Rate adaptation is an effective approach to achieve high spectrum efficiency under varying channel condition, especially for wireless communication. This paper proposes rate adaptation at receiver for wireless relay system. In this scheme, source node uses a new modulation technology, called random projections code (RPC), to achieve rate adaptation. Both relay node and destination node decode the received RPC encoding signals. If destination does not decode RPC correctly, relay node will act compressing and forwarding role by performing LDPC syndrome encoding and sending syndrome coded information to destination node. We discuss how to jointly decode at destination node when it receives RPC coded information from source node and syndrome coded information from relay node. Finally, we evaluate the scheme by bit-error-rate (BER) and good put evaluation metrics. Simulation results show that the coding gain is about 4 dB, 3.1 dB, 2.2 dB and 1.6 dB for LDPC coding rate 0.8, 0.89, 0.94, 0.99 at BER 10-5 respectively. The throughput of the schemes is at least 0.3 bit/s/Hz higher than RPC at SNR ranging from 5 dB to 25 dB.
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