Title :
Multiple-Access Network Information-Flow and Correction Codes
Author :
Dikaliotis, Theodoros K. ; Ho, Tracey ; Jaggi, Sidharth ; Vyetrenko, Svitlana ; Yao, Hongyi ; Effros, Michelle ; Kliewer, Jörg ; Erez, Elona
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
Abstract :
This work considers the multiple-access multicast error-correction scenario over a packetized network with z malicious edge adversaries. The network has min-cut m and packets of length l, and each sink demands all information from the set of sources S. The capacity region is characterized for both a “side-channel” model (where sources and sinks share some random bits that are secret from the adversary) and an “omniscient” adversarial model (where no limitations on the adversary´s knowledge are assumed). In the “side-channel” adversarial model, the use of a secret channel allows higher rates to be achieved compared to the “omniscient” adversarial model, and a polynomial-complexity capacity-achieving code is provided. For the “omniscient” adversarial model, two capacity-achieving constructions are given: the first is based on random subspace code design and has complexity exponential in lm, while the second uses a novel multiple-field-extension technique and has O(lm|S|) complexity, which is polynomial in the network size. Our code constructions are “end-to-end” in that all nodes except the sources and sinks are oblivious to the adversaries and may simply implement predesigned linear network codes (random or otherwise). Also, the sources act independently without knowledge of the data from other sources.
Keywords :
error correction codes; linear codes; multicast communication; network coding; polynomial approximation; adversarial model; capacity achieving construction; error correction Code; linear network code; malicious edge adversary; multiple access network information flow; multiple field extension technique; packetized network; polynomial complexity; random subspace code design; secret channel; subspace code; Double extended field; Gabidulin codes; network error-correction; random linear network coding; subspace codes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2095130