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

该建议建立在我们自己以前对伯努利(p)源的LDPC联合源信道编码的工作基础上，并独立地建立在我们直接将数据的马尔可夫属性（存储器）纳入信道解码器解码过程的工作基础上。这两项工作都导致了多边型LDPC设计和不同替代结构的性能比较-无论是更像Turbo还是将依赖关系纳入Tanner图。该提案的一个重要步骤是现在将这两个努力结合起来，这意味着设计一个实际的联合源信道编码多边型LDPC代码，该代码也适用于数据中的马尔可夫属性，并将这些属性引入坦纳图。期望代码优化更受非一致密度的影响，需要全密度演化，通常简化为只考虑在一致情况下相互依赖的方差或均值的演化。在实践中，全密度进化是非常苛刻的，但在这种情况下可能是不可避免的。当然，这一步骤的必要性将得到评估。极性码是一种竞争性的容量实现和低复杂度的码结构，据我们所知，源记忆在那里还没有得到适当的处理，而且联合源信道编码在那里似乎也没有得到彻底的研究。在这里，我们想研究两种选择，一种是将源依赖关系视为源极化的第一阶段，并相应地设计相应的极性源/信道编码方案。另一种选择建立在源和信道编码部分更强的集成或相互连接的基础上，以鞅的观点解决源极化的熵和信道极化的容量，当熵或容量低于某些阈值时，“刺破”和“修剪”组件，然后分别将数据视为确定性和信道视为“冻结”。

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.