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Degrees of freedom of twohop wireless networks: Everyone gets the entire cake
 IEEE Trans. Inf. Theory
, 2014
"... Abstract—We show that fully connected twohop wireless networks with K sources, K relays and K destinations have K degrees of freedom for almost all values of constant channel coefficients. Our main contribution is a new interferencealignmentbased achievability scheme which we call aligned network ..."
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Abstract—We show that fully connected twohop wireless networks with K sources, K relays and K destinations have K degrees of freedom for almost all values of constant channel coefficients. Our main contribution is a new interferencealignmentbased achievability scheme which we call aligned network diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. I.
On the Optimality of Treating Interference as Noise: General Message Sets
"... Abstract — In a Kuser Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating int ..."
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Abstract — In a Kuser Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we show that for such TINoptimal interference channels, even if the message set is expanded to include an independent message from each transmitter to each receiver, operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap. Furthermore, we extend the result to the sumGDoF optimality of TIN in the general setting of X channels with arbitrary numbers of transmitters and receivers. Index Terms — Gaussian networks, generalized degrees of freedom (GDoF), sum capacity, treating interference as noise (TIN), X channels. I.
Settling conjectures on the collapse of degrees of freedom under finite precision csit
 in Proceedings of Globecom
, 2014
"... states that the degrees of freedom (DoF) of a two user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under finite precision channel state information at the transmitter (CSIT). That this conjecture, which predates interfe ..."
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states that the degrees of freedom (DoF) of a two user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under finite precision channel state information at the transmitter (CSIT). That this conjecture, which predates interference alignment, has remained unresolved, is emblematic of a pervasive lack of understanding of the degrees of freedom of wireless networks— including interference and X networks—under channel uncertainty at the transmitter(s). In this work we prove that the conjecture is true in all nondegenerate settings (e.g., where the probability density function of unknown channel coefficients exists and is bounded). The DoF collapse even when perfect channel knowledge for one user is available to the transmitter. This also settles a related recent conjecture by Tandon et al. Reminiscent of Korner and Marton’s work on the images of a set, the key to our proof is a bound on the number of codewords that can cast the same image (within noise distortion) at the undesired receiver, while remaining resolvable at the desired receiver. We are also able to generalize the result to arbitrary number of users, including the K user interference channel. Remarkably, for the K user interference channel, this work and the earlier work by Cadambe and Jafar reveal two contrasting sides of the same coin. Both works close a gap between the best previously known DoF inner bound of 1 and the best previously known DoF outer bound of K/2. However, while Cadambe and Jafar do so in the optimistic direction, showing that K/2 is optimal under perfect CSIT, here we close the gap in the pessimistic direction, showing that 1 DoF is optimal under finite precision CSIT. I.
1WorstCase Additive Noise in Wireless Networks
"... A classical result in Information Theory states that the Gaussian noise is the worstcase additive noise in pointtopoint channels, meaning that, for a fixed noise variance, the Gaussian noise minimizes the capacity of an additive noise channel. In this paper, we significantly generalize this resul ..."
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A classical result in Information Theory states that the Gaussian noise is the worstcase additive noise in pointtopoint channels, meaning that, for a fixed noise variance, the Gaussian noise minimizes the capacity of an additive noise channel. In this paper, we significantly generalize this result and show that the Gaussian noise is also the worstcase additive noise in wireless networks with additive noises that are independent from the transmit signals. More specifically, we show that, if we fix the noise variance at each node, then the capacity region with Gaussian noises is a subset of the capacity region with any other set of noise distributions. We prove this result by showing that a coding scheme that achieves a given set of rates on a network with Gaussian additive noises can be used to construct a coding scheme that achieves the same set of rates on a network that has the same topology and traffic demands, but with nonGaussian additive noises. I.