Timing recovery in communication and storage systems requires the use of Run Length Limited (RLL) or (d,k) codes. A class of such codes is constructed by a method called coded bit stuffing. The proposed encoder does not change the main part of input data bits, and just places these bits into the code word "as is". The remaining small part of data bits is encoded into a set of short nonzero words called separators. The separators are placed between the uncoded subblock of data. Due to the nonzero nature of the separators, the coded bit stream concatenated from data sub blocks and separators always satisfies the k constraint. The uncoded part of data bits can be arbitrary permuted without nullifying the k constraint. This property of the presented codes is important when an RLL code is used in the channel with an iterative detection scheme requiring interleaving. Simulations show that the designed codes have very good suppression of error propagation.

We present a systematic way to construct multilevel concatenated codes for partial response (PR) channels using: (1) a structured set partition (SSP) of multiple channel output sets and (2) a set of conventional block codes with different error correcting capabilities. A lower bound on the minimum squared Euclidean distance of the constructed codes is given. This bound is based on the interset minimal Euclidean distances of the SSP and the minimum Hamming distances of the used block codes. An example of SSP for the extended class 4 partial response channel (EPR4) is presented. Iterative suboptimal decoding, which combines Viterbi detection on the trellis of the PR channel with algebraic error detection/correction, can be applied to the constructed concatenated codes. Truncated versions of the iterative decoding scheme are simulated and compared with each other.