  With advancements in telecommunications, data transmission over increasingly
harsher channels that produce synchronisation errors is inevitable. Coding
schemes for such channels are available through techniques such as the
Davey-MacKay watermark coding; however, this is limited to memoryless channel
estimates. Memory must be accounted for to ensure a realistic channel
approximation - similar to a Finite State Markov Chain or Fritchman Model. A
novel code construction and decoder are developed to correct synchronisation
errors while considering the channel's correlated memory effects by
incorporating ideas from the watermark scheme and memory modelling. Simulation
results show that the proposed code construction and decoder rival the first
and second-order Davey-MacKay type watermark decoder and even perform slightly
better when the inner-channel capacity is higher than 0.9. The proposed system
and decoder may prove helpful in fields such as free-space optics and possibly
molecular communication, where harsh channels are used for communication.
