Abstract
M.Ing.
In practice, channels with only insertions and deletions are rare. More commonly, additive
errors are also present. Therefore, additional redundancy bits are added to the encoded
data stream to allow for insertion/deletion correction. In this dissertation, moment balancing
templates are used to add a single insertion/deletion capability to an arbitrary
additive-error-correcting code. Moment balancing can be used for systematic encoding of
number-theoretic codes. The selection of a particular additive-error-correcting codebook
has potential influence on the moment balancing template. In direct relation to this, partition
distributions of linear sets are considered and their connection to moment balancing
templates illustrated.
As an alternative to fixed length moment balancing templates, a variable length approach
to moment balancing is also considered. It is shown that variable length moment
balancing templates result in better performance, in terms of redundancy, than the optimal
fixed length moment balancing template. It is assumed that the boundaries of
variable length Levenshtein codewords are known. To implement the variable length
template in practice, multiple markers are needed. The delimitation of variable length
codeword boundaries with these markers leads to longer marker sequences as compared
with the fixed length templates.