Combinatorial construction of high rate runlength-limited codes
Adriaan J. van Wijngaarden, Kees A. Schouhamer Immink · 2002
New combinatorial construction techniques are proposed which convert binary user information into a (0,k) constrained sequence having the virtue that at most k 'zeroes' between logical 'ones' will occur. In this way sequences are constructed which have a limited runlength. These codes find application in optical and magnetic recording systems. The new construction methods provide efficient, high rate codes with a low complexity. The low complex combinatorial structure of the encoder and the decoder ensure a very fast and efficient parallel conversion of binary information to codewords and vice versa. Specifically, we present the combinatorial structures to convert 16 data bits into a 17 bit constrained sequence to obtain an optimum (0,4) code, a (0,6) code with at most one byte error propagation, and a (0,6/6)-code, respectively. Serious error propagation is avoided by using constrained codes with several unconstrained positions, which are reserved to store the parity bits of an error control code which protects the constrained codeword.