Cosets of convolutional codes with short maximum zero-run lengths

Communication systems and storage systems derive symbol synchronization from the received symbol stream. To facilitate symbol synchronization, the channel sequences must have a short maximum zero-run length. One way to achieve this is to use a coset of an (n, k) convolutional code to generate the channel inputs. For k⩽n-2, it is shown that there exist cosets with short maximum zero-run length for any constraint length. Any coset of an (n, n-1) code with high rate and/or large constraint length is shown to have a large maximum zero-run length. A systematic procedure for obtaining cosets with short maximum zero-run length from (n, k) codes is presented, and new cosets with short maximum zero-run length and large minimum Hamming distance are tabulated