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# Performance of Efficient Balanced Codes

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## Abstract

The problem of appraising the spectral performance of codes based on a new algorithm for generating zero-disparity codewords presented by D.E. Knuth (1986) is addressed. In order to get some insight into the efficiency of Knuth's construction technique, the authors evaluate the spectral properties of its code streams. The structure of Knuth codes allows the derivation a simple expression for (an approximation to) the sum of variance of these codes. This quantity plays a key role in the spectral performance characterization of DC-balanced codes. The authors evaluate this expression and compare the sum variance of Knuth codes with the sum variance of the polarity bit codes for fixed redundancy. Under the premise that the sum variance can serve as a quantity to judge the width of the spectral notch, the authors conclude that codes based on Knuth's algorithm offer less spectral suppression than polarity bit codes with the same redundancy.

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... The code also needs to be efficient in the sense that it is easy to code a source word and easy to decode a coded word back to its source word. The information presented in this section was taken mainly from [4] and [5]. ...
... Of course, it could also be interesting to discuss other aspects of the signal such as its spectral content. For example, the effect of line coding on the spectral content of a signal is discussed in [5]. This however, is out of the scope of this paper. ...
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Method and apparatus for generating a noiseless sliding block code for a (1,7) channel with rate 2/3