A fixed-rate bit stuffing approach for high efficiency k-constrained codes

Binary sequences where successive ones are separated by at most k consecutive zeros, are said to be k-constrained. We introduce a new fixed-rate algorithm for efficiently encoding and decoding k-constrained sequences. Our approach is based on bit stuffing proposed by Bender and Wolf. Bit stuffing is a simple algorithm that can produce near-optimal codes for a wide range of constraints. While bit stuffing achieves rates very close to the noiseless capacity, encoding is variable-rate, which severely limits its practical use. In this paper, we present a fixed-rate version of the bit stuff algorithm. High encoding efficiency is achieved by iterative pre-processing of the fixed-length input data to conform it to bit insertion. The encoder then inserts bits to produce a fixed-length output word. Rate computations for the proposed encoding algorithm are discussed, and upper and lower bounds are derived for the asymptotic (in input block length) encoding rate. It is seen that encoding rates very close to the average bit stuff rate are possible with long, fixed-length, input and output blocks. Upper and lower bounds on the asymptotic encoding rate are listed for values of k = 1 to 15