# A generalized cut-set bound for deterministic multi-flow networks and its applications

@article{Shomorony2014AGC, title={A generalized cut-set bound for deterministic multi-flow networks and its applications}, author={Ilan Shomorony and Amir Salman Avestimehr}, journal={2014 IEEE International Symposium on Information Theory}, year={2014}, pages={271-275} }

We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finite-field networks, where we obtain a general outer-bound expression in terms of ranks of the transfer matrices. We then show that, even though our outer bound is for…

## 13 Citations

The Two-Unicast Problem

- Computer ScienceIEEE Transactions on Information Theory
- 2018

It is shown that despite its seeming simplicity, the two-unicast problem is a very difficult problem: the general network coding problem can be reduced to two- Unicorn, and non-Shannon inequalities are necessary for characterizing the capacity of general two- unicast networks.

Are generalized cut-set bounds tight for the deterministic interference channel?

- Computer Science2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2015

It is demonstrated that by carefully designing extended networks and applying the generalized cut-set (GCS) bound to them, the proposed approach results in deriving a tight converse for the three-user DIC in the symmetric case.

Chop and roll: Improving the cutset bound

- Computer Science2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2014

A new outer bound on the capacity region of a general noisy network with multiple messages is established, and has an intuitive interpretation as the directed information between inputs and outputs across these subsets of the partition.

Rank Matching for Multihop Multiflow

- Computer ScienceIEEE Trans. Inf. Theory
- 2015

The outer bounds of the MIMO interference channel reveal a fundamental rank-matching phenomenon, reminiscent of impedance matching in circuit theory, and results are provided to show that along with the min-cut max-flow bounds, the rank-mismatch bounds are the best possible.

Rank Matching for Multihop Multiflow

- Computer ScienceIEEE Transactions on Information Theory
- 2015

The outer bounds of the layered MIMO interference channel reveal a fundamental rank-matching phenomenon, reminiscent of impedance matching in circuit theory, and results are provided to show that along with the min-cut max-flow bounds, the rank-mismatch bounds are the best possible.

Capacity region of the symmetric injective K-user Deterministic Interference Channel

- Computer Science2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

The capacity region of the symmetric injective K-user Deterministic Interference Channel (DIC) is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region.

General Capacity Region for the Fully Connected Three-Node Packet Erasure Network

- Computer ScienceIEEE Transactions on Information Theory
- 2016

The results effectively characterize the capacity region for many important scenarios, e.g., wireless access-point networks with client-to-client cooperative communications, and wireless two-way relay networks with packet-level coding and processing.

General capacity region for the fully-connected 3-node packet erasure network

- Computer Science2015 IEEE International Symposium on Information Theory (ISIT)
- 2015

Technical contributions of this work include a new converse for many-to-many network communications and a new capacity-approaching simple linear network coding scheme.

Rate Distortion for Lossy In-Network Linear Function Computation and Consensus: Distortion Accumulation and Sequential Reverse Water-Filling

- Computer ScienceIEEE Transactions on Information Theory
- 2017

This work quantifies the accumulation of information loss in distributed computing, and obtains fundamental limits on network computation rate as a function of incremental distortions (and hence incremental loss of information) along the edges of the network.

Multihop Wireless Networks: A Unified Approach to Relaying and Interference Management

- Computer ScienceFound. Trends Netw.
- 2014

A unified approach to relaying and interference management is taken, and tools to study the fundamentals of multi-hop multi-flowwireless networks are developed, and the new notion of paths with manageable interference is introduced.

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