# Capacity theorems for the relay channel

@article{Cover1979CapacityTF, title={Capacity theorems for the relay channel}, author={T. Cover and A. Gamal}, journal={IEEE Trans. Inf. Theory}, year={1979}, volume={25}, pages={572-584} }

A relay channel consists of an input x_{l} , a relay output y_{1} , a channel output y , and a relay sender x_{2} (whose transmission is allowed to depend on the past symbols y_{1} . The dependence of the received symbols upon the inputs is given by p(y,y_{1}|x_{1},x_{2}) . The channel is assumed to be memoryless. In this paper the following capacity theorems are proved. 1)If y is a degraded form of y_{1} , then C \: = \: \max \!_{p(x_{1},x_{2})} \min \,{I(X_{1},X_{2};Y), I(X_{1}; Y_{1}|X_{2… Expand

#### 4,241 Citations

The capacity of the semideterministic relay channel

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1982

Capacity of a Class of Deterministic Relay Channels

- Computer Science, Mathematics
- 2007 IEEE International Symposium on Information Theory
- 2007

The Discrete Memoryless Relay Channel: Joint-Decoding vs. Sequential Decoding of [CE79, theorem 6]

- 2008

A new upper bound on the capacity of a class of primitive relay channels

- Mathematics, Physics
- 2008 46th Annual Allerton Conference on Communication, Control, and Computing
- 2008

Diamond channel with partially separated relays

- Physics, Computer Science
- 2010 IEEE International Symposium on Information Theory
- 2010

An upper bound on relaying over capacity based on channel simulation

- Mathematics, Computer Science
- ArXiv
- 2012

Multi-Cast Channels with Hierarchical Flow

- Mathematics, Computer Science
- 2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

Capacity of a Class of Deterministic Relay Channels

- Computer Science
- IEEE Trans. Inf. Theory
- 2008

The geometry of the relay channel

- Mathematics, Computer Science
- 2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

#### References

SHOWING 1-10 OF 18 REFERENCES

On source coding with side information at the decoder

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1975

Source coding with side information and a converse for degraded broadcast channels

- Computer Science
- IEEE Trans. Inf. Theory
- 1975

A proof of the data compression theorem of Slepian and Wolf for ergodic sources (Corresp.)

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1975

An achievable rate region for the broadcast channel

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1975

Noiseless coding of correlated information sources

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1973

Coding Theorems of Information Theory

- Mathematics
- Ergebnisse der Mathematik und Ihrer Grenzgebiete
- 1961

A survey of multi-way channels in information theory: 1961-1976

- Computer Science
- IEEE Trans. Inf. Theory
- 1977

Multiterminal source coding Lecture notes presented at the 1977 CISM Summer School

- Multiterminal source coding Lecture notes presented at the 1977 CISM Summer School
- 1977