Runlength-limited block codes with small error propagation

The principal feature of a (d, k) (or other finite-type constraints) code produced with the sliding-block code algorithm is that the coded sequences can be decoded by examining a limited number of consecutive symbols without relying on external state information. As an immediate consequence, these codes have a limited amount of error propagation. The length of the decoding window is an important design parameter as it affects both the amount of error propagation and decoding hardware. The paper describes the construction of rate m/n (d, k) codes that can be decoded with a sliding-block decoder of window length at most two n-tuples. We furnish sufficient conditions for the construction of such codes. A lower bound to the code size is given. The theory is elucidated by examples of (d,k) codes that require only part of the decoding window