New Zero-Run Length Limited Codes for Partial-Response Channels

A coset of a convolutional code may be used to generate a zerorun length limited trellis for a 1-D partial-response channel. It is well known that the free Hamming distance d/sub H/ of the convolutional code and the free squared euclidean distance of the coset, d/sup 2/sub free/, measured at the channel output, are related by d/sub 2/ /spl ges d/spl H/. In this talk we present cosets for which d/sup 2//sub free/ is larger than the free Hamming distance of any convolutional code with the same rate and constraint length. We also describe how the new bounds, described in [1, 2], on the maximum zero-run length of cosets may be used to ensure a short zero-run length at the channel output. Analytical arguments, supported by results from computer search, suggest that cosets with large free squared euclidean distance also have short maximum zerorun lengths.