This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Efficient Encoding Algorithm for Second-Order Spectral-Null Codes Using Cyclic Bit Shift
July 2008 (vol. 57 no. 7)
pp. 876-888
Some efficient second-order spectral-null codes encoded an index of random walk function recursively and ended with the short base second-order spectral-null codes. All these codes used the Tallini-Bose random walk function that exchanges two consecutive bits. In this paper, we propose a new random walk function based on cyclic bit-shift, on which the redundancy can be improved. Moreover, the bit-shift can be implemented efficiently by either software or hardware.

[1] L.G. Tallini and B. Bose, “On Efficient High-Order Spectral-Null Codes,” IEEE Trans. Information Theory, vol. 45, pp. 2594-2601, Nov. 1999.
[2] C.N. Yang, “Design of Efficient Second-Order Spectral-Null Codes,” IEEE Trans. Information Theory, vol. 51, pp. 1580-1584, Apr. 2005.
[3] C.N. Yang and D.J. Lee, “Some New Efficient Second-Order Spectral-Null Codes with Small Lookup Tables,” IEEE Trans. Computers, vol. 51, no. 7, pp. 924-927, July 2006.
[4] K.A.S. Immink, “Spectrum Shaping with Binary ${\rm DC}^{2}{\hbox{-}}{\rm Constrained}$ Channel Codes,” Philips J. Research, vol. 40, pp. 40-53, 1985.
[5] Y. Xin and I.J. Fair, “Algorithms to Enumerate Codewords for DC$^2$ -Constrained Channels,” IEEE Trans. Information Theory, vol. 47, pp. 3020-3025, Nov. 2001.
[6] R.M. Roth, P.H. Siegel, and A. Vardy, “High-Order Spectral-Null Codes—Construction and Bounds,” IEEE Trans. Information Theory, vol. 40, pp. 1826-1840, Nov. 1994.
[7] V. Skachek, T. Etzion, and R.M. Roth, “Efficient Encoding Algorithm for Third-Order Spectral-Null Codes,” IEEE Trans. Information Theory, vol. 44, pp. 846-851, Mar. 1998.
[8] T.V. Ramabadran, “A Coding Scheme for $m$ -out-of-$n$ Codes,” IEEE Trans. Information Theory, vol. 38, pp. 1156-1163, Aug. 1990.
[9] D.E. Knuth, “Efficient Balanced Codes,” IEEE Trans. Information Theory, vol. 32, pp. 51-53, Jan. 1986.
[10] S. Al-Bassam and B. Bose, “Design of Efficient Balanced Codes,” IEEE Trans. Computers, vol. 43, no. 3, pp. 362-365, Mar. 1994.
[11] L.G. Tallini, R.M. Capocelli, and B. Bose, “Design of Some New Efficient Balanced Codes,” IEEE Trans. Information Theory, vol. 42, pp. 790-802, May 1996.
[12] J.M. Berger, “A Note on Error Detecting Codes for Asymmetric Channels,” Information and Control, vol. 4, pp. 68-73, Mar. 1961.
[13] E.L. Leiss, “Data Integrity in Digital Optical Disks,” IEEE Trans. Computers, vol. 33, no. 9, pp. 818-827, Sept. 1984.
[14] E.E. Bergmann, D. Coppersmith, A.M. Odlyzko, and S.H. Sangani, “Half Weight Block Codes for Optical Communications,” AT&T Technical J., vol. 65, pp. 85-93, May/June 1986.
[15] K.A.S. Immink, Coding Techniques for Digital Recorders. Prentice Hall, 1991.
[16] L.G. Tallini and B. Bose, “Design of Balanced and Constant Weight Codes for VLSI Systems,” IEEE Trans. Computers, vol. 47, no. 5, pp. 556-572, May 1998.
[17] B. Bose and T.R.N. Rao, “Theory of Unidirectional Error Correcting/Detecting Codes,” IEEE Trans. Computers, vol. 31, no. 6, pp. 521-530, June 1982.

Index Terms:
Second-order spectral-null code, High-order spectral-null code, Balanced code, 1-EC/AUED code.
Citation:
Ching-Nung Yang, "Efficient Encoding Algorithm for Second-Order Spectral-Null Codes Using Cyclic Bit Shift," IEEE Transactions on Computers, vol. 57, no. 7, pp. 876-888, July 2008, doi:10.1109/TC.2007.70849
Usage of this product signifies your acceptance of the Terms of Use.