LDPC- and Polar-coding-based Joint Source-Channel Coding

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The proposal builds on our own previous works on LDPC joint source channel coding forBernoulli(p) sources and independently, on our works on directly including Markov properties (memory) of data into the decoding process of a channel decoder. Both works lead to multi-edge-type LDPC designs and performance comparisons for different alternative structures – be it more Turbo like or incorporating the dependencies into the Tanner graph.One important step in this proposal is to now join the two efforts, meaning designing an actual joint source-channel coding multi-edge-type LDPC code that is also suited for Markov properties in the data and introduces those properties into the Tanner graph. The code optimization is expected to be much more influenced by non-consistent densities, requiring full density evolution, which is usually simplified to just considering the evolution of the variance or the mean which are dependent on each other in the consistent case. Full density evolution is known to be very demanding in practice, but possibly unavoidable in this case. Nevertheless, of course, the necessity for this step will be evaluated.Polar codes are one of the competing capacity-achieving and low-complexity code constructions and, to our knowledge, source memory has not been properly treated there, yet, and joint source-channel coding seems also in general not thoroughly studied there. In here, we like to investigate two options, one to see source dependencies as a first stage of source polarization and design the corresponding polar source/channel coding scheme accordingly. The other option builds on a stronger integration or interlinking of the source and channel coding portions with a view onto the martingales addressing the entropy for the source polarization and the capacity for the channel polarization, “puncturing” and “pruning” components when entropies or capacities fall below certain thresholds, then seeing data as deterministic and channels as to be “frozen”, respectively.