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 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.

Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel

“…In [2], Achari and Cheng have incorporated both of these channel effects and properties and describe a synchronisation channel based on a Finite-State Markov Channel (FSMC). FSMC -also referred to as discrete finite-state channels, are primarily based on Markov processes and was presented by Claude Shannon in his landmark paper in 1948 [13].…”

“…In addition to the channel model in [2], the paper provides an algorithm to regain synchronisation by removing the effects of insertions and deletions encountered during data transmission. However, this leaves substitution errors from the decoding process and inherent substitution errors from the channel itself.…”

“…However, this leaves substitution errors from the decoding process and inherent substitution errors from the channel itself. The work in [2] is based on the memoryless synchronisation channel, and watermark decoding scheme presented by Davey and MacKay in [5], which has been used in various fields such as DNA barcoding in medicine [14], [15] to data hiding in watermarking applications [16].…”

“…In Achari and Cheng [2], consider a channel model and decoding scheme to correct insertion and deletion errors in a system based on a Synchronisation Finite-State Markov Channel (S-FSMC) where Insertion-Deletion-Substitution (IDS) errors are present. The paper presented restricts its focus to the inner decoding of the communication system, where the purpose of the inner decoder is to regain synchronisation by removing the insertion and deletion errors detected.…”

“…However, this resynchronisation process does not account for substitution errors caused by the channel or the incorrect decoding of the inner decoder. This paper aims to provide considerations and suggestions for the outer code coding parameters of the S-FSMC presented in [2] to ensure reliable communication and provide a framework for a complete system.…”