Performance comparison of combined ECC/RLL codes

The authors present a performance comparison of several combined error-correcting/run-length-limited (ECC/RLL) codes created by concatenating a convolutional code with a run-length-limited code. In each case, encoding and decoding are accomplished using a single trellis based on the combined code. Half of the codes under investigation use conventional (d,k) run-length-limited codes, where d is the minimum and k is the maximum allowable run of 0's between 1's. The other half of the combined codes use a special class of (d,k) codes known as distance-preserving codes. These codes have the property that the pairwise Hamming distances out of the (d,k) encoder are at least as large as the corresponding distances into the encoder (i.e., the codes preserve distance). Thus a combined code, created using a convolutional code concatenated with a distance-preserving (d,k) code, will have a free distance (d_free) no smaller than the free distance of the original convolutional code. It should be noted that this does not hold if the (d,k) code is not distance preserving. A computer simulation is used to compare the performance of these two types of codes over the binary symmetric channel for various (d,k) constraints, rates, free distances, and numbers of states. Of particular interest for magnetic recording applications are codes with run-length constraints (1,3), (1,7), and (2,7).