LDPC Codes for Network-Coded Bidirectional Relaying With Higher Order Modulation

We study the use of Low-Density Parity-Check (LDPC) codes for two-phase, network-coded bidirectional relaying with higher-order modulation. In the multiple-access phase, the sum of transmitted symbols scaled by the channel gains is the received relay constellation, which is network-mapped (clustered) to a transmit constellation for the ensuing broadcast phase. This operation at the relay is termed Clustered-Scaled-Sum (CSS) decoding. We propose a CSS coding scheme for bidirectional relaying using a single LDPC code over a ring with higher-order PAM or QAM alphabets. We design a message-passing decoder for CSS decoding with trade-offs possible between complexity and performance. We suggest a method for completing a Constrained Partially-filled Latin Square (CPLS) to a latin square, which is used in the construction of network maps at the relay for any channel fading state. The performance of the CSS coding scheme with LDPC codes over rings is shown to be very close to information-theoretic outer bounds.