Polynomial time algorithms for multicast network code construction
Jaggi, S.
Sanders, P.
Chou, P.A.
Effros, M.
Egner, S.
Jain, K.
Tolhuizen, L.M.G.M.
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: June 2005
Volume: 51,
Issue: 6
On page(s): 1973- 1982
ISSN: 0018-9448
INSPEC Accession Number: 8466998
Digital Object Identifier: 10.1109/TIT.2005.847712
Current Version Published: 2005-05-31
Abstract
The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures.
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