Encoding Complexity of Network Coding with Two Simple Multicast Sessions
Wentu Song, Kai Cai, Rongquan Feng, Chau Yuen

TL;DR
This paper provides efficient algorithms and bounds for solving network coding problems with two multicast sessions, significantly improving understanding of their complexity and resource requirements.
Contribution
It proves that solvability, solution construction, and optimal solutions for 2-URMS networks can be achieved in linear or polynomial time, with tight bounds on encoding links and field size.
Findings
Solvability can be decided in O(|E|) time.
A solution can be constructed in O(|E|) time.
The number of encoding links is bounded by max{3, 2N-2}.
Abstract
The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e.g., the time complexity, the required number of encoding links, and the required field size for a linear code solution. However, these issues as well as the solvability are less understood for networks with multiple multicast sessions. Recently, Wang and Shroff showed that the solvability of networks with two unit-rate multicast sessions (2-URMS) can be decided in polynomial time. In this paper, we prove that for the 2-URMS networks: the solvability can be determined with time ; a solution can be constructed with time ; an optimal solution can be obtained in polynomial time; the number of encoding links required to achieve a solution is upper-bounded by ; and the field size required to achieve a linear…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCooperative Communication and Network Coding · Full-Duplex Wireless Communications · MXene and MAX Phase Materials
