### Abstract

Digital magnetic and optical storage systems employing NRZI recording use (d, k) codes. The d-parameter specifies the minimum number of 0's occurring between 1's while the k-parameter specifies the maximum number of 0's between l's. The n-track (d,k) codes (denoted as (d,k;n) codes) are extensions of (d, k) codes for use in multiple-track systems. Instead of imposing each track to individually satisfy both constraints, (d,k;n) codes satisfy the d-constraint in each track individually while relaxing the k-constraint by allowing it to be satisfied jointly by the multiple tracks. Although (d,k;n) codes can provide significant capacity increases over (d, k) codes, they suffer from the fact that a single faulty track can cause loss of synchronization and hence, loss of the data on all tracks. Orcutt and Marcellin (see IEEE Trans. on Inform. Theory, Sept., 1993) introduced n-track (d,k) codes with a redundancy of r (denoted as (d,k;n,r) codes) which allow for r faulty tracks by mandating that all subsets of n-r tracks satisfy the joint k-constraint. We propose a new method to construct (d,k; n, r) codes. These codes have simple encoding and decoding schemes, gain a large part of the capacity increase possible when using (d,k; n,r) codes, and are considerably more robust to faulty tracks.

Original language | English (US) |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Pages | 145 |

Number of pages | 1 |

DOIs | |

State | Published - 1994 |

Event | 1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway Duration: Jun 27 1994 → Jul 1 1994 |

### Other

Other | 1994 IEEE International Symposium on Information Theory, ISIT 1994 |
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Country | Norway |

City | Trondheim |

Period | 6/27/94 → 7/1/94 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 145). [394830] https://doi.org/10.1109/ISIT.1994.394830

**A new construction for n-track (d, k) codes with redundancy.** / Ke, Ligang; Marcellin, Michael W.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Symposium on Information Theory - Proceedings.*, 394830, pp. 145, 1994 IEEE International Symposium on Information Theory, ISIT 1994, Trondheim, Norway, 6/27/94. https://doi.org/10.1109/ISIT.1994.394830

}

TY - GEN

T1 - A new construction for n-track (d, k) codes with redundancy

AU - Ke, Ligang

AU - Marcellin, Michael W

PY - 1994

Y1 - 1994

N2 - Digital magnetic and optical storage systems employing NRZI recording use (d, k) codes. The d-parameter specifies the minimum number of 0's occurring between 1's while the k-parameter specifies the maximum number of 0's between l's. The n-track (d,k) codes (denoted as (d,k;n) codes) are extensions of (d, k) codes for use in multiple-track systems. Instead of imposing each track to individually satisfy both constraints, (d,k;n) codes satisfy the d-constraint in each track individually while relaxing the k-constraint by allowing it to be satisfied jointly by the multiple tracks. Although (d,k;n) codes can provide significant capacity increases over (d, k) codes, they suffer from the fact that a single faulty track can cause loss of synchronization and hence, loss of the data on all tracks. Orcutt and Marcellin (see IEEE Trans. on Inform. Theory, Sept., 1993) introduced n-track (d,k) codes with a redundancy of r (denoted as (d,k;n,r) codes) which allow for r faulty tracks by mandating that all subsets of n-r tracks satisfy the joint k-constraint. We propose a new method to construct (d,k; n, r) codes. These codes have simple encoding and decoding schemes, gain a large part of the capacity increase possible when using (d,k; n,r) codes, and are considerably more robust to faulty tracks.

AB - Digital magnetic and optical storage systems employing NRZI recording use (d, k) codes. The d-parameter specifies the minimum number of 0's occurring between 1's while the k-parameter specifies the maximum number of 0's between l's. The n-track (d,k) codes (denoted as (d,k;n) codes) are extensions of (d, k) codes for use in multiple-track systems. Instead of imposing each track to individually satisfy both constraints, (d,k;n) codes satisfy the d-constraint in each track individually while relaxing the k-constraint by allowing it to be satisfied jointly by the multiple tracks. Although (d,k;n) codes can provide significant capacity increases over (d, k) codes, they suffer from the fact that a single faulty track can cause loss of synchronization and hence, loss of the data on all tracks. Orcutt and Marcellin (see IEEE Trans. on Inform. Theory, Sept., 1993) introduced n-track (d,k) codes with a redundancy of r (denoted as (d,k;n,r) codes) which allow for r faulty tracks by mandating that all subsets of n-r tracks satisfy the joint k-constraint. We propose a new method to construct (d,k; n, r) codes. These codes have simple encoding and decoding schemes, gain a large part of the capacity increase possible when using (d,k; n,r) codes, and are considerably more robust to faulty tracks.

UR - http://www.scopus.com/inward/record.url?scp=84894290175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894290175&partnerID=8YFLogxK

U2 - 10.1109/ISIT.1994.394830

DO - 10.1109/ISIT.1994.394830

M3 - Conference contribution

AN - SCOPUS:84894290175

SN - 0780320158

SN - 9780780320154

SP - 145

BT - IEEE International Symposium on Information Theory - Proceedings

ER -