Performance Analysis of Physical Layer Network Coding

PERFORMANCE ANALYSIS OF PHYSICAL
LAYER NETWORK CODING

By

Jinho Kim

Network coding has emerged as an innovative approach to network operation
that can significantly enhance network throughput. The key goal of this
thesis is to understand fundamental aspects of physical layer network coding,
where network coding is performed at the physical layer.

As a simple but typical example of network coding, we consider a network scenario where two users transmit messages through a common channel and the receiver reconstructs the exclusive-or of the two messages. For this channel, we investigate the error exponent which can provide guidelines for the design of efficient communication systems using network coding. From a practical point of view, we examine the performance of channel codes for this problem. Assuming that each user transmits data using the same low-density parity-check (LDPC) code and each link is an additive white Gaussian noise channel, we evaluate the noise thresholds of LDPC codes via density evolution methods.

Other important issues considered in this thesis are related to transmission over fading channels. First, we study the performance of LDPC codes over non-ergodic fading channels. In non-ergodic channels, reliable communication at a constant rate is impossible. Assuming that the fading coefficient is randomly chosen but fixed during transmission of an LDPC codeword, we derive the outage probability of LDPC-coded systems. We also propose an accurate frequency domain channel estimator based on the Slepian basis expansion. The proposed scheme operates with high accuracy requiring only the knowledge of the maximum delay spread of the channel. Finally, we investigate the capacity achieving input of non-coherent Rayleigh fading channels taking into account power constraints imposed by a non-linear power amplifier. We show that the optimal input is discrete with finite support which indicates that capacity can be computed using finite dimensional optimization.
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