Capacity Theorems for Discrete, Finite-State Broadcast Channels With Feedback and Unidirectional Receiver Cooperation

In this paper, we consider the discrete, time-varying broadcast channel (BC) with memory under the assumption that the channel states belong to a set of finite cardinality. We study the achievable rates in several scenarios of feedback and full unidirectional receiver cooperation. In particular, we focus on two scenarios: the first scenario is the general finite-state broadcast channel (FSBC) where both receivers send feedback to the transmitter while one receiver also sends its channel output to the second receiver. The second scenario is the degraded FSBC where only the strong receiver sends feedback to the transmitter. Using a superposition codebook construction, we derive the capacity regions for both scenarios. Combining elements from these two basic results, we obtain the capacity regions for a number of additional broadcast scenarios with feedback and unidirectional receiver cooperation.

[1]  Brendan J. Frey,et al.  Interactive Decoding of a Broadcast Message , 2003 .

[2]  Yossef Steinberg,et al.  Coding for the degraded broadcast channel with random parameters, with causal and noncausal side information , 2005, IEEE Transactions on Information Theory.

[3]  Yingbin Liang,et al.  Rate Regions for Relay Broadcast Channels , 2006, IEEE Transactions on Information Theory.

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

[5]  Hans-Andrea Loeliger,et al.  A Generalization of the Blahut–Arimoto Algorithm to Finite-State Channels , 2008, IEEE Transactions on Information Theory.

[6]  Haim H. Permuter,et al.  Capacity of the Trapdoor Channel With Feedback , 2006, IEEE Transactions on Information Theory.

[7]  Haim H. Permuter,et al.  Capacity Region of the Finite-State Multiple-Access Channel With and Without Feedback , 2007, IEEE Transactions on Information Theory.

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

[9]  A.J. Paulraj,et al.  Space-time processing for wireless communications , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Gerhard Kramer.  Capacity results for the discrete memoryless network , 2003, IEEE Trans. Inf. Theory.

[11]  Masoud Salehi,et al.  Multiple access channels with arbitrarily correlated sources , 1980, IEEE Trans. Inf. Theory.

[12]  Shlomo Shamai,et al.  Achievable rates for the broadcast channel with states known at the transmitter , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[13]  Paul H. Siegel,et al.  On the achievable information rates of finite state ISI channels , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

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

[15]  Aviv Rosenzweig,et al.  The Capacity of Gaussian Multi-User Channels With State and Feedback , 2007, IEEE Transactions on Information Theory.

[16]  Ron Dabora,et al.  On the Role of Estimate-and-Forward With Time Sharing in Cooperative Communication , 2006, IEEE Transactions on Information Theory.

[17]  Andrea J. Goldsmith,et al.  Finite State Channels With Time-Invariant Deterministic Feedback , 2006, IEEE Transactions on Information Theory.

[18]  John M. Cioffi,et al.  Spatio-temporal coding for wireless communication , 1998, IEEE Trans. Commun..

[19]  Emre Telatar,et al.  The Compound Channel Capacity of a Class of Finite-State Channels , 1998, IEEE Trans. Inf. Theory.

[20]  Robert G. Gallager,et al.  Capacity and coding for degraded broadcast channels , 1974 .

[21]  Andrea J. Goldsmith,et al.  The capacity region of the degraded finite-state broadcast channel , 2008, 2008 IEEE Information Theory Workshop.

[22]  Rudolf Ahlswede,et al.  Source coding with side information and a converse for degraded broadcast channels , 1975, IEEE Trans. Inf. Theory.

[23]  M. Kreĭn,et al.  On extreme points of regular convex sets , 1940 .

[24]  B. McMillan.  The Basic Theorems of Information Theory , 1953 .

[25]  Sibi Raj Bhaskaran.  Broadcasting with Feedback , 2007, 2007 IEEE International Symposium on Information Theory.

[26]  Yingbin Liang,et al.  Cooperative Relay Broadcast Channels , 2005, IEEE Transactions on Information Theory.

[27]  Lawrence H. Ozarow.  Coding and capacity for additive white Gaussian noise multi-user channels with feedback , 1979 .

[28]  Markku Renfors,et al.  DVB-T signal over cable TV network and phase noise requirements , 2001, 2001 IEEE Third Workshop on Signal Processing Advances in Wireless Communications (SPAWC'01). Workshop Proceedings (Cat. No.01EX471).

[29]  K. Weylandt,et al.  Channels , 1999, The Journal of physiology.

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

[31]  Krista S. Jacobsen,et al.  Fundamentals of DSL Technology , 2005 .

[32]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[33]  A. Sridharan.  Broadcast Channels , 2022 .

[34]  Abbas El Gamal,et al.  The feedback capacity of degraded broadcast channels (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[35]  Ron Dabora,et al.  Broadcast Channels With Cooperating Decoders , 2006, IEEE Transactions on Information Theory.

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

[37]  Andrea J. Goldsmith,et al.  Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices , 2006, IEEE Transactions on Information Theory.