Statistical Mechanics of Broadcast Channels Using Low Density Parity   Check Codes
  We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple timesharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based timesharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the timesharing limit. 
Kazutaka Nakamura, Robert Morelos-Zaragoza, David Saad and Yoshiyuki   Kabashima