Channel decomposition for multilevel codes over multilevel and partial erasure channels

We introduce the Multilevel Erasure Channel (MEC) for binary extension field alphabets. The channel model is motivated by applications such as non-volatile multilevel read storage channels. Like the recently proposed \begin{document}$q$\end{document} -ary partial erasure channel (QPEC), the MEC is designed to capture partial erasures. The partial erasures addressed by the MEC are determined by erasures at the bit level of the \begin{document}$q$\end{document} -ary symbol representation. In this paper we derive the channel capacity of the MECand give a multistage decoding scheme on the MEC using binary codes. We also present a low complexity multistage \begin{document}$p$\end{document} -ary decoding strategy for codes on the QPEC when \begin{document}$q = p^k$\end{document} .We show that for appropriately chosen component codes, capacity on the MEC and QPEC may be achieved.