Research On Bandwidth-Efficient Irregular Repeat-Accumulate Coded Physical-layer Network Coding

Physical-layer network coding (PNC) has been recognized as one of key technologiesto achieve capacity in the next generation wireless networks, and thus has been attractinggreat research attention. This is due to the fact that PNC directly utilizes the natural linearsuperimposed effect of wireless channels to boost the capacity of multi-user wirelessnetworks. In order to implement PNC in wireless networks, increasing research effort havebeen put on developing bandwidth-efficient channel-coded PNC for Gaussian and fadingchannels with acceptable complexity. Subsequent works on channel-coded PNC led byvarious researchers have made contributions that advance the implementation of PNC inwireless networks, such as binary coding and modulation based PNC scheme, binarycoding and high order modulation based PNC scheme, and Lattice code based PNC scheme.However, the aforementioned techniques are not complete solutions to the implementationsof PNC in wireless networks. Against this background, in this work we focus onchannel-coded PNC based on irregular repeat-accumulate (IRA) code over finite fieldGF(q). Our main contributions are summarized as follows:1. We propose a bandwidth-efficient IRA-PNC scheme to achieve the capacity of thetwo-way relay channel (TWRC) with additive white Gaussian noise (AWGN). Themotivation of the proposed IRA-PNC scheme is threefold. First, the bandwidth efficiencyof the binary coding and modulation PNC scheme is relatively low in the middle to highsignal-to-noise ratio regime. Second, there does not exist an optimal decoding algorithm forthe binary coding and high order modulation based PNC scheme. Third, the complexity ofthe Lattice code based PNC scheme is extremely high and the capacity approachingcapability of the low complexity implementation is limited. In the proposed IRA-PNCscheme, two users employ an identical IRA code, which enables the relay to directlyrecover the PNC messages from the received superimposed signals. We first design abandwidth-efficient IRA code with weighted combiner&accumulator (WCA) structure andrandom-coset mapping. We then propose an algorithm for the relay to decode PNCmessages from its received signals. In order to analyze and optimize the performance of theproposed IRA-PNC scheme, we extend the all-zero codeword assumption to TWRC. Byexploring the symmetry and the permutation-invariant property of the decoder messages’distribution introduced by the WCA and random-coset, we can model the decoder messages’ distribution by a multi-dimension Gaussian random vector which can becharacterized by only one parameter. This result enables the using of extrinsic informationtransfer (EXIT) chart to optimize the proposed IRA-PNC scheme. Numerical resultsdemonstrate that the proposed IRA-PNC scheme can achieve the capacity of AWGNTWRC within1dB.2. We propose a bandwidth-efficient IRA coded linear physical-layer network coding(IRA-LPNC) scheme to achieve the outage capacity of slow fading TWRC. The motivationof the proposed IRA-LPNC scheme is twofold. First, the application scope of the proposedIRA-PNC scheme is limited. Second, the complexity of the Lattice code based PNCscheme is extremely high. In the proposed IRA-LPNC scheme, we first analyze the lowerbounds of the frame error rate for the relay and the users in slow Rayleigh fading TWRC.Based on the LPNC model, we adopt the set-partition based decoding algorithm at the relayto decode the LPNC messages. We also derive the decoding error probability of LPNCmessages at the relay. In addition, we propose a minimum set-distance maximization basedIRA-LPNC design criteria. Finally, we propose the decoding algorithm used by the relay todecode LPNC messages for the IRA-LPNC scheme. Numerical results demonstrate that theproposed IRA-LPNC scheme with3/4code rate over the finite field GF(3) can achieve theoutage capacity of slow Rayleigh fading TWRC within1.2dB, which outperforms theexisting works4.5dB.3. We extend the proposed IRA-LPNC scheme to multi-user relay networks toimprove the performance of multi-user relay networks. Based on the model of themulti-user relay networks, we first propose algorithms for the relay to calculate the jointmaximum a posteriori probability of the LPNC messages and the component-wisemaximum a posteriori probability of LPNC messages. We then propose an algorithm for thedestination to calculate the maximum a posterior probability of users’ messages by usingthe side information from the relay. We then prove that minimize the symbol errorprobability of users’ messages at the destination is equivalent to minimize the symbol errorprobability of LPNC messages at the relay at high SNR regime. We derive the symbol errorprobability of LPNC messages at the relay based on the set-distance spectrum and theminimum set-distance. We then propose an algorithm to calculate multiple LPNC messagesfrom the received signals by maximize the minimum set-distance. We also proposeIRA-LPNC decoding algorithms for the relay and the destination. Numerical resultsdemonstrate that the proposed IRA-LPNC scheme for multi-user relay networks outperforms the traditional decode-and-forward scheme2dB in a relay network with4single-antenna users, a two-antenna relay, and a two-antenna destination.