The compound LDGM/LDPC codes are shown to attain the information-theoretic limits of the Gelfand-Pinsker and Wyner-Ziv problems when optimal encoding and decoding are employed. The sparse and graphical structure of this code motivates it to be implemented with message passing algorithms. In this thesis, an encoding and decoding message passing algorithm is proposed for the compound code by inspiring the belief propagation and truthiness propagation algorithms. Initial simulations show that the encoding algorithm can correctly encode half of the frames, and the decoding algorithm can successfully decode the correctly encoded frames. The drawbacks of the encoding algorithm are compensated by concatenating an outer code. With the coding scheme provided in the literature for the compound code, it is shown that a uniformly distributed message input is shaped into a non-uniformly distributed channel input, which motivates probabilistic shaping applications. Although it is widely claimed in the literature that this scheme should deliver a good performance, the scheme is not competitive compared to other schemes, e.g., to polar codes.     «

The compound LDGM/LDPC codes are shown to attain the information-theoretic limits of the Gelfand-Pinsker and Wyner-Ziv problems when optimal encoding and decoding are employed. The sparse and graphical structure of this code motivates it to be implemented with message passing algorithms. In this thesis, an encoding and decoding message passing algorithm is proposed for the compound code by inspiring the belief propagation and truthiness propagation algorithms. Initial simulations show that the e...     »