An enumerative method for runlength-limited codes: permutation codes

Permutation codes, introduced by Slepian, were shown to perform well on an additive white Gaussian noise (AWGN) channel. Unfortunately, these codes required large lookup tables, making them quite complex to implement even though the maximum-likelihood decoder is very simple. In this correspondence, we present an enumeration scheme which encodes and decodes permutation codes with low complexity. We concentrate on the use of permutation codes for constructing high-rate codes that satisfy runlength-limited constraints. Wolf showed that permutation codes can be used for runlength constraints and that they have rate that asymptotically achieves the capacity of a noiseless, runlength-limited constrained channel. Wolf, however, gave no efficient encoders/decoder. Our code construction is enumerative, but unlike other enumerative codes, has storage requirements that are a function of the runlength parameters d and k instead of the block length n. In addition, these codes have error detection and correction capabilities. Finally, we use this approach to construct (0; G=I) codes whereby all odd-numbered occurrences of double-adjacent errors are detected. As an example, a 99.2% efficient, rate 496=528, (0; 6=3) code is presented.