Computation of the spectrum of $\text{dc}^2$-balanced codes.

We apply the central limit theorem for deriving approximations to the auto-correlation function and power density function (spectrum) of second-order spectral null (dc2-balanced) codes.We show that the auto-correlation function of dc2-balanced codes can be accurately approximated by a cubic function. We show that the difference between the approximate and exact spectrum is less than 0.04 dB for codeword length n = 256.

[1]  A. R. Ndjiongue,et al.  Visible Light Communications (VLC) Technology , 2015 .

[2]  Jørn Justesen,et al.  Information rates and power spectra of digital codes , 1982, IEEE Trans. Inf. Theory.

[3]  Ivan J. Fair,et al.  A performance metric for codes with a high-order spectral null at zero frequency , 2004, IEEE Transactions on Information Theory.

[4]  Qi Wang,et al.  Visible Light Communications : Modulation and Signal Processing , 2017 .

[5]  Bella Bose,et al.  On efficient high-order spectral-null codes , 1999, IEEE Trans. Inf. Theory.

[6]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[7]  Ivan J. Fair,et al.  Algorithms to enumerate codewords for DC2-constrained channels , 2001, IEEE Trans. Inf. Theory.

[8]  A. Vardy,et al.  High-order spectral-null codes: constructions and bounds , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[9]  Kui Cai,et al.  Estimated Spectra of Higher Order Spectral Null Codes , 2019, IEEE Communications Letters.

[10]  Kheong Sann Chan,et al.  Signal Processing for Dedicated Servo Recording System , 2015, IEEE Transactions on Magnetics.

[11]  Ron M. Roth,et al.  Efficient Encoding Algorithm for Third-Order Spectral-Null Codes , 1998, IEEE Trans. Inf. Theory.

[12]  Kees A. Schouhamer Immink,et al.  Binary transmission codes with higher order spectral zeros at zero frequency , 1987, IEEE Trans. Inf. Theory.

[13]  Ching-Nung Yang Efficient Encoding Algorithm for Second-Order Spectral-Null Codes Using Cyclic Bit Shift , 2008, IEEE Transactions on Computers.

[14]  Carlo M. Monti,et al.  Codes with a multiple spectral null at zero frequency , 1989, IEEE Trans. Inf. Theory.

[15]  Helmut Prodinger On the Number of Partitions of { 1, …, n} into Two Sets of Equal Cardinalities and Equal Sums , 1982, Canadian Mathematical Bulletin.

[16]  K.A.S. Immink Spectral null codes , 1990 .

[17]  Jos H. Weber,et al.  Very Efficient Balanced Codes , 2010, IEEE Journal on Selected Areas in Communications.

[18]  J. Pierce,et al.  Spectra and Efficiency of Binary Codes Without DC , 1972, IEEE Trans. Commun..

[19]  B. S. Bosik,et al.  The spectral density of a coded digital signal , 1972 .

[20]  Minseok Oh,et al.  A flicker mitigation modulation scheme for visible light communications , 2013, 2013 15th International Conference on Advanced Communications Technology (ICACT).

[21]  Gianfranco L. Pierobon,et al.  Codes for zero spectral density at zero frequency , 1984, IEEE Trans. Inf. Theory.

[22]  Sridhar Rajagopal,et al.  IEEE 802.15.7 visible light communication: modulation schemes and dimming support , 2012, IEEE Communications Magazine.

[23]  Mu Zhang,et al.  Design of spectrum shaping codes for high-density data storage , 2017, 2018 IEEE International Conference on Consumer Electronics (ICCE).