Watermark-based code construction for finite-state Markov channel with synchronisation errors

Abstract

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 three decoders 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 using the stationary distribution values as memoryless error probabilities in the proposed code construction and decoder is a viable solution, especially in cases with low memory between errors. Further tests imply that utilising the entire transition matrix in the decoding process may be better suited for cases with more significant memory between errors. 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.