Bounds on capacity and minimum energy-per-bit for AWGN relay channels

Upper and lower bounds on the capacity and minimum energy-per-bit for general additive white Gaussian noise (AWGN) and frequency-division AWGN (FD-AWGN) relay channel models are established. First, the max-flow min-cut bound and the generalized block-Markov coding scheme are used to derive upper and lower bounds on capacity. These bounds are never tight for the general AWGN model and are tight only under certain conditions for the FD-AWGN model. Two coding schemes that do not require the relay to decode any part of the message are then investigated. First, it is shown that the "side-information coding scheme" can outperform the block-Markov coding scheme. It is also shown that the achievable rate of the side-information coding scheme can be improved via time sharing. In the second scheme, the relaying functions are restricted to be linear. The problem is reduced to a "single-letter" nonconvex optimization problem for the FD-AWGN model. The paper also establishes a relationship between the minimum energy-per-bit and capacity of the AWGN relay channel. This relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy-per-bit that do not differ by more than a factor of 1.45 for the FD-AWGN relay channel model and 1.7 for the general AWGN model.

[1]  Abdel R. El Gamal,et al.  On information flow in relay networks , 1981 .

[2]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[3]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[4]  Abbas El Gamal,et al.  Capacity of a class of relay channels with orthogonal components , 2005, IEEE Transactions on Information Theory.

[5]  Sergio Verdú,et al.  On channel capacity per unit cost , 1990, IEEE Trans. Inf. Theory.

[6]  R. Gallager.  ENERGY LIMITED CHANNELS : CODING , MULTIACCESS , AND SPREAD SPECTRUM * * ABSTRACT , 1987 .

[7]  Anders Høst-Madsen,et al.  Capacity bounds and power allocation for wireless relay channels , 2005, IEEE Transactions on Information Theory.

[8]  Abbas El Gamal,et al.  Capacity theorems for the relay channel , 1979, IEEE Trans. Inf. Theory.

[9]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[10]  M. Vetterli,et al.  On the asymptotic capacity of Gaussian relay networks , 2002, Proceedings IEEE International Symposium on Information Theory,.

[11]  Junshan Zhang,et al.  Capacity Bounds and Power Allocation for the Wireless Relay Channel , 1990 .

[12]  Sergio Verdú,et al.  Spectral efficiency in the wideband regime , 2002, IEEE Trans. Inf. Theory.

[13]  Michael Gastpar,et al.  On the capacity of wireless networks: the relay case , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[14]  Michael Gastpar,et al.  Cooperative strategies and capacity theorems for relay networks , 2005, IEEE Transactions on Information Theory.

[15]  Mohammad Reza Aref,et al.  The capacity of the semideterministic relay channel , 1982, IEEE Trans. Inf. Theory.

[16]  R. Gallager,et al.  The Gaussian parallel relay network , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[17]  Abbas El Gamal,et al.  On the capacity of AWGN relay channels with linear relaying functions , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[18]  G. Caire,et al.  Is TDMA optimal in the low power regime? , 2002, Proceedings IEEE International Symposium on Information Theory,.

[19]  Robert J. McEliece,et al.  The Theory of Information and Coding , 1979 .

[20]  R. Gallager.  Power Limited Channels: Coding, Multiaccess, and Spread Spectrum , 2002 .

[21]  A. El Gamal,et al.  Minimum energy communication over a relay channel , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[22]  P. Gupta,et al.  Towards an information theory of large networks: an achievable rate region , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[23]  Yingbin Liang,et al.  Gaussian orthogonal relay channels: optimal resource allocation and capacity , 2005, IEEE Transactions on Information Theory.

[24]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[25]  E. Meulen,et al.  Three-terminal communication channels , 1971, Advances in Applied Probability.

[26]  Teresa H. Meng,et al.  Minimum energy mobile wireless networks , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).