Physical-layer network coding (PNC) has been shown to be a feasible way to improve the spectrum efficiency and boost the network throughput in wireless communication systems. Through exploiting network coding at the physical layer, a network coded message is generated at the PNC receiver based on the superimposed version of signals from multiple transmitters. The simplest network for which PNC is applicable is the two-way relay network (TWRN) in which two end nodes exchange information with the assistance of a relay in between. End nodes transmit their messages to the relay simultaneously and the relay then generates a network coded message and broadcasts it to the end nodes. Each end node retrieves the information from the other end node based on the received signal from the rel...[ Read more ]

Physical-layer network coding (PNC) has been shown to be a feasible way to improve the spectrum efficiency and boost the network throughput in wireless communication systems. Through exploiting network coding at the physical layer, a network coded message is generated at the PNC receiver based on the superimposed version of signals from multiple transmitters. The simplest network for which PNC is applicable is the two-way relay network (TWRN) in which two end nodes exchange information with the assistance of a relay in between. End nodes transmit their messages to the relay simultaneously and the relay then generates a network coded message and broadcasts it to the end nodes. Each end node retrieves the information from the other end node based on the received signal from the relay. In this thesis, we investigate the application of channel coding on the PNC over the TWRN.

We firstly examine the convolutionally coded PNC (CC-PNC) over the TWRN in which there is no direct end-to-end link. Specifically, we focus on the joint channel-network decoding (JCND) at the relay, i.e., the joint probability density of the codewords for the two end nodes are calculated and then mapped to a network coded codeword. We first re-examine the decoding problem for the synchronous CC-PNC utilizing JCND. To improve the word error rate (WER) performance, the list-output JCND (LJCND) is adopted. The decoder at the relay generates a ranked list containing L best candidates. A decoding error occurs if the correct codeword is not included in the list. By tacking the challenge of high decoding complexity of the traditional trellis-based list decoder, we propose an efficient list-output priority-first search algorithm (LPFSA). The proposed LPFSA has two advantages. Firstly, it combines the tree and trellis structure of the linear channel code and greatly reduces the decoding complexity. Secondly, the proposed algorithm depends on the trellis structure of the code and can be extended to other linear block codes. Besides, we derive a technique to approximate the WER of LJCND with a list size of L = 2 and L = 3, respectively. The theoretical analysis matches well with the simulation result, especially at high signal-to-noise ratio (SNR).

We further examine the channel coded asynchronous PNC in which there exists symbol misalignment between the two packets arriving at the relay from two end nodes. The existing channel coding design to support asynchronous PNC requires the cyclic code structure. This restrains the possible choice of the channel codes that can be exploited on PNC. To relax the cyclic code constraint, we perform the JCND for the asynchronous channel coded PNC. Based on the sampled signals after matching filtering, an extended full-state trellis structures incorporating the code structure and the symbol misalignment is created. The JCND can be devised by applying the Viterbi algorithm on the trellis. Besides, we propose a technique to estimate the distance spectrum and the bit error rate (BER) bound of the JCND. Moreover, we apply the LPFSA on the extended full-state trellis to devise the LJCND. Similar to the synchronous counterpart, the decoding complexity of the proposed list decoder outperforms the benchmarking list decoders.

Besides, we investigate the channel coded PNC over the TWRN with a direct end-to-end link. Two end nodes work in full-duplex (FD) mode and each one receives two packets, one packet from the other user and one network coded packet from the relay. Therefore, the cooperative communication schemes need to be considered at the end nodes. The end-to-end performance suffers from the error propagation induced by the decoding error at the relay. To mitigate the error propagation, we approximate the decoding error probability at the relay as exponential functions. Based on this approximation, we propose a trellis error model (TEM) and Tanner graph error model (TGEM) for the convolutionally coded and LDPC coded FD TWRN, respectively. The prominent feature of the error models is that they incorporates the decoding errors at the relay into a product code, and convert the decoding problem in FD TWRN into an equivalent point-to-point channel. The proposed error models can provide not only better error performance compared with the existing cooperative schemes but also facilitate us to analyze the asymptotic error performance of the FD TWRN.