Compute-and-forward: Harnessing interference through structured codes

IEEE Transactions on Information Theory

Volumn 57, Issue 10, 2011, Pages 6463-6486

  Nazer, Bobak ^a   Gastpar, Michael ^b,c  

^a Boston University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c EPFL   (Switzerland)

Author keywords

Additive white Gaussian noise (AWGN) networks; cooperative communication; interference; nested lattice codes; relaying; reliable computation; structured codes

Indexed keywords

ADDITIVE WHITE GAUSSIAN NOISE (AWGN) NETWORKS; COOPERATIVE COMMUNICATION; NESTED LATTICE CODES; RELAYING; RELIABLE COMPUTATION; STRUCTURED CODES;

DECODING; FINITE ELEMENT METHOD; WHITE NOISE; WIRELESS SENSOR NETWORKS;

GAUSSIAN NOISE (ELECTRONIC);

EID: 79960678507     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2165816     Document Type: Article

References (76)

1. T. M. Cover and A. El Gamal, "Capacity theorems for the relay channel," IEEE Trans. Inf. Theory, vol. 25, pp. 572-584, Sep. 1979.
2. J. N. Laneman, D. N. C. Tse, and G. W.Wornell, "Cooperative diversity in wireless networks: Efficient protocols and outage behavior," IEEE Trans. Inf. Theory, vol. 50, pp. 3062-3080, Dec. 2004.
3. G. Kramer, M. Gastpar, and P. Gupta, "Cooperative strategies and capacity theorems for relay networks," IEEE Trans. Inf. Theory, vol. 51, pp. 3037-3063, Sep. 2005.
4. A. El Gamal, N. Hassanpour, and J. Mammen, "Relay networks with delays," IEEE Trans. Inf. Theory, vol. 53, pp. 3413-3431, Oct. 2007.
5. Y.-H. Kim, "Capacity of a class of deterministic relay channels," IEEE Trans. Inf. Theory, vol. 54, pp. 1328-1329, Mar. 2008.
6. M. Aleksic, P. Razaghi, and W.Yu, "Capacity of a class of modulo-sum relay channels," IEEE Trans. Inf. Theory, vol. 55, pp. 921-930, Mar. 2009.
7. A. Sanderovich, O. Somekh, H. V. Poor, and S. Shamai (Shitz), "Uplink macro diversity of limited backhaul cellular network," IEEE Trans. Inf. Theory, vol. 55, pp. 3457-3478, Aug. 2009.
8. S. H. Lim, Y.-H. Kim, A. El Gamal, and S.-Y. Chung, "Noisy network coding," IEEE Trans. Inf. Theory, vol. 57, pp. 3132-3152, May 2011.
9. B. Schein and R. G. Gallager, "The Gaussian parallel relay network," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2000), Sorrento, Italy, Jun. 2000.
10. M. Gastpar and M. Vetterli, "On the capacity of large Gaussian relay networks," IEEE Trans. Inf. Theory, vol. 51, pp. 765-779, Mar. 2005.
11. S. Borade, L. Zheng, and R. Gallager, "Amplify-and-forward in wireless relay networks: Rate, diversity, and network size," IEEE Trans. Inf. Theory, vol. 53, pp. 3302-3318, Oct. 2007.
12. I. Maric, A. Goldsmith, and M. Médard, "Analog network coding in the high-SNR regime," in Proc. IEEE Wireless Netw. Coding Conf. (WiNC 2010), Boston, MA, Jun. 2010.
13. V. Kawadia and P. R. Kumar, "A cautionary perspective on cross-layer design," IEEE Wireless Commun. Mag., vol. 12, pp. 3-11, Feb. 2005.
14. R. Zamir, "Lattices are everywhere," in Proc. 4th Ann. Workshop on Inf. Theory and Its Appl. (ITA 2009), La Jolla, CA, Feb. 2009.
15. U. Erez and R. Zamir, "Achieving 1/2 log (1+ SNR) on the AWGN channel with lattice encoding and decoding," IEEE Trans. Inf. Theory, vol. 50, pp. 2293-2314, Oct. 2004.
16. R. Zamir, S. Shamai (Shitz), and U. Erez, "Nested linear/lattice codes for structured multiterminal binning," IEEE Trans. Inf. Theory, vol. 48, pp. 1250-1276, Jun. 2002.
17. H. E. Gamal, G. Caire, and M. O. Damen, "Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels," IEEE Trans. Inf. Theory, vol. 50, pp. 968-985, Jun. 2004.
18. R. Ahlswede, "Group codes do not achieve Shannon's channel capacity for general discrete channels," Ann. Math. Statist., vol. 42, pp. 224-240, Feb. 1971.
19. B. Nazer and M. Gastpar, "The case for structured random codes in network capacity theorems," Eur. Trans. Telecommun., vol. 19, pp. 455-474, June 2008.
20. J. Körner and K. Marton, "How to encode the modulo-two sum of binary sources," IEEE Trans. Inf. Theory, vol. 25, pp. 219-221, Mar. 1979.
21. B. Nazer and M. Gastpar, "Computation over multiple-access channels," IEEE Trans. Inf. Theory, vol. 53, pp. 3498-3516, Oct. 2007.
22. T. Philosof and R. Zamir, "On the loss of single-letter characterization: The dirty multiple access channel," IEEE Trans. Inf. Theory, vol. 55, pp. 2442-2454, Jun. 2009.
23. T. Philosof, R. Zamir, U. Erez, and A. Khisti, "Lattice strategies for the dirty multiple access channel," IEEE Trans. Inf. Theory vol. 57, no. 8, pp. 5006-5035, Aug. 2011.
24. R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow," IEEE Trans. Inf. Theory, vol. 46, pp. 1204-1216, Jul. 2000.
25. S.-Y. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inf. Theory, vol. 49, pp. 371-381, Feb. 2003.
26. R. Koetter and M. Medard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol. 11, pp. 782-795, Oct. 2003.
27. T. Ho, M. Medard, R. Koetter, D. R. Karger, M. Effros, J. Shi, and B. Leong, "A random linear network coding approach to multicast," IEEE Trans. Inf. Theory, vol. 52, pp. 4413-4430, Oct. 2006.
28. S. Zhang, S.-C. Liew, and P. Lam, "Hot topic: Physical-layer network coding," in Proc. 12th Ann. ACM Int. Conf. Mobile Computing and Netw. (MobiCom 2006), Los Angeles, CA, Sep. 2006.
29. P. Popovski and H. Yomo, "Bi-directional amplification of throughput in a wireless multi-hop network," in Proc. 63rd IEEE Veh. Technol. Conf. (VTC 2006-Spring), Melbourne, Australia, May 2006.
30. B. Rankov and A. Wittneben, "Achievable rate regions for the two-way relay channel," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2006), Seattle, WA, Jul. 2006.
31. B. Nazer and M. Gastpar, "Computing over multiple-access channels with connections to wireless network coding," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2006), Seattle, WA, Jul. 2006.
32. B. Nazer and M. Gastpar, "Lattice coding increases multicast rates for Gaussian multiple-access networks," in Proc. 45th Ann. Allerton Conf. Commun., Contr. Comput., Monticello, IL, Sep. 2007.
33. K. Narayanan, M. P. Wilson, and A. Sprintson, "Joint physical layer coding and network coding for bi-directional relaying," in Proc. 45th Ann. Allerton Conf. Commun., Contr. Comput., Monticello, IL, Sep. 2007.
34. M. P.Wilson, K. Narayanan, H. Pfister, and A. Sprintson, "Joint physical layer coding and network coding for bidirectional relaying," IEEE Trans. Inf. Theory, vol. 11, pp. 5641-5654, Nov. 2010.
35. W. Nam, S.-Y. Chung, and Y. H. Lee, "Capacity bounds for two-way relay channels," in Proc. Int. Zurich Seminar on Commun. (IZS 2008), Zurich, Switzerland, Mar. 2008.
36. W. Nam, S.-Y. Chung, and Y. H. Lee, "Capacity of the Gaussian two-way relay channel to within 1/2 bit," IEEE Trans. Inf. Theory, vol. 56, pp. 5488-5494, Nov. 2010.
37. W. Nam, S.-Y. Chung, and Y. H. Lee, "Nested lattice codes for Gaussian relay networks with interference," IEEE Trans. Inf. Theory Feb. 2009 [Online]. Available: http://arxiv.org/abs/0902.2436, submitted for publication
38. S.-C. Liew, S. Zhang, and L. Lu, "Physical-layer network coding: Tutorial, survey, and beyond," in Phys. Commun., 2011 [Online]. Available: http://arxiv.org/abs/1105.4261
39. B. Nazer and M. Gastpar, "Reliable physical layer network coding," Proc. IEEE, vol. 99, pp. 438-460, Mar. 2011.
40. M. A. Maddah-Ali, A. S. Motahari, and A. K. Khandani, "Communication over MIMO X channels: Interference alignment, decomposition, and performance analysis," IEEE Trans. Inf. Theory, vol. 54, pp. 3457-3470, Aug. 2008.
41. V. R. Cadambe and S. A. Jafar, "Interference alignment and the degrees of freedom for the K user interference channel," IEEE Trans. Inf. Theory, vol. 54, pp. 3425-3441, Aug. 2008.
42. G. Bresler, A. Parekh, and D. Tse, "The approximate capacity of the many-to-one and one-to-many Gaussian interference channels," IEEE Trans. Inf. Theory, vol. 56, pp. 4566-4592, Sep. 2010.
43. N. Khude, V. Prabhakaran, and P. Viswanath, "Harnessing bursty interference," in Proc. IEEE Inf. Theory Workshop (ITW 2009), Volos, Greece, Jun. 2009.
44. S. Sridharan, A. Jafarian, S. Vishwanath, S. A. Jafar, and S. Shamai (Shitz), "A layered lattice coding scheme for a class of three user Gaussian interference channels," in Proc. 46th Ann. Allerton Conf. Commun., Contr. Comput., Monticello, IL, Sep. 2008.
45. B. Nazer, M. Gastpar, S. A. Jafar, and S. Vishwanath, "Ergodic interference alignment," IEEE Trans. Inf. Theory [Online]. Available: http://arxiv.org/abs/0901.4379, submitted for publication
46. S.-W. Jeon and S.-Y. Chung, "Capacity of a class of multi-source relay networks," IEEE Trans. Inf. Theory Jul. 2009 [Online]. Available: http://arxiv.org/abs/0907.2510, submitted for publication
47. A. Sanderovich, M. Peleg, and S. Shamai (Shitz), "Scaling laws in decentralized processing of interfered Gaussian channels," Eur. Trans. Telecommun., vol. 22, no. 5, pp. 240-253, Aug. 2011.
48. B. Nazer, A. Sanderovich, M. Gastpar, and S. Shamai (Shitz), "Structured superposition for backhaul constrained cellular uplink," in Proc. Int. Symp. Inf. Theory (ISIT 2009), Seoul, South Korea, Jun. 2009.
49. D. Krithivasan and S. S. Pradhan, "Lattices for distributed source coding: Jointly Gaussian sources and reconstruction of a linear function," IEEE Trans. Inf. Theory, vol. 55, pp. 5268-5651, Dec. 2009.
50. D. Krithivasan and S. Pradhan, "Distribued source coding using Abelian group codes," IEEE Trans. Inf. Theory, vol. 57, pp. 1495-1519, Mar. 2011.
51. A. B. Wagner, "On distributed compression of linear functions," IEEE Trans. Inf. Theory, vol. 57, pp. 79-94, Jan. 2011.
52. A. D. Sarwate, B. Nazer, and M. Gastpar, "Spatial filtering in sensor networks with computation codes," in Proc. IEEE Statist. Signal Process. Workshop (SSP 2007), Madison, WI, Aug. 2007.
53. B. Nazer and M. Gastpar, "Structured random codes and sensor network coding theorems," in Proc. Int. Zurich Seminar on Commun. (IZS 2008), Zurich, Switzerland, Mar. 2008.
54. R. Soundararajan and S. Vishwanath, "Communicating the difference of correlated Gaussian sources over a MAC," in Proc. Data Compression Conf. (DCC 2009), Snowbird, UT, Mar. 2009.
55. Y. Kochman and R. Zamir, "Joint Wyner-Ziv/dirty-paper coding by modulo-lattice modulation," IEEE Trans. Inf. Theory, vol. 55, pp. 4878-4889, Nov. 2009.
56. X. He and A. Yener, "Providing secrecy with structured codes: Tools and applications to two-user Gaussian channels," IEEE Trans. Inf. Theory Jul. 2009 [Online]. Available: http://arxiv.org/abs/0907.5388, submitted for publication
57. S. Agrawal and S. Vishwanath, "On the secrecy rate of interference networks using structured codes," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2009), Seoul, South Korea, Jun. 2009.
58. C. Feng, D. Silva, and F. Kschischang, "An algebraic approach to physical-layer network coding," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2010), Austin, TX, Jun. 2010.
59. B. Hern and K. Narayanan, "Multilevel coding schemes for computeand-forward," presented at the IEEE Int. Symp. Inf. Theory, St. Petersburg, Russia, Aug. 2011.
60. O. Ordentlich and U. Erez, "Achieving the gains promised by integerforcing equalization with binary codes," in Proc. 26th IEEE Convention of Elect. Electron. Eng. Israel (IEEEI 2010), Eliat, Israel, Nov. 2010.
61. U. Erez and R. Zamir, "A modulo-lattice transformation for multipleaccess channels," in Proc. 25th IEEE Convention of Elect. Electron. Eng. Israel, Eliat, Israel, Dec. 2008.
62. T. S. Han and K. Kobayashi, "A new achievable rate region for the interference channel," IEEE Trans. Inf. Theory, vol. 27, pp. 49-60, Jan. 1981.
63. R. H. Etkin, D. N. C. Tse, and H. Wang, "Gaussian interference channel capacity to within one bit," IEEE Trans. Inf. Theory, vol. 54, pp. 5534-5562, Dec. 2008.
64. U. Niesen and P. Whiting, "The degrees-of-freedom of compute-andforward," IEEE Trans. Inf. Theory Jan. 2011 [Online]. Available: http://arxiv.org/abs/1101.2182, submitted for publication
65. A. S. Motahari, S. O. Gharan, M.-A. Maddah-Ali, and A. K. Khandani, "Real interference alignment: Exploiting the potential of single antenna systems," IEEE Trans. Inf. Theory Nov. 2009 [Online]. Available: http://arxiv.org/abs/0908.2282, submitted for publication
66. C. A. Rogers, "Lattice coverings of space," Mathematica, vol. 6, pp. 33-39, 1959.
67. R. Zamir and M. Feder, "On lattice quantization noise," IEEE Trans. Inf. Theory, vol. 42, pp. 1152-1159, Jul. 1996.
68. G. Poltyrev, "On coding without restrictions for the AWGN channel," IEEE Trans. Inf. Theory, vol. 40, pp. 409-417, Mar. 1994.
69. U. Erez, S. Litsyn, and R. Zamir, "Lattices which are good for (almost) everything," IEEE Trans. Inf. Theory, vol. 51, pp. 3401-3416, Oct. 2005.
70. H.-A. Loeliger, "Averaging bounds for lattices and linear codes," IEEE Trans. Inf. Theory, vol. 43, pp. 1767-1773, Nov. 1997.
71. D. Krithivasan and S. Pradhan, A Proof of the Existence of Good Lattices Univ. Michigan, Jul. 2007 [Online]. Available: http://www.eecs. umich.edu/techreports/systems/cspl/cspl-384.pdf
72. T. Cover and J. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley-Interscience, 2006.
73. B. Nazer, A. G. Dimakis, and M. Gastpar, "Local interference can accelerate gossip algorithms," IEEE J. Sel. Topics Signal Process., vol. 5, no. 4, pp. 876-887, Aug. 2011.
74. J. Zhan, B. Nazer, U. Erez, and M. Gastpar, "Integer-forcing linear receivers," presented at the IEEE Int. Symp. Inf. Theory, Austin, TX, Jun. 2010.
75. R. Etkin and E. Ordentlich, "The degrees-of-freedom of the user Gaussian interference channel is discontinuous at rational channel coefficients," IEEE Trans. Inf. Theory, vol. 55, pp. 4932-4946, Nov. 2009.
76. S. Avestimehr, S. Diggavi, and D. Tse, "Wireless network information flow: A deterministic approach," IEEE Trans. Inf. Theory, vol. 57, pp. 1872-1905, Apr. 2011.