Abstract-We consider two-source two-destination (i.e., twounicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous distributions, then, with probability 1, two-unicast layered Gaussian networks can only have 1, 3/2 or 2 sum degrees-of-freedom (unless both source-destination pairs are disconnected, in which case no degrees-of-freedom can be achieved). We provide sufficient and necessary conditions for each case based on network connectivity and a new notion of source-destination paths with manageable interference. Our achievability scheme is based on forwarding the received signals at all nodes, except for a small fraction of them in at most two key layers. Hence, we effectively create a "condensed network" that has at most four layers (including the sources layer and the destinations layer). We design the transmission strategies based on the structure of this condensed network. The converse results are obtained by developing informationtheoretic inequalities that capture the structures of the network connectivity. Finally, we extend this result and characterize the full degrees-of-freedom region of two-unicast layered wireless networks.

We show that fully connected two-hop wireless networks with K sources, K relays and K destinations have K degrees of freedom both in the case of time-varying channel coefficients and in the case of constant channel coefficients (in which case the result holds for almost all values of constant channel coefficients). Our main contribution is a new 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. In addition, we extend our scheme to multi-hop networks with fully connected hops, and multi-hop networks with MIMO nodes, for which the degrees of freedom are also fully characterized.

Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based storage systems under a simple model, motivated by current technological constraints on DNA synthesis and sequencing. Our model captures two key distinctive aspects of DNA storage systems: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the data is read by randomly sampling from this DNA pool. Under this model, we characterize the storage capacity, and show that a simple index-based coding scheme is optimal. * Authors contributed equally and are listed alphabetically.

Long-read sequencing technologies have the potential to produce gold-standard de novo genome assemblies, but fully exploiting error-prone reads to resolve repeats remains a challenge. Aggressive approaches to repeat resolution often produce misassemblies, and conservative approaches lead to unnecessary fragmentation. We present HINGE, an assembler that seeks to achieve optimal repeat resolution by distinguishing repeats that can be resolved given the data from those that cannot. This is accomplished by adding "hinges" to reads for constructing an overlap graph where only unresolvable repeats are merged. As a result, HINGE combines the error resilience of overlap-based assemblers with repeat-resolution capabilities of de Bruijn graph assemblers. HINGE was evaluated on the long-read bacterial data sets from the NCTC project. HINGE produces more finished assemblies than Miniasm and the manual pipeline of NCTC based on the HGAP assembler and Circlator. HINGE also allows us to identify 40 data sets where unresolvable repeats prevent the reliable construction of a unique finished assembly. In these cases, HINGE outputs a visually interpretable assembly graph that encodes all possible finished assemblies consistent with the reads, while other approaches such as the NCTC pipeline and FALCON either fragment the assembly or resolve the ambiguity arbitrarily.