Iterative Decoding of LDPC Codes Over the $q$ -Ary Partial Erasure Channel


In this paper, we have a tendency to develop a replacement channel model, which we tend to name the -ary partial erasure channel (QPEC). The QPEC encompasses a -ary input, and its output is either the input symbol or a set of ( ) symbols, containing the input symbol. This channel serves as a generalization to the binary erasure channel and mimics situations when a symbol output from the channel is understood solely partially; that is, the output symbol contains some ambiguity, however is not absolutely erased. This type of channel is motivated by non-volatile memory multi-level scan channels. In such channels, the readout is obtained by a sequence of current/voltage measurements, that may terminate with a partial knowledge of the stored level. Our investigation is concentrated on the performance of low-density parity-check (LDPC) codes when used over this channel, thanks to their low decoding complexity using belief propagation. We provide the exact QPEC density-evolution equations that govern the decoding process, and counsel a cardinality-based mostly approximation as a proxy. We have a tendency to then give many bounds and approximations on the proxy density evolutions, and verify their tightness through numerical experiments. Finally, we offer tools for the sensible design of LDPC codes for use over the QPEC.

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