Systematic single limited magnitude asymmetric error correcting codes

In the asymmetric error model, a symbol a over an alphabet Z_q = {0,1,..., q - 1} may be modified during transmission into b, where b <; a (assuming that the dominant error type is the decreasing error). For some applications, the error magnitude b - a is not likely to exceed a certain threshold l. One such application is the multi-level flash memory (Cassuto et al., 2008). In this paper, we propose systematic codes which correct single limited magnitude asymmetric errors (single l-AEC codes). The proposed codes achieve higher rate than the ones given in (Cassuto) for the case where t = 1. We illustrate the main construction by the following examples.