Digital information transmission

Abstract

This thesis looks at coded information transmission through a noisy channel. The work of Viterbi [29] is extended to take into account phase asynchronous transmission and reception of the binary orthogonal, biorthogonal and transorthogonal code words in the presence of additive Gaussian noise. It is shown that asynchronous reception decreases the mean distance between code words while leaving their crosscorrelation unaltered. This results in the expressions for decoding error probabilities similar to those of Viterbi with corrections added for the change in mean distance between code words with changes in asynchronism. Also, a multilevel coding scheme proposed by Sankar and Krishnamurthy [21] is reviewed and it is shown that their method can be improved for no loss of information rate. It is demonstrated that their use of generalised Hamming codes over multisymbol N-ary words has limited error correcting capabilities which can easily be improved by using binary Hamming codes over the multisymbol words expressed in binary form rather than the more general N-ary representation. For the improved method to be used N must be a binary power.