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

Abstract

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.

Panda: A protocol-assisted network decoding algorithm

“…If F belongs to the independent part of the messages, the set of messages x that are linear combinations of the rows WY ← ∅; ⊲ Set of admissible decoding matrices 6: for all w ∈ F G q do 7: x ← wY; 8: if xΠI ∈ C (I) then 9 …”

“…However, this technique does not rely exclusively on entropy to perform the separation, as purely entropy-based methods strive to deliver good separation properties when the sources have a distribution close to uniform, which is typically the case for flows of compressed data. Thus, [9] includes a form of channel coding of the source vectors to inject an identifiable feature. This allows to reduce the search space considerably by rejecting solutions that do not carry a valid channel code.…”

“…The idea of BSS in finite field has been exploited in [9] to recover randomly network-coded packets without including the combination coefficients in the transmitted packets. However, this technique does not rely exclusively on entropy to perform the separation, as purely entropy-based methods strive to deliver good separation properties when the sources have a distribution close to uniform, which is typically the case for flows of compressed data.…”

On blind channel identification and equalization over Galois fields

“…This new paradigm was later expanded to general finite (Galois) fields of prime order P (denoted GF(P )) in [4] and of general (prime power) orders in [5,6]. While no immediate practical applications were associated with this problem at first, theoretical applications have been suggested in the context of eavesdropping on a Tomlinson-Harashima coded MIMO channel [4,6] and in the context of Network Coding [7]. Some additional contributions to this emerging topic were recently published in [8,9,10,11,12].…”

Rate-distortion-optimized multi-view streaming in wireless environment using network coding

“…In NC, instead of merely relaying packets, the intermediate nodes of a network send linear combinations of the packets they have previously received, with random coefficients taken from a finite field. The coding coefficients, needed to reconstruct the original packets, are typically sent along the combinations as headers [22][23][24][25], unless more advanced reconstruction schemes are implemented at the receiver side [26,27]. Used as an alternative to traditional routing, NC has proved beneficial to real-time streaming applications, both in terms of maximization of the throughput and in terms of reduction of the effects of losses [28][29][30][31][32][33].…”