708:
two zeros between the last one bit in the first code and the first one bit in the second code, for any two arbitrarily chosen codes. This is required because for any RLL code, the run-length limits – 0 and 2 in this case – apply to the overall modulated bitstream, not just to the components of it that represent discrete sequences of plain data bits. (This rule must hold for any arbitrary pair of codes, without exception, because the input data may be any arbitrary sequence of bits.) The IBM GCR code above meets this condition, since the maximal run length of zeros at the beginning of any 5-bit code is one, and likewise the maximal run length at the end of any code is one, making a total run length of two at the junction between adjacent codes. (An example of the maximal run length occurring between codes can be seen in the example given above, where the code for the data "0010" ends with a zero and the code for the next data, "1101", begins with a zero, forming a run of two zeros at the junction of these two 5-bit codes.)
261:, information is represented by changes in the direction of the magnetic field on the disk, and on magnetic media, the playback output is proportional to the density of flux transition. In a computer, information is represented by the voltage on a wire. No voltage on the wire in relation to a defined ground level would be a binary zero, and a positive voltage on the wire in relation to ground represents a binary one. Magnetic media, on the other hand, always carries a magnetic flux – either a "north" pole or a "south" pole. In order to convert the magnetic fields to binary data, some encoding method must be used to translate between the two.
283:
the controller itself may have small variations in speed. The problem is that, with a long string of zeros, there's no way for the disk drive's controller to know the exact position of the read head, and thus no way to know exactly how many zeros there are. A speed variation of even 0.1%, which is more precise than any practical floppy drive, could result in 4 bits being added to or removed from the 4096-bit data stream. Without some form of synchronization and error correction, the data would become completely unusable.
268:), simply encodes a 1 as a magnetic polarity transition, also known as a "flux reversal", and a zero as no transition. With the disk spinning at a constant rate, each bit is given an equal time period, a "data window", for the magnetic signal that represents that bit, and the flux reversal, if any, occurs at the start of this window. (Note: older hard disks used one fixed length of time as the data window over the whole disk, but modern disks are more complicated; for more on this, see
1502:
6400 encoded bits per inch on the tape, or 3200 data bits per inch. A (1,7) RLL encoding can also store 6400 encoded bits per inch on the tape, but since it only takes 3 encoded bits to store 2 data bits, this is 4267 data bits per inch. A (2,7) RLL encoding takes 2 encoded bits to store each data bit, but since there is guaranteed to be two 0 bits between any 1 bits, then it is possible to store 9600 encoded bits per inch on the tape, or 4800 data bits per inch.
1491:
43:
717:
constrains how closely bits can be recorded on the medium: In the worst case, with an arbitrary bit stream, there are two consecutive ones, which produces two consecutive flux transitions in time, so bits must be spaced far enough apart that there would be sufficient time between those flux transitions for the reader to detect them. But this code imposes a constraint of
308:
1246:
VFIR physical layer. Unlike magnetic encoding, this is designed for an infrared transmitter, where a 0 bit represents "off" and a 1 bit represents "on". Because 1 bits consume more power to transmit, this is designed to limit the density of 1 bits to less than 50%. In particular, it is a (1,13|5) RLL
282:
Since a disk drive is a physical piece of hardware, the rotational speed of the drive can change slightly, due to a change in the motor speed or thermal expansion of the disk platter. The physical media on a floppy disk can also become deformed, causing larger timing errors, and the timing circuit on
707:
Note that to meet the definition of (0,2) RLL, it is not sufficient only that each 5-bit code contain no more than two consecutive zeros, but it is also necessary that any pair of 5-bit codes as a combined sequentially not contain more than two consecutive zeros. That is, there must not be more than
1501:
Suppose a magnetic tape can contain up to 3200 flux reversals per inch. A modified frequency modulation, or (1,3) RLL encoding, stores each data bit as two bits on tape, but since there is guaranteed to be one 0 (no flux reversal) bit between any 1 (flux reversal) bits, then it is possible to store
404:
is the number of bits for which signal remains unchanged. A run length of 3 for bit 1, represents a sequence 111. For instance, the pattern of magnetic polarizations on the disk might be +−−−−++−−−++++++, with runs of length 1, 4, 2, 3, and 6. However, run-length limited coding terminology assumes
716:
Modified frequency modulation begins to get interesting, because its special properties allow its bits to be written to a magnetic medium with twice the density of an arbitrary bit stream. There is a limit to how close in time flux transitions can be for reading equipment to detect them, and that
278:
In a simple example, consider the binary pattern 101 with a data window of 1 ns (one nanosecond, or one billionth of a second). This will be stored on the disk as a change, followed by no change, and then another change. If the preceding magnetic polarity was already positive, the resulting
1610:
A constrained system is defined by a constrained set of 'good' or 'allowable' sequences to be recorded or transmitted. Constrained coding focuses on the analysis of constrained systems and the design of efficient encoders and decoders that transform arbitrary user sequences into constrained
1374:
The first eight rows describe a standard (1,7)-RLL code. The additional six exceptions increase the maximal run of zeros to 13 (in the legal pattern 100 000 000 000 001, which represents 10 11 10 11, followed by 01), but limit the maximal average ones density to
286:
The other problem is due to the limits of magnetic media itself: it is only possible to write so many polarity changes in a certain amount of space, so there's an upper limit to how many ones can also be written sequentially, this depends on the linear velocity and the head gap.
721: = 1, i.e. there is a minimum of one zero between each two ones. This means that in the worst case, flux transitions are two bit times apart, so the bits can be twice as close together as with the arbitrary bit stream without exceeding the reader's capabilities.
408:
Somewhat confusingly, the run length is the number of zeros (0, 3, 1, 2 and 5 in the preceding) between adjacent ones, which is one less than the number of bit times the signal actually remains unchanged. Run-length limited sequences are characterized by two parameters,
347:
hard disks began using RLL proper (i.e. variants more complex than those that had received their own proper names, such as MFM). RLL codes have found almost universal application in optical-disc recording practice since 1980. In consumer electronics, RLLs like the
279:
pattern might look like this: −−+. A value of 255, or all binary ones, would be written as −+−+−+−+ or +−+−+−+−. A zero byte would be written as ++++++++ or −−−−−−−−. A 512-byte sector of zeros would be written as 4096 sequential bits with the same polarity.
298:
between each and every one, the overall frequency of polarity changes is reduced, allowing the drive to store more data in the same amount of space, resulting in either a smaller package for the same amount of data or more storage in the same size package.
1011:
bits on the disk, like MFM, but because the minimal run length is 50% longer (3 bit times instead of 2), the bits can be written faster, achieving 50% higher effective data density. The encoding is done in 2-, 3- or 4-bit groups.
217:
the stored data, which would lead to the possible erroneous insertion or removal of bits when reading the data back. This mechanism ensures that the boundaries between bits can always be accurately found (preventing
323:
All codes used to record on magnetic disks have limited the length of transition-free runs and can therefore be characterized as RLL codes. The earliest and simplest variants were given specific names, such as
761:
Except for the clock bits not always being one, this is the same as the FM table, and that is how this code gets its name. The inserted clock bits are 0 except between two 0 data bits.
405:
NRZI encoding, so 1 bits indicate changes and 0 bits indicate the absence of change, the above sequence would be expressed as 11000101001000001, and only runs of zero bits are counted.
290:
To prevent this problem, data is coded in such a way that long repetitions of a single binary value do not occur. By limiting the number of zeros written consecutively to some maximum
724:
This doubled recording density compensates for the 1/2 coding rate of this code (it takes two bits to represent one bit of real information) and makes it equivalent to a rate-1 code.
903:(last in the table) match must be used; those are exceptions handling situations where applying the earlier rules would lead to a violation of the code constraints.
1505:
The flux-reversal densities on hard drives are significantly greater, but the same improvements in storage density are seen by using different encoding systems.
1818:
433:
In the encoded format a "1" bit indicates a flux transition, while a "0" indicates that the magnetic field on the disk does not change for that time interval.
328:(MFM), and the name "RLL" is commonly used only for the more complex variants not given such specific names, but the term technically applies to them all.
275:
This method is not quite that simple, as the playback output is proportional to the density of ones, a long run of zeros means no playback output at all.
491:
By extending the maximal run length to 2 adjacent 0 bits, the data rate can be improved to 4/5. This is the original IBM group coded recording variant
392:
are the minimal and maximal allowed run lengths. For more coverage on the storage technologies, the references cited in this article are useful.
201:
Specifically, RLL bounds the length of stretches (runs) of repeated bits during which the signal does not change. If the runs are too long,
225:
Early disk drives used very simple encoding schemes, such as RLL (0,1) FM code, followed by RLL (1,3) MFM code, which were widely used in
294:, this makes it possible for the drive controller to stay synchronized. By limiting the number of zeros written in a row to some minimum
60:
417:, which stipulate the minimal and maximal zero-bit run length that can occur in the sequence. So RLL codes are generally specified as (
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1242:
The HHH(1,13) code is a rate-2/3 code developed by three IBM researchers (Hirt, Hassner, and Heise) for use in the 16 MB/s
851:(1,7) RLL maps 2 bits of data onto 3 bits on the disk, and the encoding is done in 2- or 4-bit groups. The encoding rules are: (
79:
249:. Higher-density RLL (2,7) and RLL (1,7) codes became the de facto industry standard for hard disks by the early 1990s.
64:
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1655:, DISK/TREND, Inc., publisher of market studies of the worldwide disk drive and data storage industries. web.archive.org.
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code, where the final 5 indicates the additional constraint that there are at most 5 consecutive "10" bit pairs.
483:
Data: 0 0 1 0 1 1 0 1 0 0 0 1 1 0 Encoded: 1010111011111011101010111110 Clock: 1 1 1 1 1 1 1 1 1 1 1 1 1 1
205:
is difficult; if they are too short, the high frequencies might be attenuated by the communications channel. By
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The encoded forms begin with at most 4, and end with at most 3 zero bits, giving the maximal run length of 7.
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843:
Data: 0 0 1 0 1 1 0 1 0 0 0 1 1 0 Encoded: x010010001010001001010010100 Clock: x 1 0 0 0 0 0 0 0 1 1 0 0 0
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222:), while efficiently using the media to reliably store the maximal amount of data in a given space.
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A detailed description is furnished of the limiting properties of runlength limited sequences.
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Generally, the term "RLL code" is used to refer to more elaborate encodings, but the original
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191:
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449:, can be seen as a simple rate-1/2 RLL code. The added 1 bits are referred to as clock bits.
1778:
1713:(Second fully revised ed.). Eindhoven, The Netherlands: Shannon Foundation Publishers.
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1637:(1972), “Run-Length-Limited Variable Length Coding with Error Propagation Limitation”,
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1385:. The longest run of 1–0 pairs is 000 101 010 101 000.
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For example, let us encode the bit sequence 10110010 with different encodings
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182:, refer to the rate of the code, while the remaining two specify the minimal
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1535:
1527:
and EFMplus are DC-free (2,10) RLL codes used on CDs and DVDs, respectively.
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One of the simplest practical codes, modified non-return-to-zero-inverted (
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219:
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until the mid-1980s and are still used in digital optical discs such as
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Data: 0 0 1 0 1 1 0 1 0 0 0 1 1 0 Encoded: 101 001 010 100 100 000 001
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Where "x" is the complement of the stream's previously encoded bit.
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The first "RLL" code used in hard drives was RLL (2,7), developed by
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number of zeroes between consecutive ones. This is used in both
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engineers and first used commercially in 1979 on the IBM 3370
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Hirt, Walter; Hassner, Martin; Heise, Nyles (February 2001),
899:, 0, 0, 0). When encoding according to the table below, the
671:. In the 5 cases where this would violate one of the rules (
704:
Data: 0010 1101 0001 1000 Encoded: 10010011011101111010
230:
1767:"IrDA-VFIr (16 Mb/s): modulation code and system design"
1234:
Data: 1 1 0 1 1 0 0 1 1 Encoded: 1000 001000 00001000
158:
limits. RLL codes are defined by four main parameters:
656:
Where possible (11 out of 16 codes), the bit pattern
150:
technique that is used to send arbitrary data over a
768:
bit, the resulting encoding table for each data bit
194:
and storage systems that move a medium past a fixed
67:. Unsourced material may be challenged and removed.
1706:
660:is encoded by prefixing it with the complement of
727:The encoding is very similar to the FM encoding.
1388:This code limits the ones density to between
8:
679:), a code beginning with 11 is substituted (
27:Coding technique in communication technology
1653:Five decades of disk drive industry firsts
1625:, IBM Journal of Research and Development.
1015:Western Digital WD5010A, WD5011A, WD50C12
1623:A Quarter Century of Disk File Innovation
127:Learn how and when to remove this message
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213:, RLL reduces the timing uncertainty in
1740:Mee, C. Denis; Daniel, Eric D. (1996).
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360: = 10) are employed in the
7:
1819:Rotating disc computer storage media
65:adding citations to reliable sources
1709:Codes for Mass Data Storage Systems
25:
1590:"Innovation in Constrained Codes"
1489:
764:When combined with the previous
447:differential Manchester encoding
41:
1799:Digital Magnetic Tape Recording
339:, for use with the 4300 series
52:needs additional citations for
1:
1744:(2nd ed.). McGraw Hill.
1670:"Runlength-Limited Sequences"
380: = 10) used in the
372:code (rate = 8/16,
326:modified frequency modulation
1771:IEEE Personal Communications
1594:IEEE Communications Magazine
1525:Eight-to-fourteen modulation
1408:, with an average of 25.8%.
1850:
29:
1742:Magnetic Storage Handbook
1703:Kees A. Schouhamer Immink
819:
800:
343:. During the late 1980s,
1834:Physical layer protocols
1606:10.1109/MCOM.002.2200249
425:) RLL, e.g.: (1,3) RLL.
352:(rate = 8/17,
311:Seagate ST11R, an 8-bit
30:Not to be confused with
1674:Proceedings of the IEEE
1563:and bit synchronization
1561:Self-synchronizing code
1666:Kees Schouhamer Immink
1586:Kees Schouhamer Immink
1531:Error correcting codes
320:
152:communications channel
1640:U.S. patent 3,689,899
1157:Perstor Systems ADRC
772:effectively becomes.
310:
1635:P. A. Franaszek
443:Frequency Modulation
317:hard disk controller
76:"Run-length limited"
61:improve this article
1556:Run-length encoding
1483:0100 1000 00100100
1086:Seagate ST11R, IBM
1007:bits of data onto 2
993:(2,7) RLL is rate-
270:zoned bit recording
253:Need for RLL coding
32:run-length encoding
1166:(2,7) RLL encoded
1095:(2,7) RLL encoded
1024:(2,7) RLL encoded
445:code, also called
396:Technical overview
321:
140:Run-length limited
18:Run Length Limited
1783:10.1109/98.904900
1705:(November 2004).
1680:(11): 1745–1759.
1668:(December 1990).
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1427:
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1411:
1409:
1386:
1367:
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1359:
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1340:
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1311:
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1279:
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1268:
1267:
1263:
1260:
1259:
1255:
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1251:
1248:
1245:
1237:
1232:
1229:
1221:
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1201:
1197:
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1193:
1189:
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1177:
1173:
1170:
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1165:
1162:
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1158:
1150:
1147:
1146:
1142:
1139:
1138:
1134:
1131:
1130:
1126:
1123:
1122:
1118:
1115:
1114:
1110:
1107:
1106:
1102:
1099:
1098:
1094:
1091:
1090:
1087:
1079:
1076:
1075:
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1068:
1067:
1063:
1060:
1059:
1055:
1052:
1051:
1047:
1044:
1043:
1039:
1036:
1035:
1031:
1028:
1027:
1023:
1020:
1019:
1016:
1013:
1010:
1006:
988:
983:
975:
972:
971:
967:
964:
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959:
956:
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951:
948:
947:
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939:
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932:
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927:
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919:
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795:
791:
788:
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781:
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771:
767:
762:
759:
751:
748:
747:
743:
740:
739:
735:
732:
731:
728:
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722:
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711:
709:
702:
699:
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689:
663:
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629:
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621:
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543:
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516:
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481:
473:
470:
469:
465:
462:
461:
457:
454:
453:
450:
448:
444:
437:FM: (0,1) RLL
436:
434:
428:
426:
424:
420:
416:
412:
406:
403:
395:
393:
391:
387:
384:. Parameters
383:
379:
375:
371:
367:
363:
359:
355:
351:
346:
342:
338:
334:
329:
327:
318:
314:
309:
302:
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297:
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288:
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236:
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228:
223:
221:
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208:
204:
199:
197:
193:
189:
185:
181:
177:
173:
169:
165:
161:
157:
153:
149:
145:
141:
131:
128:
120:
109:
106:
102:
99:
95:
92:
88:
85:
81:
78: –
77:
73:
72:Find sources:
66:
62:
56:
55:
50:This article
48:
44:
39:
38:
33:
19:
1777:(1): 58–71,
1774:
1770:
1760:
1741:
1735:
1724:. Retrieved
1708:
1697:
1689:
1677:
1673:
1660:
1648:
1630:
1618:
1609:
1597:
1593:
1580:
1504:
1500:
1488:
1450:01011 10010
1415:
1387:
1373:
1365:10 11 10 11
1357:00 11 10 11
1352:101 000 000
1344:100 000 000
1336:001 000 000
1328:010 000 000
1241:
1230:
1227:
1156:
1085:
1014:
1008:
1004:
992:
981:
900:
896:
892:
888:
884:
880:
876:
872:
868:
864:
860:
856:
852:
850:
839:
793:
786:
779:
769:
765:
763:
760:
757:
726:
723:
718:
715:
706:
700:
695:
691:
687:
661:
655:
490:
479:
442:
440:
432:
422:
418:
414:
410:
407:
401:
399:
389:
385:
377:
373:
362:Compact Disc
357:
353:
330:
322:
295:
291:
289:
285:
281:
277:
274:
263:
256:
224:
200:
187:
186:and maximal
183:
179:
175:
171:
167:
163:
159:
146:coding is a
143:
139:
138:
123:
114:
104:
97:
90:
83:
71:
59:Please help
54:verification
51:
1469:10 11 00 10
875:), except (
148:line coding
1829:Line codes
1808:Categories
1726:2015-08-23
1611:sequences.
1573:References
1541:Modulation
1480:10 11 0010
402:run length
400:Generally
207:modulating
87:newspapers
1536:Line code
1497:Densities
1447:1011 0010
1422:Encoding
1349:10 11 01
1341:10 11 00
1333:00 11 01
1325:00 11 00
1238:HHH(1,13)
1231:Example:
1222:00100100
1214:00001000
1151:00100100
1143:00001000
1080:00100100
1072:00001000
989:(2,7) RLL
982:Example:
847:(1,7) RLL
840:Example:
792:Encoded (
701:Example:
480:Example:
364:(CD) and
341:mainframe
156:bandwidth
117:June 2023
1520:Bit slip
1509:See also
1477:RLL(2,7)
1466:RLL(1,7)
1458:10110010
1455:RLL(1,3)
1444:RLL(0,2)
1436:10110010
1433:RLL(0,1)
1428:Encoded
1412:Examples
1320:100 000
1312:101 000
1304:010 000
1296:001 000
1256:Encoded
976:010 000
968:001 000
960:100 000
952:101 000
912:Encoded
879:, 0, 0,
736:Encoded
686:, where
582:Encoded
504:Encoded
458:Encoded
366:MiniDisc
350:EFM code
220:bit slip
215:decoding
1403:⁄
1393:⁄
1380:⁄
1206:001000
1198:000100
1190:100100
1135:001000
1127:100100
1119:000100
1064:001000
1056:000100
1048:100100
998:⁄
901:longest
370:EFMPlus
303:History
247:Blu-ray
101:scholar
1748:
1717:
1317:11 11
1309:11 10
1301:01 11
1293:01 10
973:10 01
965:10 00
957:00 01
949:00 00
895:, NOT
871:, NOT
785:Data (
778:Data (
646:01111
638:01110
630:01101
622:11110
614:01011
606:01010
598:01001
590:11010
568:10111
560:10110
552:10101
544:11101
536:10011
528:10010
520:11011
512:11001
429:Coding
103:
96:
89:
82:
74:
1425:Data
1219:0110
1211:0111
1182:0100
1174:1000
1148:0010
1140:0011
1111:0100
1103:1000
1077:0010
1069:0011
1040:0100
1032:1000
643:1111
635:1110
627:1101
619:1100
611:1011
603:1010
595:1001
587:1000
565:0111
557:0110
549:0101
541:0100
533:0011
525:0010
517:0001
509:0000
257:On a
243:Hi-MD
154:with
108:JSTOR
94:books
1746:ISBN
1715:ISBN
1551:PRML
1398:and
1288:101
1280:100
1272:001
1264:010
1253:Data
1244:IrDA
1203:001
1195:010
1187:000
1163:Data
1132:011
1124:010
1116:000
1092:Data
1061:011
1053:010
1045:000
1021:Data
944:010
936:001
928:100
920:101
909:Data
891:AND
867:AND
733:Data
681:11be
677:ab00
673:000d
669:abcd
658:abcd
579:Data
501:Data
455:Data
413:and
388:and
337:DASD
315:RLL
266:NRZI
245:and
211:data
209:the
80:news
1779:doi
1682:doi
1602:doi
1285:11
1277:10
1269:01
1261:00
1179:10
1171:11
1108:10
1100:11
1037:10
1029:11
941:11
933:10
925:01
917:00
834:01
826:01
815:00
807:10
787:n-1
766:n-1
752:01
744:x0
698:).
675:or
474:11
466:10
382:DVD
333:IBM
313:ISA
272:.)
235:DVD
144:RLL
142:or
63:by
1810::
1773:,
1769:,
1688:.
1678:78
1676:.
1672:.
1608:.
1598:60
1596:.
1592:.
1395:12
887:,
863:,
855:,
820:1
801:0
796:)
749:1
741:0
694:∨
690:=
664::
471:1
463:0
345:PC
241:,
239:MD
237:,
233:,
231:CD
198:.
170:,
166:,
162:,
1786:.
1781::
1775:8
1754:.
1729:.
1684::
1643:.
1604::
1405:3
1401:1
1391:1
1382:3
1378:1
1009:n
1005:n
1000:2
996:1
897:y
893:y
889:x
885:x
881:y
877:x
873:y
869:y
865:x
861:x
857:y
853:x
831:1
823:0
812:1
804:0
794:n
789:)
782:)
780:n
770:n
719:d
696:d
692:a
688:e
683:a
667:a
662:a
423:k
421:,
419:d
415:k
411:d
390:k
386:d
378:k
374:d
358:k
354:d
296:d
292:k
188:k
184:d
180:n
178:/
176:m
172:k
168:d
164:n
160:m
130:)
124:(
119:)
115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
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