Bounds on the Capacity of the Relay Channel with Noncausal State Information at Source

We consider a three-terminal state-dependent relay channel with the channel state available non-causally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and non-cognitive radios. We study the capacity of this communication model. One principal problem in this setup is caused by the relay's not knowing the channel state. In the discrete memoryless (DM) case, we establish lower bounds on channel capacity. For the Gaussian case, we derive lower and upper bounds on the channel capacity. The upper bound is strictly better than the cut-set upper bound. We show that one of the developed lower bounds comes close to the upper bound, asymptotically, for certain ranges of rates.Comment: 5 pages, submitted to 2010 IEEE International Symposium on Information Theor

Extended windmill polynomials

We present a generalization of a class of characteristic polynomials used for linear feedback shift registers (LFSRs). In previous works, several restrictions have been demonstrated for the windmill polynomials. Most notably, no irreducible windmill polynomial was found for a degree d = 3 mod 8. We show how to modify the original definition to overcome those restrictions. We also assess the security of our extended windmill generator considering the case of a filtered LFSR. This paper concerns LFSRs but it can be extended to any kind of shift registers including feedback with carry shift registers (FCSRs) and non-linear feedback shift registers (NLFSRs). We also establish the number of extended windmill polynomials for v = 4,8,16,32 and 64 vanes up to the degree 160