Group coded recording

In computer science, group coded recording or group code recording (GCR) refers to several distinct but related encoding methods for representing data on magnetic media. The first, used in 6250 bpi magnetic tape since 1973, is an error-correcting code combined with a run-length limited (RLL) encoding scheme, belonging into the group of modulation codes.[1] The others are different mainframe hard disk as well as floppy disk encoding methods used in some microcomputers until the late 1980s. GCR is a modified form of a NRZI code, but necessarily with a higher transition density.[1]

Magnetic tape

Group coded recording was first used for magnetic-tape data storage on 9-track reel-to-reel tape.[1] The term was coined during the development of the IBM 3420 Model 4/6/8 Magnetic Tape Unit[2] and the corresponding 3803 Model 2 Tape Control Unit,[3][2] both introduced in 1973.[2][4] IBM referred to the error correcting code itself as "group coded recording". However, GCR has come to refer to the recording format of 6250 bpi (250 bits/mm[1]) tape as a whole, and later to formats which use similar RLL codes without the error correction code.

In order to reliably read and write to magnetic tape, several constraints on the signal to be written must be followed. The first is that two adjacent flux reversals must be separated by a certain distance on the media, defined by the magnetic properties of the media itself. The second is that there must be a reversal often enough to keep the reader's clock in phase with the written signal; that is, the signal must be self-clocking and most importantly to keep the playback output high enough as this is proportional to the density of flux transitions. Prior to 6250 bpi tapes, 1600 bpi tapes satisfied these constraints using a technique called phase encoding (PE), which was only 50% efficient. For 6250 bpi GCR tapes, a (0, 2) RLL code is used, or more specifically a 4/5 (0, 2) block code[1] sometimes also referred to as GCR (4B-5B) encoding.[5] This code requires five bits to be written for every four bits of data.[1] The code is structured so that no more than two zero bits (which are represented by lack of a flux reversal) can occur in a row,[1] either within a code or between codes, no matter what the data was. This RLL code is applied independently to the data going to each of the nine tracks.

Of the 32 five-bit patterns, eight begin with two consecutive zero bits, six others end with two consecutive zero bits, and one more (10001) contains three consecutive zero bits. Removing the all-ones pattern (11111) from the remainder leaves 16 suitable code words.

The 6250 bpi GCR RLL code:[6][7][8][5]

4-bit valueGCR code[6][7]
hexbinbinhex
0x000001.10010x19
0x100011.10110x1B
0x200101.00100x12
0x300111.00110x13
0x401001.11010x1D
0x501011.01010x15
0x601101.01100x16
0x701111.01110x17
4-bit valueGCR code[6][7]
hexbinbinhex
0x810001.10100x1A
0x910010.10010x09
0xA10100.10100x0A
0xB10110.10110x0B
0xC11001.11100x1E
0xD11010.11010x0D
0xE11100.11100x0E
0xF11110.11110x0F

11 of the nibbles (other than xx00 and 0001) have their code formed by prepending the complement of the most significant bit; i.e. abcd is encoded as aabcd. The other five values are assigned codes beginning with 11. Nibbles of the form ab00 have codes 11baa, i.e. the bit reverse of the code for ab11. The code 0001 is assigned the remaining value 11011.

Because of the back then extremely high density of 6250 bpi tape, the RLL code is not sufficient to ensure reliable data storage. On top of the RLL code, an error-correcting code called the Optimal Rectangular Code (ORC) is applied.[9] This code is a combination of a parity track and polynomial code similar to a CRC, but structured for error correction rather than error detection. For every seven bytes written to the tape (before RLL encoding), an eighth check byte is calculated and written to the tape. When reading, the parity is calculated on each byte and exclusive-ORed with the contents of the parity track, and the polynomial check code calculated and exclusive-ORed with the received check code, resulting in two 8-bit syndrome words. If these are both zero, the data is error free. Otherwise, error-correction logic in the tape controller corrects the data before it is forwarded to the host. The error correcting code is able to correct any number of errors in any single track, or in any two tracks if the erroneous tracks can be identified by other means.

In newer IBM half-inch 18-track tape drives recording at 24000 bpi, 4/5 (0, 2) GCR was replaced by a more efficient 8/9 (0, 3) modulation code, mapping eight bits to nine bits.[1]

Hard disks

In the mid-1970s, Sperry Univac, ISS Division was working on large hard drives for the mainframe business using group coding.[10]

Floppy disks

Like magnetic tape drives, floppy disk drives have physical limits on the spacing of flux reversals (also called transitions, represented by one-bits).

Micropolis

Offering GCR-compatible diskette drives and floppy disk controllers (like the 100163-51-8 and 100163-52-6[11]), Micropolis endorsed data encoding with group coded recording[12] on 5¼-inch 100 tpi 77-track diskette drives to store twelve 512-byte sectors per track since 1977 or 1978.[13][14][15][16]

Micro Peripherals

Micro Peripherals, Inc. (MPI) marketed double-density 5¼-inch disk drives (like the single-sided B51 and double-sided B52 drives) and a controller solution implementing GCR since early 1978.[17][18]

Durango

The Durango Systems F-85 (introduced in September 1978[19][20]) used single-sided 5¼-inch 100 tpi diskette drives providing 480 KB utilizing a proprietary high-density 4/5 group coded encoding. The machine was using a Western Digital FD1781 floppy disk controller, designed by a former Sperry ISS engineer,[16] with 77-track Micropolis drives.[21] In later models such as the Durango 800[22] series this was expanded to a double-sided option for 960 KB (946 KB formatted[22][nb 1]) per diskette.[20][23][21][13]

Apple

For the Apple II floppy drive, Steve Wozniak invented a floppy controller which (along with the Disk II drive itself) imposed two constraints:

  • Between any two one bits, there may be a maximum of one zero bit.
  • Each 8-bit byte must start with a one bit.

The simplest scheme to ensure compliance with these limits is to record an extra "clock" transition before each data bit according to differential Manchester encoding or (digital) FM (Frequency Modulation). Known as 4-and-4 encoding, the resulting Apple implementation allowed only ten 256-byte sectors per track to be recorded on a single-density 5¼-inch floppy. It uses two bytes for each byte.

,

Close to a month prior to the shipment of the disk drive in spring 1978,[25] Wozniak realized that a more complex encoding scheme would allow each eight-bit byte on disk to hold five bits of useful data rather than four bits. This is because there are 34 bytes which have the top bit set and no two zero bits in a row. This encoding scheme became known as 5-and-3 encoding, and allowed 13 sectors per track; it was used for Apple DOS 3.1, 3.2, and 3.2.1, as well as for the earliest version of Apple CP/M:[26]

,

Reserved GCR-codes: 0xAA and 0xD5.[26]

Wozniak called the system "my most incredible experience at Apple and the finest job I did".[25]

Later, the design of the floppy drive controller was modified to allow a byte on disk to contain up to one pair of zero bits in a row. This allowed each eight-bit byte to hold six bits of useful data, and allowed 16 sectors per track. This scheme is known as 6-and-2 encoding,[26] and was used on Apple Pascal, Apple DOS 3.3[26] and ProDOS,[28] and later with Apple FileWare drives in the Apple Lisa and the 400K and 800K 3½-inch disks on the Macintosh and Apple II.[29][30] Apple did not originally call this scheme "GCR", but the term was later applied to it[30] to distinguish it from IBM PC floppies which used the MFM encoding scheme.

,

Reserved GCR-codes: 0xAA and 0xD5.[26][28]

Commodore

Independently, Commodore Business Machines (CBM) created a group coded recording scheme for their Commodore 2040 floppy disk drive (launched in the spring of 1979). The relevant constraints on the 2040 drive were that no more than two zero bits could occur in a row; the drive imposed no special constraint on the first bit in a byte. This allowed the use of a scheme similar to that used in 6250 bpi tape drives. Every four bits of data are translated into five bits on disk, according to the following table:

4-bit valueGCR code[31]
hexbinbinhex
0x000000.10100x0A
0x100010.10110x0B
0x200101.00100x12
0x300111.00110x13
0x401000.11100x0E
0x501010.11110x0F
0x601101.01100x16
0x701111.01110x17
4-bit valueGCR code[31]
hexbinbinhex
0x810000.10010x09
0x910011.10010x19
0xA10101.10100x1A
0xB10111.10110x1B
0xC11000.11010x0D
0xD11011.11010x1D
0xE11101.11100x1E
0xF11111.01010x15

Each code starts and ends with at most one zero bit, ensuring that even when the codes are concatenated, the encoded data will never contain more than two zero bits in a row. With this encoding at most eight one bits in a row are possible. Therefore, Commodore used sequences of ten or more one bits in a row as synchronization mark.

This more efficient GCR scheme, combined with an approach at constant bit-density recording by gradually increasing the clock rate (zone constant angular velocity, ZCAV) and storing more physical sectors on the outer tracks than on the inner ones (zone bit recording, ZBR), enabled Commodore to fit 170 kB on a standard single-sided single-density 5.25-inch floppy, where Apple fit 140 kB (with 6-and-2 encoding) or 114 kB (with 5-and-3 encoding) and an FM-encoded floppy held only 88 kB.

Sirius/Victor

Similar, the 5.25-inch floppy drives of the Victor 9000 aka Sirius 1, designed by Chuck Peddle in 1981/1982, used a combination of ten-bit GCR and constant bit-density recording by gradually decreasing a drive's rotational speed for the outer tracks in nine zones (a form of zoned constant linear velocity (ZCLV)) while increasing the number of sectors per track (a variant of zone bit recording (ZBR)) to achieve formatted capacities of 606 kB (single sided) / 1188 kB (double-sided) on 96 tpi media.[32][33][34][35]

Brother

Starting around 1985, Brother introduced a family of dedicated word processor typewriters with integrated 3.5-inch 38-track[nb 2] diskette drive. Early models of the WP and LW series used a Brother-specific group-coded recording scheme with twelve 256-byte sectors to store up to 120 KB[nb 3] on single-sided and up to 240 KB[nb 3] on double-sided double-density (DD) diskettes.[16][36][37][38] Reportedly, prototypes were already shown at the Internationale Funkausstellung 1979 (IFA) in Berlin.

Sharp

In 1986, Sharp introduced a turnable 2.5-inch pocket disk drive solution (drives: CE-1600F, CE-140F; internally based on the FDU-250 chassis; media: CE-1650F) for their series of pocket computers with a formatted capacity of 62464 bytes per side (2× 64 kB nominal, 16 tracks, 8 sectors/track, 512 bytes per sector, 48 tpi, 250 kbit/s, 270 rpm) with GCR (4/5) recording.[39][40]

Other uses

GCR was also evaluated for a possible use in bar code encoding schemes (packing efficiency, timing tolerances, amount of storage bytes for timing information, and DC output level).[41]

See also

Notes
  1. The product flyer for the Durango 800 series documents a formatted "on-line capacity" of 1.892 MB for the diskette drives. The system, however, was equipped with two 5¼-inch Micropolis 100 tpi 77-track floppy drives by default, and 1.892 MB is about twice as large as the physical drive capacity documented in various other sources (480 KB per side), therefore, by "on-line capacity" they must have meant the available storage capacity available to users for the combination of two drives.
  2. The sources give slightly contradicting parameters regarding the Brother diskette formats. 12 sectors á 256 bytes would give 120 KB per side on a 40-track drive, but one source claims the drives were 38-track only.
  3. The following Brother models are known to support a 120 KB diskette format (incomplete list): WP-1 (1985/1987), WP-5 (1987/1989), WP-6 (1989), WP-55 (1987/1989), WP-500 (1987/1989). The following models are known to support a 240 KB format (incomplete list): WP-70, WP-75 (1989), WP-80 (1985/1989), WP-3400, WP-3410, WP-3550, WP-3650D, WP-760D, WP-760D+, LW-1 (1989), LW-20, LW-30, LW-100, LW-400.

References
  1. Patel, Arvind Motibhai (1988). "5. Signal and Error-Control Coding". In Mee, C. Denis; Daniel, Eric D. (eds.). Magnetic Recording. Vol. II: Computer Data Storage (1st ed.). McGraw-Hill Book Company. ISBN 0-07-041272-3.
  2. CW staff (1973-03-14). "6,250 Byte/In. Density - IBM 3420 Storage More Than Tripled". Computerworld. White Plains, New York, USA. VII (11): 1–2. Retrieved 2017-03-23. IBM added three new models to the 3420 magnetic tape system than can record data at the "densest recording capability yet offered", according to the company. Using a new method called Group Coded Recording (GCR), the IBM drives can handle tapes containing a data density of 6,250 byte/in. compared with 1,600 byte/in. on earlier models of the 3420. […] An upgraded control unit was also announced - the 3803 Model 2 - which operates with both the earlier and latest 3420 tape units. The Model 2 includes the capability of correcting errors in one or two tracks "simultaneously while the tape is in motion", IBM said. […] The GCR method segments data written on tape into groups of characters to which a special coding character is added. And the higher density is based on a combination of a modified coding scheme, a smaller interrecord gap (called an interblock gap) and modified electronics and electromechanical components, IBM said. Installed 3803/3420 tape systems can be converted to the higher densities in the field. […]
  3. "The Gallery of Old Iron". 2004. Archived from the original on 2008-12-25. […] I moved to the lab at Poughkeepsie in 1958 […] I later was Lead designer and architect for the 2802 Tape Control Unit and a few years after that, Lead Designer and Architect of the 3803 which was a very large modification based on the 2802. Three of us shared a Corporate Award for the 3803 and I, along with Planner Charlie Von Reyn, came up with the name "Group Coded Recording (GCR)" as the name of the recording method. […] (NB. An anonymous comment by one of the developers on the origin of the name "Group Coded Recording".)
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  13. "NCC Preview: OEMs at NCC - Micropolis Corp". Computerworld. CW Communications, Inc. XII (22): P/50. 1978-05-28. Retrieved 2017-06-12. […] Micropolis has extended the capacity of 5.25-in. floppy disk subsystems via double-sided models with formatted file storage of up to nearly 2 million bytes […] The Megafloppy series also features an intelligent controller that facilitates interconnection of four subsystems to a common host interface for a total on-line storage capacity of more than 15M bytes […] Double-sided versions of the product line will be implemented first in two OEM series - Model 1015 and Model 1055 […] The Model 1015 is an unpackaged drive designed for the manufacturer who integrates floppy disk storage into his own system enclosure. A range of storage capacities from 143,000 to 630,000 bytes per drive is available […] Model 1015 customers have the option of using the Micropolis intelligent controller and Group Code Recording (GCR) method to further expand file space up to 946,000 bytes […] Offering GCR and a microprocessor-based controller as standard features, the Model 1055 5.25-in. floppy has four soft-sectored formats for each of its 77 tracks, yielding a maximum capacity of 1,892,000 bytes of file space on its double-sided version […] An add-on module available for the 1055 is comprised of two read/write heads and two drives, sharing a common controller. The subsystem capacity (formatted) with the module is 3,784,000 bytes […] Up to four 1055s, each with an add-on module, can be daisy-chained to a common host for a maximum on-line storage capacity of more than 15M bytes […]
  14. Micropolis Maintenance Manual Floppy Disk Subsystem (PDF) (revision 1, 1st ed.). Micropolis Corporation. February 1979. 1082-04. Archived (PDF) from the original on 2017-06-12. Retrieved 2017-06-12. (NB. Micropolis 100163-51-8 and 100163-52-6 are GCR-based.)
  15. "InfoNews/Hardware: Hardware/Briefs". InfoWorld. 2 (2): 19. 1980-03-03. Retrieved 2017-06-12. […] Four new 96 tracks-per-inch products have been added to Micropolis' current line of 100 tpi single-sided and double-sided floppy disks. The 96 tpi drives offer 70 tracks-per-side, as opposed to the 77 offered by the MegaFloppy line. The four models are: 1) The 1015-V: 436 KB, unformatted, FM/MFM recording […] 2) The 1016-V: 532 KB unformatted, Group Coded Recording (GCR) […] 3) The 1015-VI: a two-head version of the MFM drive, 872 KB […] 4) The 1016-VI: also a two-head drive, 1.064 MB GCR encoding […]
  16. Guzis, Charles "Chuck" P. (2015-09-20). "Multi-platform distribution format". Sydex. Archived from the original on 2017-06-14. Retrieved 2017-06-14. […] At the same time Micropolis was working a 5.25" drive that could hold about as much as an 8", using some tricks. The Micropolis drive was 100 tpi, 77 track and, by using GCR, could hold 12 512-byte sectors per track. That's 462 KiB. This was about 1977-78. […] The […] drive and controller implementation (ours was done by a guy we'd recruited from Sperry ISS) was […] complex and expensive […] Brother WP disks […] are 38 track, single-sided, Brother-encoded GCR that hold […] 120K on 2D floppies. […]
  17. Allen, David (February 1978). "A Minifloppy Interface" (PDF). BYTE. Kansas City, USA. 3 (2): 114, 116–118, 120, 122, 134–125. Archived from the original (PDF) on 2017-06-14. Retrieved 2017-06-14. […] Of the alternative codes used to achieve double density, GCR (Group Coded Recording) looks quite attractive. Micro Peripherals Inc has implemented double density using GCR in a full size floppy disk and controller system currently being marketed. […] GCR is nothing more than the old standby NRZ with its attendant advantages, but, since ordinary NRZ has no clocking information and a potentially high DC content during long strings of ones or zeros, the data is reformatted to eliminate the long strings. The reformatting converts each four bit group of original data into five bits of group coded data; the five bits in the encoded version will always have a mix of ones and zeros, even if the real data is all in one state. Reformatting in GCR can be accomplished in software, as opposed to MFM, etc, which almost unavoidably must be encoded and decoded in hardware. Thus, GCR has good possibilities as a low cost, high reliability scheme for achieving double density. […]
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  33. "Supplemental Technical Reference Material". Revision 0 (1st printing ed.). Scotts Valley, CA, USA: Victor Publications. 1983-03-23. Application Note: 002. […] Single-sided floppy drive offers 80 tracks at 96 TPI […] Double-sided floppy drive offers 160 tracks at 96 TPI […] Floppy drives have 512 byte sectors; utilising a GCR, 10-bit recording technique. […] Although the Victor 9000 uses 5 1/4-inch minifloppies of a similar type to those used in other computers, the floppy disks themselves are not readable on other machines, nor can the Victor 9000 read a disk from another manufacturers machine. The Victor 9000 uses a unique recording method to allow the data to be packed as densely as 600 kbytes on a single-sided single-density minifloppy; this recording method involves the regulation of the speed at which the floppy rotates, explaining the fact that the noise from the drive sometimes changes frequency.
  34. "Chapter 7. Disk Drive Assembly". Victor 9000 Technical Reference Manual (PDF). Victor Business Products, Inc. June 1982. pp. 7–1..7–9. 710620. Archived (PDF) from the original on 2017-03-23. Retrieved 2017-03-23. […] Track density is 96 tracks per inch, and recording density is maintained at approximately 8000 bits per inch on all tracks. […] The VICTOR 9000 uses an encoding technique called group code recording (GCR) to convert the data from internal representation to an acceptable form. GCR converts each (4-bit) nibble into a 5-bit code that guarantees a recording pattern that never has more than two zeros together. Then data is recorded on the disk by causing a flux reversal for each "one" bit and no flux reversal for each "zero" bit. […]
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  37. French, Mick (2002-09-13). "Brother WP-6". Archived from the original on 2017-11-22. Retrieved 2017-06-14. […] The 3.5" 240Kb disk drive is a single head Brother part no.13194989 and is connected with a 15 pin ribbon. […] it initializes (formats) the disk to a capacity of 236.5Kb. […]
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  39. "Model CE-1600F". Sharp PC-1600 Service Manual (PDF). Yamatokoriyama, Japan: Sharp Corporation, Information Systems Group, Quality & Reliability Control Center. July 1986. pp. 98–104. Archived (PDF) from the original on 2017-05-07. Retrieved 2017-03-23. GCR is an abbreviation of Group Coded Recording. A single byte, 8 bits, data are divided into two 4-bit data which is also converted onto a 5-bit data. Thus, a single byte (8 bits) is recorded on the media as a 10-bit data.
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Further reading
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