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

该建议建立在我们自己以前的工作LDPC联合信源信道编码的Bernoulli（p）源和独立，我们的工作直接包括马尔可夫性质（记忆）的数据到解码过程中的信道解码器。这两项工作导致多边缘类型的LDPC码的设计和性能比较不同的替代结构-它更像Turbo或将依赖关系到坦纳graph.One重要的一步，在这个建议是现在加入这两个努力，这意味着设计一个实际的联合信源信道编码的多边缘类型的LDPC码，也适用于数据中的马尔可夫属性，并将这些属性到坦纳图。预计代码优化将受到非一致密度的影响，需要全密度演化，这通常被简化为仅考虑在一致情况下相互依赖的方差或均值的演化。众所周知，全密度进化在实践中要求非常高，但在这种情况下可能是不可避免的。然而，当然，将评估该步骤的必要性。极化码是竞争性容量实现和低复杂度码构造中的一种，并且据我们所知，在那里还没有适当地处理源存储器，并且联合源信道编码似乎通常也没有在那里被彻底研究。在这里，我们想研究两个选项，一个是将源依赖性视为源极化的第一阶段，并相应地设计相应的极化源/信道编码方案。另一种选择建立在信源和信道编码部分的更强的集成或互连上，着眼于解决信源极化的熵和信道极化的容量的鞅，当熵或容量下降到特定阈值以下时“打孔”和“修剪”分量，然后分别将数据视为确定性的并且将信道视为“冻结”的。

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.