Group coded recording
In computer science, group coded recording or group code recording (GCR) refers to several distinct but related encoding methods for magnetic media. The first, used in 6250bpi 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. 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.
GCR for magnetic tape
Group coded recording was first used for magnetic tape data storage on 9-track reel-to-reel tape. The term was coined during the development of the IBM 3420 Model 4/6/8 Magnetic Tape Unit and the corresponding 3803 Model 2 Tape Control Unit, both introduced in 1973. IBM referred to the error correcting code itself as "group coded recording". However, GCR has come to refer to the recording format of bpi (250 bits/mm 6250) 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. The second is that there must be a flux reversal often enough to keep the reader's clock in phase with the written signal; that is, the signal must be self-clocking. Prior to bpi tapes, 6250 bpi tapes satisfied these constraints using a technique called 1600phase encoding (PE), which was only 50% efficient. For bpi GCR tapes, a (0, 2) 6250RLL code is used, or more specifically a 4/ (0, 2) block code. This code requires five bits to be written for every four bits of data. 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, 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.
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 extremely high density of bpi tape, the RLL code is not sufficient to ensure reliable data storage. On top of the RLL code, an 6250error-correcting code called the Optimal Rectangular Code (ORC) is applied. 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 000 bpi, 244/ (0, 2) GCR was replaced by a more efficient 8/ (0, 3) modulation code, mapping eight bits to nine bits.
GCR for hard disks
GCR for 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).
Offering GCR-compatible diskette drives and floppy disk controllers (like the 100163-51-8 and 100163-52-6), Micropolis endorsed data encoding with group coded recording on 5¼-inch 100 tpi 77-track diskette drives to store twelve 512-byte sectors per track since 1977 or 1978.
The Durango Systems F-85 (introduced in September 1978) 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, with 77-track Micropolis drives. In later models such as the Durango 800 series this was expanded to a double-sided option for 960 KB (946 KB formatted[nb 1]) per diskette.
- 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.
Close to a month prior to the shipment of the disk drive in spring 1978, 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:
Reserved GCR-codes: 0xAA and 0xD5.
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, and was used on Apple Pascal, Apple DOS 3.3 and ProDOS, and later with Apple FileWare drives in the Apple Lisa and the 400K and 800K 3½-inch disks on the Macintosh and Apple II. Apple did not originally call this scheme "GCR", but the term was later applied to it to distinguish it from IBM PC floppies which used the MFM encoding scheme.
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, and no more than eight one bits 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 bpi tape drives. Every four bits of data are translated into five bits on disk, according to the following table: 6250
Inhere, no code starts with two zero bits, nor ends with two zero bits. This ensures that regardless of the input data, the encoded data will never contain more than two zero bits in a row. With this encoding not more than 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.
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 to achieve formatted capacities of 606 kB (single sided) / kB (double-sided) on 118896 tpi media.
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. Reportedly, prototypes were already shown at the Internationale Funkausstellung 1979 (IFA) in Berlin.
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 464 bytes per side (2× 64 kB nominal, 16 tracks, 8 sectors/track, 512 bytes per sector, 6248 tpi, 250 kbits/s, 270 rpm) with GCR (4/5) recording.
- Modified Frequency Modulation (MFM)
- Run Length Limited (RLL)
- Eight-to-Fourteen Modulation (EFM)
- Error-correcting code
- 8b/10b encoding
- Group code
- Integrated Woz Machine (IWM)
- 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.
- 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.
- 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.
- Patel, Arvind Motibhai (1988). "5. Signal and Error-Control Coding". In Mee, C. Denis; Daniel, Eric D. Magnetic Recording. II: Computer Data Storage (1st ed.). McGraw-Hill Book Company. ISBN 0-07-041272-3.
- 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. Archived from the original on 2017-03-23. 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. […]
- "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".)
- Harris, John P.; Phillips, William B.; Wells, Jack F.; Winger, Wayne D. (September 1981). "Innovations in the Design of Magnetic Tape Subsystems". IBM Journal of Research and Development. International Business Machines Corporation. 25 (5): 691–700. Archived from the original on 2017-05-07. Retrieved 2017-03-23.
- Keong, Kwoh Chee, Computer Peripherals (PDF), School of Computer Engineering, Nanyang Technological University, Singapore, Chapter 7. Magnetic Recording Fundamentals, archived (PDF) from the original on 2017-03-23, retrieved 2017-03-23
- Watkinson, John (1990). "3.4. Group codes". Coding for Digital Recording. Stoneham, MA, USA: Focal Press. pp. 51–61. ISBN 0-240-51293-6. ISBN 978-0-240-51293-8.
- Patel, Arvind Motibhai; Hong, Se June (1974). "Optimal Rectangular Code for High Density Magnetic Tapes". IBM Journal of Research and Development. 18 (6): 579–588.
- Jacoby, George V. (2003-01-06) [September 1977]. "A new look-ahead code for increased data density". IEEE Transactions on Magnetics. Sperry Univac, ISS Division, Cupertino, CA, USA: IEEE. 13 (5): 1202–1204. doi:10.1109/TMAG.1977.1059670. (NB. This article about the 3PM code was also presented at the Intermag 1977 in June 1977.)
- US 4261019, McClelland, S. Barry, "Compatible Digital Magnetic Recording System", published 1981-04-07, assigned to Micropolis Corporation  (NB. Application Number: US 06/098381)
- "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[disambiguation needed] to a common host for a maximum on-line storage capacity of more than 15M bytes […]
- 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.)
- "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 […]
- Guzis, Charles 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. […]
- 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. […]
- "Floppies Claim Improved Performance". Computerworld. CW Communications, Inc. XIII (7): 90. 1979-02-12. Retrieved 2017-06-14.
- Schultz, Brad (1978-10-02). "Business Mini Weighs 65 Pound - What is Durango?". Computerworld. CW Communications, Inc. XII (40): 1, 4. Retrieved 2017-06-13.
- Comstock, George E. (2003-08-13). "Oral History of George Comstock" (PDF). Interview with Hendrie, Gardner. Mountain View, California, USA: Computer History Museum. CHM X2727.2004. Archived (PDF) from the original on 2017-03-23. Retrieved 2017-03-23.
- Guzis, Charles P. (2009-09-13). "Durango GCR". Sydex. Retrieved 2017-03-25.
- "800 Technical Summary - 800 Series Business Computer System" (PDF). San Jose, CA, USA: Durango Systems, Inc. Archived (PDF) from the original on 2017-03-23. Retrieved 2017-03-23.
- Guzis, Charles P. (October 2006). "The Durango F-85 Computer". Sydex. Archived from the original on 2017-03-23. Retrieved 2017-03-23.
- Copy II Plus Version 9 - ProDOS/DOS Utilities - Data Recovery, File Management, Protected Software Backup (PDF). 9.0. Central Point Software, Inc. 1989-10-31 . Retrieved 2017-03-21.
- Williams, Gregg; Moore, Rob (January 1985). "The Apple Story / Part 2: More History and the Apple III". BYTE (interview): 166. Archived from the original on 2012-02-12. Retrieved 2013-10-26.  (NB. Interview with Steve Wozniak, where he describes creating the Apple version of GCR.)
- Worth, Don D.; Lechner, Pieter M. (May 1982) . Beneath Apple DOS (4th printing ed.). Reseda, CA, USA: Quality Software. Retrieved 2017-03-21. 
- Sather, James Fielding (1983). Understanding the Apple II - A Learning Guide and Hardware Manual for the Apple II Computer (1st ed.). Chatsworth, CA, USA: Quality Software. pp. 9–26, 9–27. ISBN 0-912985-01-1. Archived from the original on 2016-05-27. Retrieved 2017-03-21.
- Worth, Don D.; Lechner, Pieter M. (March 1985) . Beneath Apple ProDOS - For Users of Apple II Plus, Apple IIe and Apple IIc Computers (PDF) (2nd printing ed.). Chatsworth, CA, USA: Quality Software. ISBN 0-912985-05-4. LCCN 84-61383. Archived (PDF) from the original on 2017-03-21. Retrieved 2017-03-21. 
- Feichtinger, Herwig (1987). Arbeitsbuch Mikrocomputer (in German) (2 ed.). Munich, Germany: Franzis-Verlag GmbH. pp. 223–224. ISBN 3-7723-8022-0.
- Apple Computer, Inc. (February 1982) . Integrated Woz Machine (IWM) Specification (PDF) (19 ed.). DigiBam Computer Museum. Archived (PDF) from the original on 2016-08-06. Retrieved 2016-08-06.
- Hildon, Karl J. H. (March 1985). "GCR codes". The Complete Commodore Inner Space Anthology (PDF). Milton, Ontario, Canada: Transactor Publishing Incorporated. p. 49. ISBN 0-9692086-0-X. Archived (PDF) from the original on 2017-03-23. Retrieved 2017-03-23.  (NB. Commodore GCR codes—but this reference erroneously claims that a 1-bit indicates a lack of a transition.)
- "Victor 9000/Sirius 1 Specification" (PDF). commodore.ca. Archived (PDF) from the original on 2017-03-23. Retrieved 2017-03-23.
- "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.
- "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 represenation 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. […]
- Gieseke, Hans-Werner (2003-08-27). "Brother WP-1" (in German). Archived from the original on 2017-06-14. Retrieved 2017-06-14. (NB. Reportedly, the Brother WP-1 technical data was derived from page 109 of the user manual.)
- French, Mick (2002-09-13). "Brother WP-6". Archived from the original on 2017-06-14. 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. […]
- Cotgrove, Michael S. (2009-02-26). "archaic floppy disc format". Retrieved 2017-06-14.
[…] There were several 3.5" Brother disks that are completely nonstandard. […] One had 1296 byte sectors and another had 12 x 256 byte GCR sectors […]
- "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.
- Sharp Service Manual Model CE-140F Pocket Disk Drive (PDF). Sharp Corporation. 00ZCE140F/SME. Archived (PDF) from the original on 2017-03-11. Retrieved 2017-03-11.
- Moseley, Robin C. (April 1979). "Technical Forum: A Comparison of Bar Code Encoding Schemes" (PDF). BYTE. Andover, MA, USA. 4 (4): 50, 52. Retrieved 2017-06-14.
- ANSI INCITS 40-1993 (R2003) Unrecorded Magnetic Tape for Information Interchange (9 track, 800 bpi, NRZI; bpi, 1600PE; and bpi, GCR) 6250
- ANSI INCITS 54-1986 (R2002) Recorded Magnetic Tape for Information Interchange ( bpi, GCR) 6250
- Sallet, Herbert W. (July 1977). "Magnetic tape: A high performer: Magnetic tape has evolved into a highly effective medium for high-density and low-cost-per-bit data recording". IEEE Spectrum. 14 (7): 26–31. doi:10.1109/MSPEC.1977.6501525. Retrieved 2017-06-14.
- Sidhu, Pawitter S. (December 1976). "Group-Coded Recording Reliably Doubles Diskette Capacity". Computer Design: 84–88.
- "(unknown)". Perkin-Elmer Data Systems News. Perkin-Elmer Data Systems. 1977-06-14.
- Hsiao, (Ben) M. Y.; Carter, William C.; Thomas, James W.; Stringfellow, William R. (September 1981). "Reliability, Availability, and Serviceability of IBM Computer Systems". IBM Journal of Research and Development. 25 (5): 462. doi:10.1147/rd.255.0453. (NB. Mentions the 5/4 RLL code used on bpi tape drives.) 6250
- Qualstar 34XX Technical Service Manual (PDF) (Revision J ed.), Canoga Park, CA, USA: Qualstar Corporation, pp. 3–4..3–7, 500450, archived (PDF) from the original on 2011-09-30, retrieved 2017-03-23 (NB. Additional detail on the GCR tape format.)
- US 3685033, Agrawala, Ashok K. & Keshava Srivastava, "Block encoding for magnetic recording systems", published 1972-08-15, assigned to Honeywell Inc.  (NB. Application No: US 199. See also: CA993998A, CA993998A1, DE2142428A1) 66
- US 4210959, Wozniak, Stephen G., "Controller for magnetic disc, recorder, or the like", published 1980-07-01, assigned to Apple Computer, Inc.  (NB. Application Number: US 5/904420)
- US 4564941, Woolley, Richard N.; Neal Glover & Richard Williams, "Error detection system", published 1986-01-14, assigned to Apple Computer, Inc.  (NB. Application Number: US 06/559210. See also: CA1208794A, CA1208794A1, DE3443272A1, DE3443272C2)
- Dockery, Sean Brendan. "Apple II disk encoding".
- NEC µPD72070 - Floppy Disk Controller Specification Version 2.0 (PDF). 2.0 preliminary. NEC Corporation. October 1991. Archived (PDF) from the original on 2017-03-20. Retrieved 2017-03-20.
- Akesson, Linus (2013-03-31). "GCR decoding on the fly". Archived from the original on 2017-03-21. Retrieved 2017-03-21.
- Trikaliotis, Spiro (2010-03-05). "Commodore GCR "mysteries"". Archived from the original on 2014-08-05.
- "GCR ROM en-/decoder in Commodore 8050 and 8250 disk drives". Forum 64. Archived from the original on 2010-03-12.