References & Further Reading

References

1. E. C. van der Meulen, Three-Terminal Communication Channels, 1971

   The original paper introducing the relay channel model. Establishes the basic framework and initiates the study of multi-terminal cooperation.

2. T. M. Cover and A. A. El Gamal, Capacity Theorems for the Relay Channel, 1979

   The foundational paper on relay channel coding. Introduces the cut-set bound, decode-and-forward, and compress-and-forward. Every result in this chapter traces back to this paper.

3. A. El Gamal and Y.-H. Kim, Network Information Theory, Cambridge University Press, 2011

   The definitive textbook on network information theory. Chapters 16--18 cover relay channels, relay networks, and multi-hop communication with complete proofs and extensive commentary.

4. B. Nazer and M. Gastpar, Compute-and-Forward: Harnessing Interference through Structured Codes, 2011

   Introduces the compute-and-forward framework. Shows that nested lattice codes enable relays to decode integer linear combinations of codewords, bridging channel coding and network coding.

5. U. Erez and R. Zamir, Achieving 1/2 log(1+SNR) on the AWGN Channel with Lattice Encoding and Decoding, 2004

   Proves that nested lattice codes achieve the AWGN capacity. This result is the foundation for compute-and-forward and other structured coding approaches.

6. A. S. Avestimehr, S. N. Diggavi, and D. N. C. Tse, Wireless Network Information Flow: A Deterministic Approach, 2011

   Introduces the deterministic approach to wireless networks and quantize-map-and-forward. Shows that capacity can be approximated to within a constant gap using simple strategies.

7. G. Kramer, M. Gastpar, and P. Gupta, Cooperative Strategies and Capacity Theorems for Relay Networks, 2005

   Extends relay channel results to networks with multiple relays. Derives capacity bounds for the diamond network and general relay networks.

8. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, 2nd ed., 2006

   Chapter 16 provides a concise introduction to the relay channel with the essential results (cut-set bound, DF, CF) and clean proofs.

9. J. N. Laneman, D. N. C. Tse, and G. W. Wornell, Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior, 2004

   Bridges relay channel theory with practical wireless protocol design. Introduces cooperative diversity protocols and analyzes outage probability in fading channels.

10. Y.-H. Kim, Coding Techniques for Primitive Relay Channels, 2008

    Develops improved coding techniques for relay channels and establishes partial results on capacity. Important for understanding the gap between DF/CF and capacity.

11. A. Host-Madsen and J. Zhang, Capacity Bounds and Power Allocation for Wireless Relay Channels, 2005

    Derives capacity bounds for the Gaussian relay channel with fading and studies optimal power allocation between source and relay.

Further Reading

• The general relay channel capacity problem

  Y.-H. Kim, "Coding Techniques for Primitive Relay Channels," in Proc. Allerton Conference, 2007. Also: A. El Gamal and Y.-H. Kim, "Network Information Theory," Ch. 16, Cambridge University Press, 2011.

  Provides a complete picture of what is and is not known about relay channel capacity, including partial results, counterexamples to the cut-set bound tightness, and the relationship between different relay coding strategies.

• Lattice codes and compute-and-forward

  B. Nazer and M. Gastpar, "Compute-and-Forward: Harnessing Interference through Structured Codes," IEEE Trans. Inf. Theory, 2011. Also: U. Erez and R. Zamir, "Achieving 1/2 log(1+SNR) on the AWGN Channel," IEEE Trans. Inf. Theory, 2004.

  For readers interested in the algebraic structure underlying compute-and-forward. Erez-Zamir provides the lattice coding foundation; Nazer-Gastpar builds the network coding application.

• Relay channels in 5G and beyond

  3GPP TR 36.806, "Relay architectures for E-UTRA (LTE-Advanced)," v9.0.0, 2010. Also: Y. Yang et al., "Relay Technologies for WiMAX and LTE-Advanced Mobile Systems," IEEE Communications Magazine, 2009.

  Connects the information-theoretic results to practical wireless standards. Describes how DF and CF map to Type I and Type II relays in 3GPP.

• Diamond networks and multi-relay cooperation

  G. Kramer, M. Gastpar, and P. Gupta, "Cooperative Strategies and Capacity Theorems for Relay Networks," IEEE Trans. Inf. Theory, 2005.

  The go-to reference for extending single-relay results to networks. Covers the diamond network, multiple relay chains, and general cooperative strategies.