Convolutional encoding and decoding for channels exhibiting synchronisation errors

Abstract

Synchronisation errors include the random insertion and deletion of bits from the transmitted bit-stream. Standard convolutional codes are used to correct these types of errors with changes being made only to the decoder. To correct synchronisation errors the Trellis diagram of the convolutional decoder is modified such that it caters for insertions and deletions. This modification was first proposed by Mansour and Tewfik. In this dissertation, their work is simplified for clearer understanding and enhanced flexibility resulting in additional improvements without effecting the code's error-correcting capabilities. The MAP decoding algorithm is modified accordingly to work on this newly proposed Trellis diagram. As a further modification a random sequence known to both the encoder and decoder is added, resulting in a Bit Error Rate improvement of up to 99% and an increase in decoder complexity of just 0.63%. Furthermore, the number of states in the Trellis diagram arc adjusted according to the current channel conditions which leads to a reduction in complexity without a loss in error-correcting performance. The channel metric (y) used in the MAP algorithm is optimised, achieving a performance improvement of up to 283 whilst decreasing complexity by a maximum of 33.