check (CRC) module that performs ECC and CRC, where K is an integer greater than one, and R parity drives each including an ECC/CRC module that performs ECC and CRC, where R is an integer greater than zero. 
     In other features, the mapping module maps the parity drives to lowest positions in the index. The RAID ECC encoder module is configured to handle a maximum number of data drives k_max and to have a maximum correction power t_max. A RAID ECC decoder module decodes the code words. 
     In other features, a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes RAID error correction code (ECC) encoder means for receiving data for storage and for generating code words for data drives and one or more parity drives, which have physical locations. The code words are generated based on the data and a cyclic code generator polynomial. Logical locations correspond to index positions in the cyclic code generator polynomial. Mapping means maps the physical locations of the data and parity drives to the logical locations. The mapping means adds a new data drive to an unused one of said logical locations. Difference generating means generates a difference code word based on the new data drive. The RAID ECC encoder means encodes the difference code word and adds the encoded difference code word to an original code word generated before the new data drive is added. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The RAID ECC encoder means is configured in an erasure decoding mode. A RAID system includes the RAID controller, K data drives each including ECC/cyclic redundancy check (CRC) means for performing ECC and CRC, where K is an integer greater than one, and R parity drives each including ECC/CRC means for performing ECC and CRC, where R is an integer greater than zero. The mapping means maps the parity drives to lowest positions in the index. The RAID ECC encoder means is configured to handle a maximum number of data drives k_max and to have a maximum correction power t_max. RAID ECC decoder means decodes the code words. 
     In other features, a method for operating a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes: receiving data for storage; generating code words for data drives and one or more parity drives, which have physical locations; and generating the code words based on the data and a cyclic code generator polynomial. Logical locations correspond to index positions in the cyclic code generator polynomial. The physical locations of the data and parity drives are mapped to the logical locations. A new data drive is added to an unused one of said logical locations. A difference code word is generated based on the new data drive. The difference code word is encoded. The encoded difference code word is added to an original code word generated before the new data drive is added. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The Reed Solomon code is configured in erasure decoding mode. The method includes mapping the parity drives to lowest positions in the index. 
     In other features, a computer method stored on a medium for use by a processor for operating a Redundant Array of Inexpensive Disks (RAID) controller is provided and includes: receiving data for storage; generating code words for data drives and one or more parity drives, which have physical locations; and generating the code words based on the data and a cyclic code generator polynomial. Logical locations correspond to index positions in the cyclic code generator polynomial. The physical locations of the data and parity drives are mapped to the logical locations. A new data drive is added to an unused one of said logical locations. A difference code word is generated based on the new data drive. The difference code word is encoded. The encoded difference code word is added to an original code word generated before the new data drive is added. 
     In other features, the cyclic code generator polynomial generates Reed Solomon code. The Reed Solomon code is operated in erasure decoding mode. The computer method includes mapping the parity drives to lowest positions in the index. 
     Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, are intended for purposes of illustration only and are not intended to limit the scope of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will become more fully understood from the detailed description and the accompanying drawings. 
         FIG. 1  is a block diagrammatic view of a RAID system according to the prior art. 
         FIG. 2  illustrates RAID ECC codewords and data on drives according to prior art. 
         FIG. 3  is illustrates an exemplary logical to physical mapping of drives. 
         FIG. 4  is a flowchart of a first method/architecture for removing a data drive according to the prior art. 
         FIG. 5  is a block diagrammatic view of the RAID controller according to the present disclosure. 
         FIG. 6  is flowchart of a method/architecture for removing a data drive according to the present disclosure. 
         FIG. 7  is a flowchart for adding a data drive according to the present disclosure. 
         FIG. 8  is a flowchart of a method/architecture of adding a data drive according to the prior art. 
         FIG. 9  is a table illustrating comparing operations of the method/architectures described herein. 
         FIG. 10  is a flowchart of a method/architecture of modifying a data drive. 
     
    
    
     DETAILED DESCRIPTION 
     The following description is merely exemplary in nature and is in no way intended to limit the disclosure, its application, or uses. As used herein, the term module refers to an Application Specific Integrated Circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality. For purposes of clarity, the same reference numbers will be used in the drawings to identify similar elements. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A or B or C), using a non-exclusive logical or. It should be understood that steps within a method may be executed in different order without altering the principles of the present disclosure. 
     To allow relatively seamless removal of drives, the present disclosure maintains the logical-to-physical mapping during drive removal. Artificial zeros are assigned to removed positions associated with the removed drive. In other words, the cyclic code generator polynomial remains unchanged when the drives are added and removed. 
     The system may be configured with predefined maximum parameters. For example, a maximum number of data drives k_max and a maximum desired RAID correction power t_max can be specified. The RAID system can be operated with fewer data and parity drives than the maximum. Drives can be added as long as the maximum number of drives is not exceeded. 
     The cyclic code generator polynomial may include a Reed Solomon (RS) code generator polynomial. The RAID RS ECC may be operated in erasure mode only. In other words, one of the drives has failed and therefore the “correction power” coincides with RS ECC redundancy count. 
     The RAID RS ECC encoder may encode to the maximum correction power. The number of parity drives may be greater than or equal to one and less than t_max. In this case, some of the RS ECC redundancies are dropped and are treated as erasures by the decoder. This configuration allows flexible correction power without adding additional complexity to the RAID RS ECC encoder and decoder to support multiple RS ECC codes corresponding to various levels of correction power. 
     This RS ECC configuration allows relatively seamless removal of parity drives. In other words, the corresponding RS ECC symbol in each RAID ECC codeword may be marked as an erasure. 
     Referring now to  FIG. 5 , a data storage system  140  includes data drives  142  d 1 -d k  and parity hard drives  144  p 1 -p r . The number of data drives k may be different than the number of parity drives r. The drives may perform ECC and CRC at the drive level as described above. The data drives  142  and parity drives  144  communicate via a bus  146 . The bus  146  also communicates with a RAID control module  148 , which communicates with a system  150 , such as a computer or a network of computers. 
     The RAID control module  148  includes a RAID ECC encoder module  152 , a RAID ECC decoder module  154 , a mapping module  156 , a code word difference module  158  and a drive failure/change detector module  170 . The RAID ECC encoder module  152  generates ECC redundancy corresponding to the information contained in the array of drives  12  and forms code words in response to a code generator polynomial. The generator polynomial may be a cyclic code generator polynomial such as a Reed-Solomon code generator polynomial. 
     The RAID ECC decoder module  154  recovers the data when a drive failure occurs. The RAID ECC encoder module  152  and the RAID ECC decoder module  154  can be combined into a single module. 
     The mapping module  156  determines the mapping between logical locations and physical locations of the data. The logical locations of data may be referenced to index positions of data in a cyclic (such as RS) code word of length k+r. This mapping may change as needed. The code word difference module  158  determines a difference between two code words. 
     The drive failure/change detector module  170  determines whether a change in the arrays  12 ,  14  is being performed or is about to be performed. The change may include identifying drive failures, removing a data or parity drive, inserting a new data or parity drive, or modifying a data drive. An input device  172  may provide data relating to an impending change so that data from the drive may optionally be read before the change takes place. 
     Referring now to  FIG. 6 , a method for removing a hard drive and changing the code word according to the present disclosure is shown. Steps  200 ,  202  and  204  are similar to steps  100 ,  102  and  104  and, therefore, will not be discussed further. In this approach, the physical-to-logical mapping does not change when a data drive is removed. As a result, except for the removed drive, the remaining drives do not need to be read and there is no down-time for the remaining data drives. In step  205 , control determines whether a drive needs to be removed. 
     In step  206 , the removed data drive is read. In step  210 , the data drive is removed. In step  212 , a zero is assigned to the logical location corresponding to the removed drive. In step  220 , a difference codeword is generated. 
     As mentioned above, a first set of code words is determined as:
         (d 1 , . . . ,d i , . . . ,d k ,p 1 ,p 2 , . . . ,p n−k )
 
The new code word for the system is:
   (d 1 , . . . ,d* i , . . . ,d k ,p* i ,p* 2 , . . . ,p* n−k )
 
The difference code word is, thus, set forth as:
   (0,0,Δd i ,0,0,d* i , . . . 0,Δp 1 ,Δp 2 , . . . , Δp n−k )
 
Where:
   Δd i =d i +d* i ,Δp 1 =p 1 +p* 1 ,Δp 2 =p 2 +p* 2 , . . . Δp n−k =p n−k +p* n−k )
 
In step  222 , the parity drives are modified in response to the difference code word.
       

     This approach avoids reading all of the data drives during drive removal. This approach reads the information from the drive that is being removed, followed by read/write operation on the parity drives. 
     Let (d 1 , . . . ,d i , . . . ,d k ,p 1 ,p 2 , . . . ,p n−k ) be the current value of an RAID ECC codeword, and further assume that symbol d i  comes the i th  drive that is marked for removal. The RAID control module  148  forms new ECC word (0,0,d i ,0,0, . . . 0) and proceeds to encode it to form “difference” RS ECC codeword (0,0,d i ,0,0, . . . 0,p* 0 ,p* 1 , . . . ,p* n−k ). Adding the original ECC codeword to the difference ECC codeword produces another ECC codeword (d 1 , . . . d i−1 , 0,d i+1  . . . ,d k ,p 1 +p* 1 ,p 2 +p* 2 , . . . ,p r +p* r ), which has desired values corresponding to the data drives. Furthermore, note that the symbol corresponding to the i th  drive is now 0 as desired since it is being removed. The original parity values, say p1, is updated by p 1 +p 1 *. 
     The operation of adding new data drives to the RAID system of  FIGS. 6 and 7  is described below. The algorithm is similar to that used for drive removal. To insert new drive, the number of data drives needs to be less than the maximum possible k_max. If the RAID system is not full, one of the drive slots has a symbol zero in each RAID ECC codeword. 
     Without loss of generality, assume that the i th  logical slot is not used. In other words, the current RAID ECC codeword has the form (d 1 , . . . d i−1 ,0,d i+1  . . . ,d k ,p 1 ,p 2 , . . . ,p r ). RAID control module forms new ECC word (0,0,d 1 ,0,0, . . . 0) and proceeds to encode it to form “difference” RS ECC codeword (0,0,d 1 ,0,0, . . . 0,p* 0 ,p* 1 , . . . ,p* r ). Adding the original ECC codeword to the difference ECC codeword produces another ECC codeword (d 1 , . . . d i−1 ,d i ,d i+1  . . . ,d k ,p 1 +p* 1 ,p 2 +p* 2 , . . . ,p r +p* r ), that has desired values corresponding to data drives. 
     Referring now to  FIG. 7 , a method for adding a drive is set forth. The physical-to-logical mapping is not changed and the insertion position keeps its old logical location (not necessarily the highest degree location). In step  300 , control determines whether a new drive is being added. If step  300  is true, control determines whether the number of drives is less than a maximum number of drives k_max in step  302 . If step  302  is false, a new data drive is added at a zero location previously set to zero or a next unused logical position in step  304 . In step  306 , a difference code word is determined in a similar manner to that set forth above. In step  308 , the parity drives are updated using the difference code word. 
     Referring now to  FIG. 8 , a method for adding a new hard drive to the system described in  FIG. 4  is set forth. As was previously described above, when a new drive is added to the RAID system of  FIG. 4 , the conventional system reads all of the data disks, generates new code words and writes parity. 
     A similar difference generating technique is used to reduce downtime. The location mapping of the data is changed by adding one more location to the highest degree location. In step  350 , control determines whether a new drive is to be added. In step  352 , a new drive is added to a physical location, which is mapped to the highest degree position in the logical locations of the code word. In step  354 , the new data drive is read. In step  356 , a difference code word is generated. In step  358 , the parity drive(s) is/are modified in response to the difference code word. 
     Referring now to  FIG. 9 , a table illustrating the difference between the methods of  FIGS. 4 and 7  is illustrated. The table  500  has two rows corresponding to  FIG. 4  and  FIG. 6 . The first column is code length. In  FIG. 4 , the code length is changed by moving the logical locations toward the low degree position. As can be seen, the removed data drive does not have to be read while the remaining drives are read. The parity drives are written in  FIG. 4 . In  FIG. 7 , the removed data drives are read and the remaining drives are not read. The parity drives are read and written. 
     Referring now to  FIG. 10 , another implementation of the disclosure is set forth. In this implementation, one of the hard data drives is modified. In this case, the mapping from physical to logical locations remains unchanged. 
     In step  550 , the polynomial representation is determined. In step  552 , the code words are formed and saved to the disks in stripes. In step  554 , the first code words are stored on the various drives. In step  556 , control determines whether a data drive in the system needs to be modified. In step  558 , a difference code word is determined in code word difference determination module  32 . By adding the difference of the parity to the original parity, the new code word is formed. In step  564 , parity is modified. As mentioned above, a first set of code words is determined as:
         (d 1 , . . . d i , . . . ,d k ,p 1 ,p 2 , . . . ,p n−k )
 
which represents the original information written on the RAID system. If the data written on the i-th drive is modified, the new information on the RAID system has the form (d 1 , . . . ,d* i , . . . ,d k ,p* i ,p* 2 , . . . ,p* n−k ). Note that besides changing the data on i-th data drive, parity drives also have to be modified. Instead of encoding (d 1 , . . . d* i , . . . ,d k ) directly (this once again would require to read all the data drives), the modified word (0,0,Δd i ,0,0, . . . 0) is encoded to obtain RS ECC codeword (0,0,Δd i  0,0, . . . 0,Δp 1 ,Δp 2 , . . . ,Δ n−k ) where Δd i =d i +d* i ,Δp 1 =p 1 +p* 1 ,Δp 2 =p 2 +p* 2 , . . . ,Δp n−k =p n−k +p* n−k . Observe that carrying out symbol-wise addition of original RAID ECC codeword (d 1 , . . . ,d i , . . . ,d k ,p 1 ,p 2 , . . . ,p n−k ) and difference RS ECC codeword (0,0,Δd i ,0,0, . . . 0,Δp 1 ,Δp 2 , . . . ,Δp n−k ) gives desired new RS ECC codeword (d 1 , . . . d i , . . . ,d k ,p 1 ,p 2 , . . . ,p n−k ).
       

     Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.