The study of feedback has been mostly limited to single-hop communication settings. In this paper, we consider Gaussian networks where sources and destinations can communicate with the help of intermediate relays over multiple hops. We assume that links in the network can be bidirected providing opportunities for feedback. We ask the following question: can the information transfer in both directions of a link be critical to maximizing the end-to-end communication rates in the network? Equivalently, could one of the directions in each bidirected link (and more generally at least one of the links forming a cycle) be shut down and the capacity of the network still be approximately maintained? We show that in any arbitrary Gaussian network with bidirected edges and cycles and unicast traffic, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. For Gaussian networks with multiple-access and broadcast traffic, an acyclic subnetwork is sufficient to achieve every rate point in the capacity region of the original network, however, there may not be a single acyclic subnetwork that maintains the whole capacity region. For networks with multicast and multiple unicast traffic, on the other hand, bidirected information flow across certain links can be critically needed to maximize the end-to-end capacity region. These results can be regarded as generalizations of the conclusions regarding the usefulness of feedback in various single-hop Gaussian settings and can provide opportunities for simplifying operation in Gaussian multihop networks.

We consider the$N$-relay Gaussian diamond network where a source node communicates to a destination node via$N$parallel relays through a cascade of a Gaussian broadcast (BC) and a multiple access (MAC) channel. Introduced in 2000 by Schein and Gallager, the capacity of this relay network is unknown in general. The best currently available capacity approximation, independent of the coefficients and the SNRs of the constituent channels, is within an additive gap of$1.3 N$bits, which follows from the recent capacity approximations for general Gaussian relay networks with arbitrary topology. In this paper, we approximate the capacity of this network within 2 log$N$bits. We show that two strategies can be used to achieve the information-theoretic cut-set upper bound on the capacity of the network up to an additive gap of$O(\log N)$bits, independent of the channel configurations and the SNRs. The first of these strategies is simple partial decode-and-forward. Here, the source node uses a superposition codebook to broadcast independent messages to the relays at appropriately chosen rates; each relay decodes its intended message and then forwards it to the destination over the MAC channel. A similar performance can be also achieved with compress-and-forward type strategies (such as quantize-map-and-forward and noisy network coding) that provide the$1.3 N$-bit approximation for general Gaussian networks, but only if the relays quantize their observed signals at a resolution inversely proportional to the number of relay nodes$N$. This suggests that the rule-of-thumb to quantize the received signals at the noise level in the current literature can be highly suboptimal.

We consider wireless relay networks where a source node communicates to a destination node with the help of multiple intermediate relay nodes. In wireless, if a node can send information to another node, typically it can also receive information from that node. Therefore, inherently there are many possibilities for feeding back information in wireless networks. However, transmissions are not isolated but usually subject to broadcast and interference. In this paper, we ask the following question: Can the information transfer in both directions of a link be critical to maximizing the end-to-end communication rate in such networks? Equivalently, could one of the directions in each bidirected link (and more generally at least one of the links forming a cycle) be shut down and the capacity of the network still be approximately maintained? Our main result is to show that in any arbitrary Gaussian relay network with bidirected edges and cycles, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. The edges of this subnetwork can be identified as the information carrying links, and the remaining links as feedback, which can only provide limited contribution to capacity.

We consider the N-relay Gaussian diamond network where a source node communicates to a destination node via N parallel relays. We show that several strategies can achieve the capacity of this network within O(log N) bits independent of the channel configurations and the operating SNR. The first of these strategies is partial decode-and-forward: the source node broadcasts independent messages to the relays at appropriately chosen rates, which in turn decode and forward these messages to the destination over a MAC channel. The same performance can be also achieved by compress-and-forward, quantize-map-and-forward or noisy network coding if relays quantize their observations at a decreasing resolution with N, instead of quantizing at the noise-level. The best capacity approximations currently available for this network are within O(N) bits which follow from the corresponding capacity approximations for general Gaussian relay networks.

DNA sequencing technology has advanced to a point where storage is becoming the central bottleneck in the acquisition and mining of more data. Large amounts of data are vital for genomics research, and generic compression tools, while viable, cannot offer the same savings as approaches tuned to inherent biological properties. We propose an algorithm to compress a target genome given a known reference genome. The proposed algorithm first generates a mapping from the reference to the target genome, and then compresses this mapping with an entropy coder. As an illustration of the performance: applying our algorithm to James Watson's genome with hg18 as a reference, we are able to reduce the 2991 megabyte (MB) genome down to 6.99 MB, while Gzip compresses it to 834.8 MB.

Wavelet-based spatial quantization is a technique to compress image data that adapts the compression to the data in each region of an image. This approach is motivated because quantization with a single step-size does not result in a uniform visual effect across each spatial location; different types of image content mask quantization errors in different ways. While many spatial quantization techniques determine step-sizes via local activity measures, the proposed method induces local quantization distortion based on experiments that quantify human detection of this distortion as function of both the contrast and the type of the image data. Three types in particular, textures, structures and edges, are considered. A classifier is utilized to detect to which of these three categories a local region of image data belongs, and step-sizes are then derived based on the contrast and class of each region. Class and contrast data are conveyed to the coder with explicit side information. For images compressed at threshold, the proposed method requires 3-10 % less rate than a similar previous approach without classification, and on average produces images that are preferred by 2/3 of tested viewers.