Quasi-Enumerative Coding of Balanced Run-Length Limited Codes

Various methods have been proposed for the construction of balanced run-length limited codes. Amongst these methods is the enumerative coding approach by Kurmaev. The advantage of this approach is that the code has maximum cardinality and thus approaches capacity with increasing codeword length. However, enumerative coding has the disadvantage of becoming prohibitively complex for large codeword lengths. We propose an alternative enumerative coding method that reduces the encoding and decoding complexity. We call it quasi-enumerative coding as it does not follow a strict lexicographic order, but retains a one-to-one mapping between rank and the corresponding balanced run-length limited codeword.