Reliability-based hybrid ARQ (RB-HARQ) is a kind of incremental-redundancy ARQ recently introduced. In the RB-HARQ, the receiver returns both NAK signal and set of unreliable bit indices if the received sequence is not accepted. Since each unreliable bit index is determined by the bitwise posterior probability, better approximation of that probability becomes crucial as the number of retransmissions increases. Assuming the systematic code for the initial transmission, the proposed RB-HARQ scheme has the following two features: (a) the sender retransmits newly encoded and interleaved parity bits corresponding to the unreliable information bits; (b) the retransmitted parity bits as well as the initial received sequence are put all together to perform the message passing decoding i.e. the suboptimal MAP decoding. Finally, simulation results are shown to evaluate the above two features.

We propose a new fixed-rate error correction system with a feedback channel. In our system, the receiver transmits a list of positions of unreliable information bits based on the log a-posteriori probability ratios by outputs of a soft-output decoder to the transmitter. This method is just like that of the reliability-based hybrid ARQ scheme. To dynamically select an appropriate interleaving function with feedback information is a key feature of our system. By computer simulations, we show that the performance of a system with a feedback channel is improved by dynamically selecting an appropriate interleaving function.

We propose transformation of a parity-check matrix of any low-density parity-check code. A code with transformed parity-check matrix is an equivalent of a code with the original parity-check matrix. For the binary erasure channel, performance of a message-passing algorithm with a transformed parity-check matrix is better than that with the original matrix.