Error-Correcting Balanced Knuth Codes

Knuth's celebrated balancing method consists of inverting the first bits in a binary information sequence, such that the resulting sequence has as many ones as zeroes, and communicating the index to the receiver through a short balanced prefix. In the proposed method, Knuth's scheme is extended with error-correcting capabilities, where it is allowed to give unequal protection levels to the prefix and the payload. The proposed scheme is very general in the sense that any error-correcting block code may be used for the protection of the payload. Analyses with respect to redundancy and block and bit error probabilities are performed, showing good results while maintaining the simplicity features of the original scheme. It is shown that the Hamming distance of the code is of minor importance with respect to the error probability.