## Runlength-Limited Sequences (1990)

Venue: | Proc. IEEE |

Citations: | 11 - 1 self |

### BibTeX

@INPROCEEDINGS{Immink90runlength-limitedsequences,

author = {Kees A. Schouhamer Immink},

title = {Runlength-Limited Sequences},

booktitle = {Proc. IEEE},

year = {1990},

pages = {1745--1759}

}

### OpenURL

### Abstract

this paper will concentrate, accepts the bit stream (extra bits added by the error-correction system included) as its input and converts the stream to a waveform suitable for the specific recorder requirements. The object of the recording code is to bring structure into a data stream that is generally not present in the information supplied by the user. All the aforementioned coding stages are present in a modern dig- ital video recorder [1]

### Citations

658 |
Matrix iterative analysis
- Varga
- 1962
(Show Context)
Citation Context ...tor v is usual ly called the approximate eigenvector. For a given code rate R = m/nsC(d, k), the existence of such an eigenvector is guaranteed by the Perron -Frobenius theory of nonnegative matrices =-=[19]-=-. It is not difficult to see that the set {oil, ' ' ' , o#} for which vi, =s= vi = 1 is the set of principal states. The following illustrations have been chosen to clarify some of the points dealt wi... |

67 |
A mathematical theory of communication," Bell Sys
- Shannon
- 1948
(Show Context)
Citation Context ...ranslated into n channel sym bols. What is the maximum value of R = rain that can be attained for some specified values of the minimum and maximum runlength dand k? The answer was provided by Shannon =-=[11]-=-. The maximum value of R that can be achieved is termed the capacity. The capacity, denoted by C(d, k), is governed by the specified constraints and is given by C(d, k) = lim I log z N(n). (5) Table I... |

48 | Coding Techniques for Digital Recorders - Immink |

36 |
Fibonacci codes for synchronization control
- Kautz
- 1965
(Show Context)
Citation Context ...ation (EFM), a rate 8/17, (d = 2, k = 10) code, which is the basis of the Compact Disc [4]. Runlength-limited codes, in their general form, were pioneered in the 1960s by Freiman and Wyner [5], Kautz =-=[6]-=-, Gabor [7], Tang and Bahl [8], and notably Franaszek [9]. It is undoubtedly the case that RLL codes have generated a high and sustained level of interest amongst workers ever since the introduction o... |

26 |
Block codes for a class of constrained noiseless channels
- Tang, Bahl
- 1970
(Show Context)
Citation Context ... 2, k = 10) code, which is the basis of the Compact Disc [4]. Runlength-limited codes, in their general form, were pioneered in the 1960s by Freiman and Wyner [5], Kautz [6], Gabor [7], Tang and Bahl =-=[8]-=-, and notably Franaszek [9]. It is undoubtedly the case that RLL codes have generated a high and sustained level of interest amongst workers ever since the introduction of the basic ideas, and there i... |

24 |
On runlength codes
- Zehavi, Wolf
- 1988
(Show Context)
Citation Context ...l RLL sequence, that is, a sequence with maximum information content, has a truncated geometric runSCHOUHAMER IMMINK: RUNLENGTH-LIMITED SEQUENCES 1749 length distribution with parameter X [13], [14], =-=[15]-=-. Then Pt(T,) = X-T', T, = d + 1, ..s, k + 1, (21) where X is the largest real root of (10). Substitution of the distribution (21) provides a straightforward method of determining the spectrum of idea... |

23 |
Algorithms for sliding block codes - an application of symbolic dynamics to information theory
- Adler, Coppersmith, et al.
- 1983
(Show Context)
Citation Context ...d without ambiguity, because all three bits of the succeeding codeword are simultaneously "zero." H. Sliding Block Code Algorithm The sliding block coding algorithm of Adler, Coppersmith, an=-=d Hassner [33]-=- evolved from a field of abstract mathematics known as symbolic dynamics. The key idea in this construction method is that one modifies the fi nite-state transition machine by splitting and merging so... |

17 |
Recording codes for digital magnetic storage
- Siegel
- 1985
(Show Context)
Citation Context ... in this construction method is that one modifies the fi nite-state transition machine by splitting and merging some of the channel states to obtain a new finite-state machine. An example, taken from =-=[34]-=-, may serve to illustrate the idea. Example 6: We construct a rate 2/3, (0, 1) code. The connection matrices D and D 3 are The finite-state transition diagrams associated with D and D 3 are shown in F... |

14 | A survey of coding schemes for transmission or recording of digital data - Kobayashi - 1971 |

13 | The Art of Digital Audio - WATKINSON - 1988 |

12 |
Optimum block codes for noiseless input restricted channels
- Freiman, Wyner
- 1964
(Show Context)
Citation Context ...rteen Modulation (EFM), a rate 8/17, (d = 2, k = 10) code, which is the basis of the Compact Disc [4]. Runlength-limited codes, in their general form, were pioneered in the 1960s by Freiman and Wyner =-=[5]-=-, Kautz [6], Gabor [7], Tang and Bahl [8], and notably Franaszek [9]. It is undoubtedly the case that RLL codes have generated a high and sustained level of interest amongst workers ever since the int... |

11 |
Magnetic Recording
- Mee, Daniel
- 1996
(Show Context)
Citation Context ...ation can be obtained to create simple Boolean equations for encoding and decoding. The codeword 1754 PROCEEDINGS OF THE IEEE, VOL. 70, NO. 11, NOVEMBER 1990 assignment, which was given by Patel (see =-=[24], volume 2-=-), provides simple and inexpensive encoder and decoder logic. The allocation is based on the "divide and conquer" principle. Any 9-bit codeword is partitioned into three parts: two 4-bit sub... |

11 |
Run-length-limited variable length coding with error propagation limitation
- Franaszek
- 1972
(Show Context)
Citation Context ...data bit and up to one preceding data bit. Thus, no error in a received bit is propagated beyond at maximum four decoded data bits: The correspondence Table 13(a) as originally presented by Franaszek =-=[28]-=- has the drawback that it needs a shift register of length twelve, which increases error extension to at most six decoded symbols. This example demonstrates that the allocation of codewords in a varia... |

10 |
Sequence-state methods for run-length-limited coding
- Franaszek
- 1970
(Show Context)
Citation Context ...rging bits, which are preset to "zero", completes the design of a rate 7/(12 + 2), (2, o) block code. The shortest fixed-length codes for a selection of (d, k) combinations were computed by =-=Franaszek [20]-=- with the successive elimination procedure; the results are collected in Table 6. We draw attention to the fact that the minimum Table 6 Shortest Fixed-Length Block Codes of Given BitPer -Symbol Value... |

10 |
A Generalized Method For Encoding and Decoding Run-LengthLimited Binary Sequences
- Beenker, Immink
- 1983
(Show Context)
Citation Context ...fined to be the rank of x denoted by r(x), i.e, r(x) is the number of all y in Twith ysTheorem 1: The rank r(x) of the (d) sequences xsT can be calculated according to r(x) =sNt(j)xi. (27) Proof: See =-=[21]-=-. Example 4: Consider the set: T(d, n) = T(1, 4) of (d = 1) sequences of length four. We have N(0) = 1, N(1) = 2, N(2) = 3, N(3) = 5, and N(4) = 8. For instance, r(1001) = N(3) + N(0) = 5 + I = 6. We ... |

9 |
Zero modulation encoding in magnetic recording
- Patel
- 1975
(Show Context)
Citation Context ... the variable-length synchronous code is much more attractive with respect to hardware requirements. G. Look-Ahead Encoding Technique Another class of design techniques documented in the l iteratu re =-=[29]-=-, [22], [30], [31], [18], [32] is called future-dependent or look-ahead (LA) coding. A block code is said to be look-ahead if the encoding and decoding of a current block may depend on upcoming symbol... |

9 | Cattermole, Principles of Pulse Code Modulation - W - 1973 |

7 |
Statistical properties of selected recording codes,” IBM Res. Rep., Aug. 1987. et al
- Howell
- 1959
(Show Context)
Citation Context ...that an ideal RLL sequence, that is, a sequence with maximum information content, has a truncated geometric runSCHOUHAMER IMMINK: RUNLENGTH-LIMITED SEQUENCES 1749 length distribution with parameter X =-=[13]-=-, [14], [15]. Then Pt(T,) = X-T', T, = d + 1, ..s, k + 1, (21) where X is the largest real root of (10). Substitution of the distribution (21) provides a straightforward method of determining the spec... |

6 |
Schouhamer Immink, “Compact Disc: System Aspects and Modulation
- Heemskerk, A
- 1982
(Show Context)
Citation Context ...2, (d = 2, k = 7) code which is applied in the IBM3380 rigid disk drive [2], [3], and the Eight-to-Fourteen Modulation (EFM), a rate 8/17, (d = 2, k = 10) code, which is the basis of the Compact Disc =-=[4]-=-. Runlength-limited codes, in their general form, were pioneered in the 1960s by Freiman and Wyner [5], Kautz [6], Gabor [7], Tang and Bahl [8], and notably Franaszek [9]. It is undoubtedly the case t... |

5 |
The power spectrum of run-length-limited codes
- Gallopoulos, Heegard, et al.
- 1989
(Show Context)
Citation Context ...symbols whose runlengths Ts{d + 1,s-s, k + 1} are i.i.d. variables. Let the probability of occurrence of runlength T, be denoted by Pr(T), then the power spectral density function can be expressed by =-=[12]-=-: I I-IG()lsH() -ssin2 /2 il + G()I z' (18) where and k+l G() = , Pr(T)e , j = /-, (19) k+l '= ,, IPr(T). (20) I-d+1 Using information theoretical arguments, it can be shown that an ideal RLL sequence... |

5 |
Method for Encoding Binary Data
- Immink, Ogawa
- 1985
(Show Context)
Citation Context ...olumn) and its 14-bit channel representation (right column). Space limitations prohibit the presentation of the complete table, for full details the reader is advised to consult the patent literature =-=[26]-=-. The merging bits are primarily intended to ensure that the runlength conditions continue to be satisfied when the codewords are cascaded. If the runlength is in danger of becoming too short, we choo... |

5 | Magnetic recording systems - Wood - 1986 |

4 |
Look ahead coding for input restricted channels
- Lempel, Cohn
- 1982
(Show Context)
Citation Context ...he set of principal states, The foregoing analysis which is due to Franaszek, can be cast into a form that is of use later. We introduce an approximate eigenvalue inequality to guide the construction =-=[18]-=-. Let v = (v,s- , v k + ])r, vis{0, 1 }, be a vector with binary elements. ^ fixed-length code of the specified runlength constraints and parameters can be ascertained if there is a binary vector v th... |

4 | The Complete Handbook of Magnetic Recording - Jorgensen - 1988 |

3 |
Sequential encoding and decoding of variable word length, fixed rate data codes
- Eggenberger, Hodges
- 1978
(Show Context)
Citation Context ...hannel response, the desired information density, and the jitter and noise characteristics. Archetypal RLL codes are the rate 1/2, (d = 2, k = 7) code which is applied in the IBM3380 rigid disk drive =-=[2]-=-, [3], and the Eight-to-Fourteen Modulation (EFM), a rate 8/17, (d = 2, k = 10) code, which is the basis of the Compact Disc [4]. Runlength-limited codes, in their general form, were pioneered in the ... |

3 |
Analysis of correctable errors in the IBM 3380 disk file
- Howell
- 1984
(Show Context)
Citation Context ...l response, the desired information density, and the jitter and noise characteristics. Archetypal RLL codes are the rate 1/2, (d = 2, k = 7) code which is applied in the IBM3380 rigid disk drive [2], =-=[3]-=-, and the Eight-to-Fourteen Modulation (EFM), a rate 8/17, (d = 2, k = 10) code, which is the basis of the Compact Disc [4]. Runlength-limited codes, in their general form, were pioneered in the 1960s... |

3 |
Optimization of Low-frequency Properties of Eight-to-Fourteen Modulation’, The Radio and
- Immink, Gross
- 1983
(Show Context)
Citation Context ...system, by Iooki ng more than SCHOUHAMER IMMINK: RUNLENGTH-LIMITED SEQUENCES 1755 oneword ahead, since minimization of the RDS in the short term does not always contribute to longer-term minimization =-=[27]-=-. This more sophisticated algorithm is not implemented in the present equipment. F. Variable-Length Synchronous Codes As we have learned in the preceding section, attempts to increase fixed-lenth stat... |

3 |
Construction of bounded delay codes for discrete noiseless channels
- Franaszek
- 1982
(Show Context)
Citation Context ...e-length synchronous code is much more attractive with respect to hardware requirements. G. Look-Ahead Encoding Technique Another class of design techniques documented in the l iteratu re [29], [22], =-=[30]-=-, [31], [18], [32] is called future-dependent or look-ahead (LA) coding. A block code is said to be look-ahead if the encoding and decoding of a current block may depend on upcoming symbols. The codin... |

3 |
Binary two-thirds rate code with full word look-ahead
- Jacoby, Kost
- 1984
(Show Context)
Citation Context ...us code is much more attractive with respect to hardware requirements. G. Look-Ahead Encoding Technique Another class of design techniques documented in the l iteratu re [29], [22], [30], [31], [18], =-=[32]-=- is called future-dependent or look-ahead (LA) coding. A block code is said to be look-ahead if the encoding and decoding of a current block may depend on upcoming symbols. The coding schemes may also... |

2 |
On synchronous variable-length coding for discrete noiseless channels
- Franaszek
- 1969
(Show Context)
Citation Context ...naszek [9] developed a technique of successive elimination for determining the existence of a set of principal states through operations on the connection matrix. The subsequent procedure, taken from =-=[17]-=-, decides whether there exists a set of principal states for the specified parameters. Let the codeword length n and the source word length m be given. The specified channel constraints dand kdefine a... |

2 |
The compact disc digital audio system
- Carasso, Peek, et al.
- 1982
(Show Context)
Citation Context ...traint, namely that the dc-content or low-frequency content of the coded bit stream should be as small as possible. The reason for this is that the servo systems used for track following and focusing =-=[25]-=- are controlled by the low-frequency components of the signal read from the disc, and the signal could therefore interfere with the servo systems. In the Compact Disc system, the frequency range from ... |

2 |
Run-length reduction of 3PM code via lookahead technique
- Cohn, Jacoby
- 1982
(Show Context)
Citation Context ...th synchronous code is much more attractive with respect to hardware requirements. G. Look-Ahead Encoding Technique Another class of design techniques documented in the l iteratu re [29], [22], [30], =-=[31]-=-, [18], [32] is called future-dependent or look-ahead (LA) coding. A block code is said to be look-ahead if the encoding and decoding of a current block may depend on upcoming symbols. The coding sche... |

2 | Videodisc and Optical Memory Systems - Isailovic - 1985 |

1 |
de With, "An experimental digital VCR with 40 mm drum, single actuator and DCT-based bit-rate red uction
- Borgers, Heijnemans, et al.
- 1988
(Show Context)
Citation Context ...ode is to bring structure into a data stream that is generally not present in the information supplied by the user. All the aforementioned coding stages are present in a modern digital video recorder =-=[1]. Schemati-=-cally the elements of the coding steps in a digital recorder as shown in Fig. 1 are similar to those of a "pointto -point" communication link. For examp!e, in a radio or satellite link the e... |

1 |
Adaptive coding Jor selJ-clocking recording
- Gabor
- 1967
(Show Context)
Citation Context ..., a rate 8/17, (d = 2, k = 10) code, which is the basis of the Compact Disc [4]. Runlength-limited codes, in their general form, were pioneered in the 1960s by Freiman and Wyner [5], Kautz [6], Gabor =-=[7]-=-, Tang and Bahl [8], and notably Franaszek [9]. It is undoubtedly the case that RLL codes have generated a high and sustained level of interest amongst workers ever since the introduction of the basic... |

1 |
Sequence-state encoding for digital transmission, " Bell $yst
- Franaszek
- 1968
(Show Context)
Citation Context ...es of short and long word lengths, are frequently profitable in terms of hardware complexity. The basis of variable-length synchronous codes was laid by Franaszek with his pioneering work reported in =-=[9]-=-. Variable-length codes offer the possibility of using short words more frequently than those of longer lengths. This often permits a marked reduction in coder and decoder complexity relative to a fix... |

1 |
Some statistical properties of maxentropic ru nlength-limited sequences
- Immink
- 1983
(Show Context)
Citation Context ...n ideal RLL sequence, that is, a sequence with maximum information content, has a truncated geometric runSCHOUHAMER IMMINK: RUNLENGTH-LIMITED SEQUENCES 1749 length distribution with parameter X [13], =-=[14]-=-, [15]. Then Pt(T,) = X-T', T, = d + 1, ..s, k + 1, (21) where X is the largest real root of (10). Substitution of the distribution (21) provides a straightforward method of determining the spectrum o... |

1 |
Coding using multiple block (d, k) codes
- Fredrickson, Wolf
- 1989
(Show Context)
Citation Context ...er, a detailed study might save many logic gates. ^ systematic approach of choosing a specific assignment that simplifies the look-up function is not available, and only little progress has been made =-=[16]-=-. It is quite straightforward to generalize the preceding implementation example to encoders that generate sequences with an arbitrary value of the minimum runlength. To that end, choose some appropri... |

1 |
new look-ahead codefor increasing data density, " lEEk Trans
- Jacoby, A
- 1977
(Show Context)
Citation Context ... it obeys the specified constraints. A simple look-up table is used for encoding and decoding. $ PM Code The basic parameters of the 3PM (Three Position Modulalion) code, which was invented by Jacoby =-=[22]-=-, are d = 2, k: 11 and R = 112. The encoding mechanism of the 3PM code is similar to fixed-length block encoding and decoding with one extra rule. The encoding is explained by looking at Table 10. As ... |

1 |
Improved encoder and decoder for a byte-oriented rate 8/9
- Patel
- 1938
(Show Context)
Citation Context ...ficulty that o and (2 are the principal states (cr] and o4 are deleted). From any principal state there are at least 293 > 256 sequences available. This, in principle, concludes the discussion. Patel =-=[23]-=- showed, however, that we can do slightly better. By judiciously discarding a number of potential codewords he arrived at a code in which the pattern Sy = 100010001 is not a codeword and also does not... |

1 | Principles of digital line coding - Cattermole - 1983 |

1 | q'he choice of a recording code - Mackintosh - 1979 |

1 | Principles and Practice of Information Theory - glahut - 1987 |