LP decoding of LDPC codes in HARQ systems

The combination of low density parity check (LDPC) Codes and Automatic Repeat reQuest (ARQ) has shown to be a promising option to increase the throughput of a communication system. A recently proposed method uses the decoding result to request unreliable bits for retransmission (reliability-based Hybrid ARQ). Commonly, Belief Propagation is used to decode LDPC codes. The result of this algorithm naturally provides an estimate for the probability of a bit to be erroneous. Another possibility to decode LDPC codes is via linear programming (LP) decoding. Despite some drawbacks (e.g. in terms of implementation complexity), linear programming decoding provides an interesting alternative to Belief Propagation. This work investigates the feasibility of combining LP decoding with ARQ. In lack of a probability measure for the decoded bits, when using LP decoding, request criteria using the integrality of the values in the LP solution are proposed. We present statistical investigations on the proposed criteria and the results of throughput simulations demonstrating the gains achievable by the proposed methods.