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Double Polar Codes for Joint Source and Channel Coding

In this paper, we design a joint source and channel coding (JSCC) framework combining the source polar coding and the channel polar coding. The source is first compressed using a polar code (PC), and source check decoding is employed to construct an error set containing the index of all source decoding errors. Then, the proposed JSCC system employs another PC or systematic PC (SPC) to protect the compressed source and the error set against noise, which is called double PC (D-PC) or systematic double PC (SD-PC), respectively. For a D-PC JSCC system, we prove a necessary condition for the optimal mapping between the source PC and the channel PC. On the receiver side, by introducing the joint factor graph representation of the D-PC and SD-PC, we propose two joint source and channel decoders: a joint belief propagation (J-BP) decoder, and a systematic joint belief propagation (SJ-BP) decoder. In addition, a biased extrinsic information transfer (B-EXIT) chart is developed for various decoders as a theoretical performance evaluation tool. Both B-EXIT and simulation results show that the performance of the proposed JSCC scheme has no error floor and outperforms the turbo-like BP decoder.