\begin{abstract} 
Recently there has been a growing interest in improving the performance of the wireless relay networks, 
especially using physical layer coding techniques (also referred to as Analog Network Coding). The
physical layer network coding technique allows the two terminals to transmit simultaneously to the relay node 
and decode the modulo-2 sum of the bits at the relay. This technique improves the performance considerably over 
Digital Network Coding.  In this paper, we present an algorithm for joint decoding of the modulo-2 sum of the 
bits transmitted from two unsynchronized transmitters. We address the problems that arise when the boundaries of 
the signals do not align with each other and when the channel parameters are slowly varying and are not known to 
the receiver at the relay node. Our approach first estimates jointly the timing and fading gains of both the 
signals, and uses a state-based Viterbi decoding scheme that takes into account the timing offsets between the
interfering signals. We also track the amplitude and phase of the channel which may be slowly varying.
Lastly, simulation results demonstrate the sensitivity of the detection performance at the relay node to the 
relative offset of the timings of the two user's signals as well as the improvement of our algorithm over previously 
published algorithms.
\end{abstract}