3 research outputs found
Error Correcting Coding for a Non-symmetric Ternary Channel
Ternary channels can be used to model the behavior of some memory devices,
where information is stored in three different levels. In this paper, error
correcting coding for a ternary channel where some of the error transitions are
not allowed, is considered. The resulting channel is non-symmetric, therefore
classical linear codes are not optimal for this channel. We define the
maximum-likelihood (ML) decoding rule for ternary codes over this channel and
show that it is complex to compute, since it depends on the channel error
probability. A simpler alternative decoding rule which depends only on code
properties, called \da-decoding, is then proposed. It is shown that
\da-decoding and ML decoding are equivalent, i.e., \da-decoding is optimal,
under certain conditions. Assuming \da-decoding, we characterize the error
correcting capabilities of ternary codes over the non-symmetric ternary
channel. We also derive an upper bound and a constructive lower bound on the
size of codes, given the code length and the minimum distance. The results
arising from the constructive lower bound are then compared, for short sizes,
to optimal codes (in terms of code size) found by a clique-based search. It is
shown that the proposed construction method gives good codes, and that in some
cases the codes are optimal.Comment: Submitted to IEEE Transactions on Information Theory. Part of this
work was presented at the Information Theory and Applications Workshop 200