Capacity theorems for relay channels with ISI

In this paper we initially study degraded relay channels with finite-length intersymbol interference (ISI). For such channels, we show that the decode-and-forward strategy achieves the capacity, and prove a special structure for the capacity achieving distributions of the source and relay signals. We also prove that a general memoryless relay channel used with delayed feedback from the destination node to the relay node is an instance of a degraded relay channel with ISI, and observe that the delayed feedback from the destination node to the relay node does not decrease the capacity compared to instantaneous feedback. In all cases where the channel is used with delayed feedback from the destination node to the relay node the decode-and-forward scheme is optimal and the capacity is not decreased by delaying the feedback from the destination node. We extend these results to general (non-degraded) relay channels with ISI to obtain upper and lower bounds on their capacities.

[1]  Edward C. van der Meulen,et al.  A survey of multi-way channels in information theory: 1961-1976 , 1977, IEEE Trans. Inf. Theory.

[2]  Javier Valls-Coquillat,et al.  64-QAM 4×4 MIMO decoders based on Successive Projection Algorithm , 2008, 2008 15th IEEE International Conference on Electronics, Circuits and Systems.

[3]  Illtyd Trethowan.  Causality , 1938 .

[4]  J. Massey.  CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

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

[6]  R. A. McDonald,et al.  Noiseless Coding of Correlated Information Sources , 1973 .

[7]  Sekhar Tatikonda,et al.  Feedback capacity of finite-state machine channels , 2005, IEEE Transactions on Information Theory.

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

[9]  Sekhar Tatikonda,et al.  On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory , 2007, IEEE Transactions on Information Theory.

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

[11]  James L. Massey,et al.  Conservation of mutual and directed information , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[12]  Xiao Ma,et al.  Binary intersymbol interference channels: Gallager codes, density evolution, and code performance bounds , 2003, IEEE Transactions on Information Theory.

[13]  Gerhard Kramer,et al.  Directed information for channels with feedback , 1998 .

[14]  R. Gray.  Entropy and Information Theory , 1990, Springer New York.

[15]  H. Marko,et al.  The Bidirectional Communication Theory - A Generalization of Information Theory , 1973, IEEE Transactions on Communications.