Rami Cohen – Low-density parity-check codes over the q-ary partial erasure channel

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In this talk, we present a new channel model, which we named the q-ary
partial erasure channel (QPEC).
The QPEC has a q-ary input, and its output is either one symbol or a set
of M symbols. This channel mimics
situations when current/voltage levels in measurement channels are
partially known, due to high read rates or imperfect
current/voltage sensing. 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
a probabilistic analysis (known as density evolution) of the decoding
process, and show that exact analysis is related to an
open problem in the field of additive combinatorics. Therefore, we suggest
several bounds and approximations.