A Lower Bound to the Maximal Entropy of Line Codes
Josef K Forster · International Symposium on Information Theory and its Applications · 1994
A lower bound to the maximal entropy line codes can transmit (capacity of line codes) is presented. The bound is very useful if line codes should be objectively compared. It takes advantage of some fundamental relations between a sequence with a first order spectral null and its running digital sum (RDS). The width of the spectral null is determined by the ratio of the output sequence power to the RDS sequence power. The maximum entropy of the sequence is found by maximizing the entropy of the generating first order Markov process. The bound approaches asymptotically the theoretical maximum (capacity). One interesting result shows that the AMI code is not maxentropic. There exists a Markov process with a cut-off frequency of half the Nyquist frequency that supports an entropy of 1.11 bit. That is 0.11 bit more than the AMI code at the same cut-off frequency.