We investigate higher order code word moments [1,2,3] to shape the power spectral density of codes (PSD). By selecting appropriate values for the k-th order ...
CHANNEL ADAPTIVE CODING TECHNIQUES THROUGH APPLICATION OF HIGHER ORDER MOMENTS. W.A. Clarke, L. Fouch6, A.S.J. Helberg and H.C. Ferreira Laboratory for Cybernetics, Rand Afrikaans University, P.O. Box 524, AUCKLANDPARK, 2006, South Africa Abstruct - We investigate the use of higher order code word moments to shape the power spectral density of codes. Several codes are presented that combine different spectral shaping techniques. T h e insertion/deletion and additive error correcting capabilities of these codes are investigated and simple decoding procedures are presented. Finally, we give an example for the use of a higher order spectral zero code.
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I. SUMMARY
We investigate higher order code word moments [1,2,3] to shape the power spectral density of codes (PSD). By selecting appropriate values for the k-th order moment it was shown how higher suppression of the PSD at DC may be obtained for block codes [I]. We give an example of how this suppression was used to transmit analogue signals (i.e. speech) concurrently with baseband digital data. lmmink [2] and Karabed and Siegel [3] showed that code books having all k moments equal to zero exhibit error correcting properties. We give simple additive error correcting procedures for codes with k = 1, 2 and 3.
R. Karabed and P. Siegel, "Matched spectral-null codes for partial-response channels," IEEE Transactions on Information Theory, vol. 37, no. 3, pp. 818 - 855, May 1991. J.E. Baek and J.K. Kim, "New DC-free line code of minimum bandwidth with increased eye width," Electronic Letters, vol. 21, no. 17, pp. 755 - 757, August 15, 1985 D.Y. Kim and J.K. Kim, "A condition for stable minimum bandwidth line codes", IEEE TransactionsonCommunications, vol. 33,pp. 152 157, 1985.
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Kim [4,5] proved that codes with spectral zeros at the Nyquist frequency (f = J/2) can be successfully transmitted by using only half the bandwidth normally required for transmission. We present an important new class of codes that combine second order spectral zeros at both DC and the Nyquist frequency. We show that these codes can correct two adjacent additive errors and we derive procedures for the detection and correction of single or two adjacent additive errors. It is also shown that for binary codes, single insertions or deletions can be corrected. Examples of spectra are shown in Figures 1 and 2.
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Fig. 1. Binary 8-bit code with second order zeros at both DC and the Nyquist frequency
REFERENCES [I]
E. Elefiheriou and R.D. Cideciyan, "On codes satisfying M'th-order running digital sum constraints," IEEE Transactions on Information Theory, vol. 37, no. 5, pp. 1294 - 1313, September
Fig. 2. Binary 16-Bit code with second order zeros at both DC and the Nyquist frequency.
1991.
[2]
K.A.S. lmmink and G.F.M. Beenker, "Binary transmission codes with higher order spectral zeros at zero frequency," IEEE Transactions on Information Theoty, vol. 33, no. 3, pp. 425 - 454, May 1987.
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