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...es and the challenges inherent in a wireless communication network [2]. On the one hand, interference alignment schemes show remarkable potential to increase the number of available signal dimensions =-=[3]-=-. On the other hand, most interference alignment schemes assume global availability of vast amounts of channel knowledge (even if it is delayed [4, 5]), which implies excessive training and feedback o...

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...nt out that with perfect CSIT, this network has 4 DoF. This can be seen as follows. Messages a1, b1 cannot have a total of more than 2 DoF, because of the MIMO interference channel DoF outer bound of =-=[22]-=-. By symmetry, messages a2, c1 cannot have more than 2 DoF either, which limits the total DoF to 4. Achievability of 4 DoF is also easy because after removing the interference, receivers a1, c1 are le...

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...o increase the number of available signal dimensions [3]. On the other hand, most interference alignment schemes assume global availability of vast amounts of channel knowledge (even if it is delayed =-=[4, 5]-=-), which implies excessive training and feedback overheads. The extent to which these substantial overheads are essential, is the central issue that could define the role of interference alignment sch...

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...will be presented in a later section of this paper. 1.2 Background The idea of interference alignment highlights both the opportunities and the challenges inherent in a wireless communication network =-=[2]-=-. On the one hand, interference alignment schemes show remarkable potential to increase the number of available signal dimensions [3]. On the other hand, most interference alignment schemes assume glo...

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..., they have the same ability to decode messages and hence may be combined into one equivalent user without loss of generality, as shown in Fig. 1(b), producing a partially connected X network setting =-=[1]-=- with 8 independent messages, one from 2 each transmitter to each connected receiver. So, e.g., the receiver labeled ‘ab’ wants to decode two independent messages sent from transmitters labeled A,B. W...

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...., DoF with no CSIT, remain unknown in general for all those wireless networks where interference alignment is relevant in the presence of CSIT. Conventional wisdom, consistent with a few conjectures =-=[6, 7]-=-, has consistently predicted a collapse of DoF, and therefore the infeasibility of interference alignment, with no CSIT. However, except under additional assumptions of homogeneity1 such as isotropic ...

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...coding problem is itself an open problem. In fact, it is known that in its generality the index coding problem is rich enough to capture the entirety of the multiple unicast problem in network coding =-=[19]-=-, which points to the difficulty of obtaining systematic solutions for blind cellular interference alignment with arbitrary connectivities and arbitrary message sets. However, approximations, heuristi...

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...t under additional assumptions of homogeneity1 such as isotropic fading conditions, degradedness or statistical indistinguishability of receivers where indeed the collapse of DoF has been established =-=[8, 9, 10, 11]-=-, the DoF remain unknown. A case in point is the Lapidoth-Shamai-Wigger conjecture [6] on the collapse of DoF of a MISO BC (multiple input single output broadcast channel) which remains unresolved, ex...

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...., DoF with no CSIT, remain unknown in general for all those wireless networks where interference alignment is relevant in the presence of CSIT. Conventional wisdom, consistent with a few conjectures =-=[6, 7]-=-, has consistently predicted a collapse of DoF, and therefore the infeasibility of interference alignment, with no CSIT. However, except under additional assumptions of homogeneity1 such as isotropic ...

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...eless networks, with arbitrary message sets and no CSIT, and relate it to the index coding problem, which, incidentally, is the context that produced the first known example of interference alignment =-=[16, 2]-=-. We start with a description of the index coding problem. 5.1 Index Coding Problem IC(Wr,Wr) Index coding is a network coding problem that is surprisingly easy to describe but can be challenging to s...

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...o increase the number of available signal dimensions [3]. On the other hand, most interference alignment schemes assume global availability of vast amounts of channel knowledge (even if it is delayed =-=[4, 5]-=-), which implies excessive training and feedback overheads. The extent to which these substantial overheads are essential, is the central issue that could define the role of interference alignment sch...

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...e) number of states where the DoF are shown to be robust to channel uncertainty [12]. Perhaps the strongest evidence so far, of the feasibility of interference alignment with no CSIT, is presented in =-=[13, 14, 15]-=- through the idea of blind interference alignment. The central idea of blind interference alignment, introduced in [13], is that the knowledge of distinct channel coherence patterns associated with di...

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...t under additional assumptions of homogeneity1 such as isotropic fading conditions, degradedness or statistical indistinguishability of receivers where indeed the collapse of DoF has been established =-=[8, 9, 10, 11]-=-, the DoF remain unknown. A case in point is the Lapidoth-Shamai-Wigger conjecture [6] on the collapse of DoF of a MISO BC (multiple input single output broadcast channel) which remains unresolved, ex...

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...of interference alignment even with channel uncertainty. A notable example is the compound setting with arbitrary (finite) number of states where the DoF are shown to be robust to channel uncertainty =-=[12]-=-. Perhaps the strongest evidence so far, of the feasibility of interference alignment with no CSIT, is presented in [13, 14, 15] through the idea of blind interference alignment. The central idea of b...

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...erence alignment with arbitrary connectivities and arbitrary message sets. However, approximations, heuristic approaches and even optimal solutions for special cases, e.g., symmetric network settings =-=[20, 21]-=- or small networks, are often readily available, tractable, even quite simple as they are mostly just linear beamforming solutions. Consider for example, our aligned frequency-reuse solutions, which c...

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...the much more general “network equivalence” result of Koetter et al. [17]. Interestingly, in the network coding formulation over finite fields, it is known that linear coding is not always sufficient =-=[18]-=-. While it seems that the equivalence of the two networks might imply a similar insufficiency result for the Gaussian index coding problem, to the best of our knowledge, such a result has not been for...

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...the capacity of the Gaussian link in the Gaussian index coding problem. The equivalence is readily seen as a direct consequence of the much more general “network equivalence” result of Koetter et al. =-=[17]-=-. Interestingly, in the network coding formulation over finite fields, it is known that linear coding is not always sufficient [18]. While it seems that the equivalence of the two networks might imply...

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...erence alignment with arbitrary connectivities and arbitrary message sets. However, approximations, heuristic approaches and even optimal solutions for special cases, e.g., symmetric network settings =-=[20, 21]-=- or small networks, are often readily available, tractable, even quite simple as they are mostly just linear beamforming solutions. Consider for example, our aligned frequency-reuse solutions, which c...

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...t under additional assumptions of homogeneity1 such as isotropic fading conditions, degradedness or statistical indistinguishability of receivers where indeed the collapse of DoF has been established =-=[8, 9, 10, 11]-=-, the DoF remain unknown. A case in point is the Lapidoth-Shamai-Wigger conjecture [6] on the collapse of DoF of a MISO BC (multiple input single output broadcast channel) which remains unresolved, ex...

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...e) number of states where the DoF are shown to be robust to channel uncertainty [12]. Perhaps the strongest evidence so far, of the feasibility of interference alignment with no CSIT, is presented in =-=[13, 14, 15]-=- through the idea of blind interference alignment. The central idea of blind interference alignment, introduced in [13], is that the knowledge of distinct channel coherence patterns associated with di...