Bidirectional broadcasting by using multi-edge type LDPC convolutional codes

In this paper we propose multi-edge type (MET) LDPC convolutional codes for the bidirectional broadcast channel with common message (BBC-CM). It describes a two-user broadcast channel in which different subsets of the broadcasted messages are a priori known at the receivers. This situation occurs, e.g., in the second transmission phase of a bidirectional relaying protocol. In the proposed scheme, the transmitter broadcasts codewords of an MET LDPC convolutional code. Each user tries then to recover the unknown messages by decoding a two-edge type code which is embedded in the MET code. We prove for each user that the two-edge type LDPC convolutional code has the same properties as a standard LDPC convolutional code, and therefore it is capacity achieving for the binary erasure channel (BEC) and the general binary memoryless symmetric (BMS) channel. Meanwhile, we show that the capacity region of the BBC-CM is achieved. Numerical results with finite node degrees show that the achievable rates approach the channel capacities in both BECs and BI-AWGN channels.