CONSTRUCTIONS OF ERROR-CORRECTING DC-FREE BLOCK-CODES

A (2n.l,c.d) dc-free binary block code is a code of length 2n constant weight n, maximum runlength of a symbol l, maximum accumulated charge c, and minimum distnce d. The requirements are that / and c will be small. We present two dc-free codes with distance 2d, b ≥ 1 length 2n +2r(d - 1) for d ≤ 3 and length 2n + 2r(d - 1)(2d - 1) for d > 3, where r ≤ [log2(2n + 1)]. For the first code l = 4, c = 2, and the asymptotic rate of this code is 0.7925. For the second code l = 6, c = 3, and the asymptotic rate of this code i 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes does not achieve the best rate. As an example of codes of short length with good rate, we first present a (30,10,6,4) dc-free block code with 221codewords. Finally, we present a construction for which from a given code Clof length n, even weight, and distance 4, we obtin a (4n,l,c,4) dc-free block code C2, where l is 4, 5 or 6, and c is not greater than n + 1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. We discuss the encoding and decoding procedures for all the codes. © 1990 IEEE