Coding for a non-symmetric ternary channel

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 d_A-decoding, is then proposed. It is shown that d_A-decoding and ML decoding are equivalent for values of p under a certain threshold. Assuming d_A-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.