A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For QPSK unchannel-coded PNC, with a half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC.
The use of BP has also been proposed in a number of places in the literature in the context of multi-user detection BoutrosIT02 @cite_23 and joint detection and decoding in the presence of phase noise and frequency offset BarbieriTCom07 @cite_19 . In ZhuTWireless09 @cite_6 , BP over a factor graph that describes the joint probability law of all unknowns and observations, as in the framework used in our paper here, is used to decode one of two users in the presence of Gauss-Markov (non-block) fading. This work is along the line of collision resolution CRESM @cite_2 rather than PNC mapping. In this paper, we assume that the channels can be perfectly estimated, leaving out the detailed estimation procedure. Ref. ZhuTWireless09 @cite_6 provides a nice way to integrate the problem of channel estimation and detection using BP. The application of the technique in PNC is an interesting area for further work.
@cite_19 @cite_6 @cite_23 @cite_2
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We present a new algorithm for joint detection and decoding of iteratively decodable codes transmitted over channels affected by a time-varying phase noise (PN) and a constant frequency offset. The proposed algorithm is obtained as an application of the sum-product algorithm to the factor graph representing the joint a posteriori distribution of the information symbols and the channel parameters given the channel output. The resulting algorithm employs the soft-output information on the coded symbols provided by the decoder and performs forward-backward recursions, taking into account the joint probability distribution of phase and frequency offset. We present simulation results for high-order coded modulation schemes based on low-density parity-check codes and serially concatenated convolutional codes, showing that, despite its low complexity, the algorithm is able to cope with a strong PN and a significant uncompensated frequency offset, thus avoiding the use of complicated data-aided frequency-estimation schemes operating on a known preamble. The robustness of the algorithm in the presence of a time-varying frequency offset is also discussed Channel uncertainty and co-channel interference are two major challenges in the design of wireless systems such as future generation cellular networks. This paper studies receiver design for a wireless channel model with both time-varying Rayleigh fading and strong co-channel interference of similar form as the desired signal. It is assumed that the channel coefficients of the desired signal can be estimated through the use of pilots, whereas no pilot for the interference signal is available, as is the case in many practical wireless systems. Because the interference process is non-Gaussian, treating it as Gaussian noise generally often leads to unacceptable performance. In order to exploit the statistics of the interference and correlated fading in time, an iterative message-passing architecture is proposed for joint channel estimation, interference mitigation and decoding. Each message takes the form of a mixture of Gaussian densities where the number of components is limited so that the overall complexity of the receiver is constant per symbol regardless of the frame and code lengths. Simulation of both coded and uncoded systems shows that the receiver performs significantly better than conventional receivers with linear channel estimation, and is robust with respect to mismatch in the assumed fading model. The synchronous chip-rate discrete-time CDMA channel with channel coding is analysed and the corresponding factor graph is presented. Iterative joint decoding can be derived in a simple and direct way by applying the sum-product algorithm to the factor graph. Since variables have degree 2, no computation takes place at the variable nodes. Computation at the code nodes is just soft-in soft-out (SISO) decoding, whose output is the extrinsic PMF of the coded symbols. Computation at the channel transition nodes is equivalent to MAP symbol-by-symbol multiuser detection, whose complexity is generally exponential in K. We show that several previously proposed low-complexity algorithms based on interference cancellation (IC) can be derived in a simple direct way by approximating the extrinsic PMF output by the SISO decoders either as a single mass-point PMF (hard decision) or as a Gaussian PDF with the same mean and variance (moment matching). Differently from all previously presented methods (derived from heuristic reasoning), we see clearly that extrinsic rather than a posteriori PMF should be fed back. This yields important advantages in terms of limiting achievable throughput. This paper presents CRESM, a novel collision resolution method for decoding collided packets in random-access wireless networks. In a collision, overlapping signals from several sources are received simultaneously at a receiver. CRESM exploits symbol misalignment among the overlapping signals to recover the individual packets. CRESM can be adopted in 802.11 networks without modification of the transmitter design; only a simple DSP technique is needed at the receiver to decode the overlapping signals. Our simulations indicate that CRESM has better BER performance than the simplistic Successive Interference Cancellation (SIC) technique that treats interference as noise, for almost all SNR regimes. The implication of CRESM for random-access networking is significant: in general, using CRESM to resolve collisions of up to n packets, network throughput can be boosted by more than n times if the transmitters are allowed to transmit more aggressively in the MAC protocol.