## Maximum Transition Run Codes for Generalized Partial Response Channels (2001)

Venue: | IEEE J. SELECT. AREAS COMMUN |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Cideciyan01maximumtransition,

author = {Roy D. Cideciyan and Evangelos Eleftheriou and Brian H. Marcus and Dharmendra S. Modha},

title = {Maximum Transition Run Codes for Generalized Partial Response Channels},

journal = {IEEE J. SELECT. AREAS COMMUN},

year = {2001},

volume = {19},

number = {4},

pages = {619--634}

}

### OpenURL

### Abstract

A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors for generalized partial response channels with spectral nulls both at dc and at the Nyquist frequency. Two variants of the twins constraint that depend on whether the generalized partial response detector trellis is unconstrained or j-constrained are studied. Deterministic finite-state transition diagrams that present the twins constraint are specified, and the capacity of the new class of MTR constraints is computed. The connection between (G, I) constraints and MTR(j) constraints is clarified. Code design methodologies that are based on look-ahead coding in combination with violation detection/substitution as well as on state splitting are used to obtain several specific constructions of high-rate MTR codes.

### Citations

7540 |
The Mathematical Theory of Communication
- Shannon, Weaver
- 1949
(Show Context)
Citation Context ...gation. I. INTRODUCTION THE THEORETICAL foundation of coding for input-constrained channels, also known as modulation coding, was established in Shannon’s classic study of discrete noiseless channel=-=s [1]-=-. Among the various methods for constructing efficient modulation codes that have been developed in the past 50 years, the state-splitting algorithm of Adler et al. [2] provides a systematic and mathe... |

636 |
An Introduction to Symbolic Dynamics and Coding
- Lind, Marcus
- 1995
(Show Context)
Citation Context ... second one involves the state-splitting algorithm and is based on the mathematical discipline of symbolic dynamics. For an introduction into symbolic dynamics, the reader is referred to the textbook =-=[11]-=-. The paper is organized as follows. In Section II, we describe the recording system model, emphasizing modulation coding, generalized partial response shaping, and detection. In Section III, we chara... |

90 |
P.H.: Constrained systems and coding for recording channels. In: Handbook of Coding Theory
- Marcus, Roth, et al.
- 1998
(Show Context)
Citation Context ... of an encoder generating sequences from . It is given by Cap , where is the largest real eigenvalue of the adjacency matrix associated with a deterministic FSTD that presents For instance [1], [11], =-=[23]. -=-Cap Cap Cap For an MTR constraint , the adjacency matrix, and therefore the capacity, can be computed from (2) and (4). Tables I–III list the capacity of various constraints for , 3, and 4 by trunca... |

78 | Codes for digital recorders
- Immink, Siegel, et al.
- 1998
(Show Context)
Citation Context ...t the right choices be made during the code construction procedure in order to obtain good codes. For an extensive discussion of the large body of work on modulation coding, the reader is referred to =-=[3]-=-. Peak detection systems employing runlength-limited (RLL) ( ) constrained codes are predominant in digital magnetic storage at low densities. RLL( ) codes reduce the effects of pulse interference and... |

56 |
Finite-state modulation codes for data storage
- Marcus, Siegel, et al.
(Show Context)
Citation Context ...able input sequences are drawn from the set of all possible binary sequences. The modulation encoder generates binary sequences that satisfy a desired constraint, such as PRML( ) constraints [4]–[6]=-=, [12] or -=-MTR constraints [7]–[9], [13]–[16]. The modulation encoder is followed by a precoder of the form (in the MTR case) or (in the ( ) case). The output of the precoder is then mapped into two-level ch... |

33 | Maximum transition run codes for data storage systems
- Moon, Brickner
- 1996
(Show Context)
Citation Context ...or propagation at the modulation decoder. More recently, maximum transition run (MTR) ( ) codes have been introduced by Moon and Brickner to provide coding gain for extended partial response channels =-=[7]-=-. The maximum possible code rate for the original MTR( ) constraints was less than 8/9, leading to an unacceptable loss of performance due to the low code rate. Time-varying MTR constraints permit the... |

28 |
A PRML system for digital magnetic recording
- Cideciyan, Dolivo, et al.
- 1992
(Show Context)
Citation Context ....com). Publisher Item Identifier S 0733-8716(01)01748-6. 0733–8716/01$10.00 © 2001 IEEE erate storage densities, the introduction of partial response maximum-likelihood sequence detection (PRML) (s=-=ee [4]-=- and references therein) requires a different class of constrained codes. This class of codes, collectively known as PRML( ) codes, facilitates timing recovery and gain control, and limits the path me... |

17 |
Noise-predictive maximum likelihood (NPML) detection
- Coker, Eleftheriou, et al.
- 1998
(Show Context)
Citation Context ... This class of generalized partial response channel polynomials is significant in practice and, when combined with sequence detection, gives rise to noise-predictive maximum-likelihood (NPML) systems =-=[18]-=-, [19]. The Viterbi detector in Fig. 1 performs maximum-likelihood sequence detection on the generalized partial response trellis and provides an estimate of the channel input sequence , where is the ... |

16 | Constrained coding for binary channels with high intersymbol interference
- Karabed, Siegel, et al.
- 1999
(Show Context)
Citation Context ... memory for the sequence detector in order to avoid significant performance degradation. Lucid treatments of these issues in connection with partial response channels of the form can be found in [3], =-=[15]-=-, and [20]. It can readily be seen that the same results hold for generalized partial response channels of the form (again, has no roots on the unit circle). In order to facilitate timing and gain con... |

14 |
An 8/9 rate time-varying trellis code for high density magnetic recording
- Bliss
- 1997
(Show Context)
Citation Context ...owever, the distance gain by eliminating these error events is offset by a significant rate loss penalty. For example, the capacity of the mod 2 MTR constraint (with period 2) is approximately 0.9162 =-=[8]-=-. It has been observed that for the Lorentzian recording model and NPML detection, the most dominant error events are and (see, e.g., [10]). An alternative coding strategy is therefore to allow the er... |

14 |
Time-varying MTR codes for high density magnetic recording
- Fitzpatrick, Modlin
- 1997
(Show Context)
Citation Context ...16-state detector, i.e., by implementing a time-varying trellis in the sequence detector. The rates of the codes that have been designed to satisfy time-varying MTR constraints are 8/9 [8] and higher =-=[9]-=-, [10]. These various classes of MTR codes increase the minimum Euclidean distance in the sequence detector by eliminating the dominant error events and are therefore known as distance-enhancing codes... |

13 |
Calderbank "Coset codes for partial response channels; or, coset codes with spectral nulls
- Forney, R
- 1989
(Show Context)
Citation Context ... Another desirable code property is the elimination of quasi-catastrophic error propagation that is inherent in maximum-likelihood sequence detection for partial response channels with spectral nulls =-=[21]-=-. This property allows a reduction of the path memory size of the sequence detector without degrading its bit error rate performance. Quasi-catastrophic error propagation is avoided by eliminating cha... |

12 | Error-event characterization on partial-response channels
- Altekar, Berggren, et al.
(Show Context)
Citation Context ...r the sequence detector in order to avoid significant performance degradation. Lucid treatments of these issues in connection with partial response channels of the form can be found in [3], [15], and =-=[20]-=-. It can readily be seen that the same results hold for generalized partial response channels of the form (again, has no roots on the unit circle). In order to facilitate timing and gain control algor... |

10 | Bounds on the number of states in encoder graphs for input-constrained channels - Marcus, Roth - 1991 |

7 | Immink, “Combinatorial construction of high rate runlength-limited codes
- Wijngaarden, S
- 1996
(Show Context)
Citation Context ...d violation detection combined with substitution have been successfully applied in the past to design efficient constrained codes such as RLL( ) codes [25], [33], MTR( ) codes [26], and PRML( ) codes =-=[27]-=-. The MTR code design methodologies presented in this section are based on the use of the state transition diagrams for MTR constraints and the application of the look-ahead coding technique and viola... |

6 |
personal communication
- Olson, Corp, et al.
- 1978
(Show Context)
Citation Context ... high-density magnetic recording, write precompensation schemes are used to mitigate the problem of nonlinear transition shift, a deleterious effect of intersymbol interference. One particular scheme =-=[28]-=- would adjust the writing of the string 11011 such that the two dibits collide (more precisely, such that the second transition of the first dibit collides with the first transition of the second dibi... |

5 |
Method and apparatus for implementing optimum PRML codes,” U.S. Patent 4,707,681
- Eggenberger, Patel
(Show Context)
Citation Context ...e path memory length of the sequence detector, and therefore the decoding delay, without significant degradation of detector performance. The most widely used code rates in the industry have been 8/9 =-=[5]-=- and 16/17 [6]. In general, high code rates and small error bursts at the modulation decoder output are desirable in order to minimize performance degradation due to rate loss and error propagation at... |

5 |
Noise predictive partial-response equalizers and applications
- Chevillat, Eleftheriou, et al.
- 1992
(Show Context)
Citation Context ...hitening. In particular, we will consider the important class of channel polynomials of the form , where , is an approximation of a predictor filter and is assumed to have no roots on the unit circle =-=[17]-=-. In this case, the output of the partial response channel is , and the noise at the input to the detector can be approximated by an additive white Gaussian noise (AWGN) source, provided that the equa... |

5 |
Design of a rate 6/7 maximum transition run code
- Brickner, Moon
- 1997
(Show Context)
Citation Context ... of look-ahead coding and violation detection combined with substitution have been successfully applied in the past to design efficient constrained codes such as RLL( ) codes [25], [33], MTR( ) codes =-=[26]-=-, and PRML( ) codes [27]. The MTR code design methodologies presented in this section are based on the use of the state transition diagrams for MTR constraints and the application of the look-ahead co... |

5 |
On Future-Dependent Block Coding for Input-Restricted Channels
- Franaszek
- 1979
(Show Context)
Citation Context ...varying mod 2 MTR@� aQY RA constraint. Fig. 11. FSTD presenting constrained system MTR@� aPY™aPA. indexed by the states of the FSTD and satisfying the vector inequality (an algorithm due to Fran=-=aszek [29] (se-=-e also [23]) can be applied to find an approximate eigenvector with minimal maximum entry). The entries of an approximate eigenvector are often called “weights.” The idea is that beginning with th... |

4 | Art of constructing lowcomplexity encoders/decoders for constrained block codes
- Modha, Marcus
- 2001
(Show Context)
Citation Context ...arrive at a rate 7 : 8 encoder, which is sliding-block decodable with a sliding window equal to two blocks. Moreover, the complexity is reasonable. Using the data-to-codeword assignment heuristics in =-=[31]-=- and the Berkeley SIS logic synthesis program, we constructed such an encoder with approximately 400 multiple-input gates and a corresponding total of 1900 cells in CMOS 6SF. For this assignment, we d... |

3 |
The performance of generalized maximum transition run trellis codes
- Bliss, She, et al.
- 1998
(Show Context)
Citation Context ...om the set of all possible binary sequences. The modulation encoder generates binary sequences that satisfy a desired constraint, such as PRML( ) constraints [4]–[6], [12] or MTR constraints [7]–[=-=9], [13]��-=-�[16]. The modulation encoder is followed by a precoder of the form (in the MTR case) or (in the ( ) case). The output of the precoder is then mapped into two-level channel input sequences , where and... |

3 |
Binary two-thirds rate code with full word look-ahead
- Jacoby, Kost
- 1984
(Show Context)
Citation Context ...TION RULES The techniques of look-ahead coding and violation detection combined with substitution have been successfully applied in the past to design efficient constrained codes such as RLL( ) codes =-=[25]-=-, [33], MTR( ) codes [26], and PRML( ) codes [27]. The MTR code design methodologies presented in this section are based on the use of the state transition diagrams for MTR constraints and the applica... |

2 | Algorithms for sliding-block codes: An application of symbolic dynamics to information theory
- Adler, Coppersmith, et al.
- 1983
(Show Context)
Citation Context ... of discrete noiseless channels [1]. Among the various methods for constructing efficient modulation codes that have been developed in the past 50 years, the state-splitting algorithm of Adler et al. =-=[2]-=- provides a systematic and mathematically rigorous approach to designing finite-state encoders and sliding-block decoders for finite-type constrained systems. In practice, however, all approaches to c... |

2 |
Channel capacity of (0, G/I) codes
- Stefanovic, Vasic
- 1993
(Show Context)
Citation Context ...invertible rate-1 code (such as a precoder), we conclude the following. Corollary: Cap Cap . This result is consistent with computed capacities (compare the capacity of the ( ) constraint (see, e.g., =-=[24]) -=-with the capacity of the corresponding MTR constraint in Tables I–III). The connection between ( ) and MTR constraints suggests a new approach for constructing a ( ) code that employs the precoder i... |

2 |
Time-varying encoders for constrained systems: An approach to limiting error propagation
- Ashley, Marcus
- 2000
(Show Context)
Citation Context ...gher rate finite-state code that satisfies . In order to control complexity as well as decoder error propagation, we make use of a time-varying version of the state-splitting algorithm, introduced in =-=[32]-=-. This technique yields a time-varying encoder in two alternating phases, one at rate 8 : 9 and the other at rate 8 : 10, for an overall rate of 16 : 19. As in the preceding example, we could begin wi... |

1 |
Rate 16/17 (0,6/6) code
- Patel
- 1989
(Show Context)
Citation Context ...length of the sequence detector, and therefore the decoding delay, without significant degradation of detector performance. The most widely used code rates in the industry have been 8/9 [5] and 16/17 =-=[6]-=-. In general, high code rates and small error bursts at the modulation decoder output are desirable in order to minimize performance degradation due to rate loss and error propagation at the modulatio... |

1 | Distance enhancing constraints for noise predictive maximum likelihood detectors
- Moision, Siegel
- 1998
(Show Context)
Citation Context ...ate detector, i.e., by implementing a time-varying trellis in the sequence detector. The rates of the codes that have been designed to satisfy time-varying MTR constraints are 8/9 [8] and higher [9], =-=[10]-=-. These various classes of MTR codes increase the minimum Euclidean distance in the sequence detector by eliminating the dominant error events and are therefore known as distance-enhancing codes. In g... |

1 |
TurboEEPRML: An EEPR4 channel with an error-correcting post-processor designed for 16/17 rate quasi-MTR code
- Nishiya, Tsukano, et al.
- 1998
(Show Context)
Citation Context ..., which track the run of all four phases of patterns of type (0011) arriving at a state, has been taken in [16]. A special case of the constrained system described in (5)–(7) has been used in [8] an=-=d [14]-=- to eliminate period-4 quasi-catastrophic sequences of type (0011) at the input of the precoder for E PR4 and modified E PR4 systems. Note, though, that for , these sequences are not necessarily perio... |

1 |
Nonquasicatastrophic maximum transition run codes
- Cideciyan, Eleftheriou
- 2000
(Show Context)
Citation Context ...e set of all possible binary sequences. The modulation encoder generates binary sequences that satisfy a desired constraint, such as PRML( ) constraints [4]–[6], [12] or MTR constraints [7]–[9], [=-=13]–[16]-=-. The modulation encoder is followed by a precoder of the form (in the MTR case) or (in the ( ) case). The output of the precoder is then mapped into two-level channel input sequences , where and deno... |

1 |
0,G/I) codes are a subclass of MTR codes
- Cideciyan, Eleftheriou
- 2000
(Show Context)
Citation Context ...rs , where is the runlength of ones ending at the current state, is the runlength of zeros ending at the current state, and is the runlength of binary sequences of type or ending at the current state =-=[22]-=-. For example, 10001111 leads to the state (4, 6), whereas 100011110 leads to the state ( 1, 7), indicating that there is a transition from the state (4, 6) to the state ( 1, 7) labeled 0. The set of ... |

1 |
Cideciyan (S’82–M’86–SM’98) received the Dipl.-Ing. degree from Aachen University of Technology
- Cohn, Jacoby, et al.
- 1982
(Show Context)
Citation Context ...ULES The techniques of look-ahead coding and violation detection combined with substitution have been successfully applied in the past to design efficient constrained codes such as RLL( ) codes [25], =-=[33]-=-, MTR( ) codes [26], and PRML( ) codes [27]. The MTR code design methodologies presented in this section are based on the use of the state transition diagrams for MTR constraints and the application o... |