  A three terminal relay system with binary erasure channel (BEC) was
considered, in which a source forwarded information to a destination with a
relay's "assistance". The nested LDGM (Low-density generator-matrix) -LDPC
(low-density parity-check) was designed to realize Compress-and-forward (CF) at
the relay. LDGM coding compressed the received signals losslessly and LDPC
realized the binning for Slepian-Wolf coding. Firstly a practical coding scheme
was proposed to achieve the cut-set bound on the capacity of the system,
employing LDPC and Nested LDGM-LDPC codes at the source and relay respectively.
Then, the degree distribution of LDGM and LDPC codes was optimized with a given
rate bound, which ensured that the iterative belief propagation (BP) decoding
algorithm at the destination was convergent. Finally, simulations results show
that the performance achieved based on nested codes is very close to
Slepian-Wolf theoretical limit.
