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Abstract

The prior art construction of sets of balanced codewords by Knuth is attractive for its simplicity and absence of look-up tables, but the redundancy of the balanced codes generated by Knuth's algorithm falls a factor of two short with respect to capacity. We present a new construction, which is simple, does not use look-up tables, and is less redundant than Knuth's construction. In the new construction, the user word is modified in the same way as in Knuth's construction, that is by inverting a segment of user symbols. The prefix that indicates which segment has been inverted, however, is encoded and decoded in a different, more efficient, way.

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In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of 1s and 0s, called balanced codes. Knuth's algorithm is, since look-up tables are absent, well suited for use with large codewords. The redundancy of Knuths balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In our paper we will present results of our attempts to improve the performance of Knuths balanced codes.
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