Coding for a non-symmetric ternary channel
Nicolas Bitouzé, Alexandre Graell i Amat · 2009
Non-symmetric ternary channels can be used to model the behavior of some memory devices. In this work, error correction coding for a non-symmetric ternary channel where some of the error transitions are not allowed, is considered. We study distance properties of ternary codes over this channel and define the maximum likelihood (ML) decoding rule. It is shown that the ML decoding rule is too complex, since it depends on the channel error probability. A simpler alternative decoding rule, called dA-decoding, is then proposed. It is shown that dA-decoding and ML decoding are equivalent for values of p under a certain threshold. Assuming dA-decoding we characterize the error correction capabilities of ternary codes over the non-symmetric ternary channel. We also provide an upper bound and a constructive lower bound on the size of such codes given the code length and the minimum distance.