On a practical approach to source separation over finite fields for network coding applications

In Blind Source Separation, or BSS, a set of source signals are recovered from a set of mixed observations without knowledge of the mixing parameters. Originated for real signals, BSS has recently been applied to finite fields, enabling more practical applications. However, classical entropy-based techniques do not perform well in finite fields. Here, we propose a non-linear encoding of the sources to increase the discriminating power of the separation methods. Our results show that the encoding improves the success rate of the separation for sources with few samples in large finite fields, both conditions met in practical networking applications. Our results open new possibilities in the context of network coding-wherein linear combinations of packets are sent in order to maximize throughput and increase loss immunity- by relieving the nodes from the need to send the combination coefficients, thus reducing the overhead cost.