On codes with local joint constraints

Linear Algebra and Its Applications

Volumn 422, Issue 2-3, 2007, Pages 442-454

  Moision, Bruce ^a   Orlitsky, Alon ^b   Siegel, Paul H ^c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Forbidden words; Generalized spectral radius; Information capacity; Joint spectral radius

Indexed keywords

CHANNEL CAPACITY; COMPUTATIONAL METHODS; CONSTRAINT THEORY; HEURISTIC METHODS; MATRIX ALGEBRA; PROBLEM SOLVING;

FORBIDDEN WORDS; GENERALIZED SPECTRAL RADIUS; JOINT SPECTRAL RADIUS;

CODES (SYMBOLS);

EID: 33847320752     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.11.002     Document Type: Article

References (23)

1. Moision B.E., Orlitsky A., and Siegel P.H. On codes that avoid specified differences. IEEE Trans. Inform. Theory 47 1 (2001) 433-441
2. Immink K.A.S., Siegel P.H., and Wolf J.K. Codes for digital recorders. IEEE Trans. Inform. Theory 44 6 (1998) 2260-2299
3. Soljanin E., and Georghiades C.N. Coding for two-head recording systems. IEEE Trans. Inform. Theory 41 (1995) 747-755
4. Kurtas E., Proakis J.G., and Salehi M. Coding for multitrack magnetic recording systems. IEEE Trans. Inform. Theory 43 6 (1997) 2020-2023
5. Caroselli J., and Wolf J.K. Error event characterization of partial response systems in magnetic recording systems with media noise. Proceedings IEEE Global Telecommunications Conference vol. 5 (1998), IEEE, Sydney, Australia 2724-2729
6. E. Soljanin, On-track and off-track distance properties of class 4 partial response channels, in: M.R. Raghuveer, S.A. Dianat, S.W. McLaughlin, M. Hassner (Eds.), Proceedings of the SPIE, vol. 2605, Philadelphia, PA, USA, 1995, pp. 92-102.
7. Tsitsiklis J.N., and Blondel V.D. The Lyapunov exponent and joint spectral radius of pairs of matrices are hard-when not impossible-to compute and to approximate. Math. Control Signals Syst. 10 (1997) 31-40
8. Blondel V.D., and Tsitsiklis J.N. The boundedness of all products of a pair of matrices is undecidable. Syst. Control Lett. 41 2 (2000) 135-140
9. Graham R.L., Rothschild B.L., and Spencer J.H. Ramsey Theory (1990), John Wiley & Sons
10. Horn R.A., and Johnson C.R. Matrix Analysis (1988), Cambridge University Press, New Jersey
11. Rota G.C., and Strang G. A note on the joint spectral radius. Indagationes Mathematicae 22 (1960) 379-381
12. Daubechies I., and Lagarias J.C. Two-scale difference equations. II. Local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal. 23 (1992) 1031-1079
13. Berger M.A., and Wang Y. Bounded semi-groups of matrices. Linear Algebra Appl. 166 (1992) 21-27
14. Marcus B.H., Roth R.M., and Siegel P.H. Constrained systems and coding for recording channels. In: Pless V.S., and Huffman W.C. (Eds). Handbook of Coding Theory (1998), Elsevier Science (Chapter 20)
15. Daubechies I., and Lagarias J.C. Sets of matrices all infinite products of which converge. Linear Algebra Appl. 161 (1992) 227-263
16. Gurvits L. Stability of discrete linear inclusion. Linear Algebra Appl. 231 (1995) 47-85
17. Barabanov N.E. Lyapunov indicators of discrete inclusions. I. Automat. Remote Control 49 2 (1988) 152-157
18. Gripenberg G. Computing the joint spectral radius. Linear Algebra Appl. 234 (1996) 43-60
19. Maesumi M. An efficient lower bound for the generalized spectral radius of a set of matrices. Linear Algebra Appl. 240 (1996) 1-7
20. M. Maesumi, Spectral radius of sets of matrices, in: Proceedings of the SPIE, vol. 2303, San Diego, CA, USA, 1994, pp. 27-29.
21. Colella D., and Heil C. The characterization of continuous, four-coefficient scaling functions and wavelets. IEEE Trans. Inform. Theory 38 2 (1992) 876-881
22. Lagarias J., and Wang Y. The finiteness conjecture for the generalized spectral radius of a set of matrices. Linear Algebra Appl. 214 (1995) 17-42
23. Bousch T., and Mairesse J. Asymptotic height optimization for topical IFS, Tetris heaps and the finiteness conjecture. J. Amer. Math. Soc. 15 (2002) 77-111