Knuth's Balanced Codes Revisited

In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of “ $1$”s and “${-1}$”s, called balanced codes. Knuth's algorithm is well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In this paper, we will present results of our attempts to improve the performance of Knuth's balanced codes.