Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer nonbinary low-density parity-check code or a polar code and either an inner convolutional code or a time-varying block code. We propose two novel decoding algorithms for inference from multiple received sequences, both combining the inner code and channel to a joint hidden Markov model to infer symbolwise a posteriori probabilities (APPs). The first decoder computes the exact APPs by jointly decoding the received sequences, whereas the second decoder approximates the APPs by combining the results of separately decoded received sequences. Using the proposed algorithms, we evaluate the performance of decoding multiple received sequences by means of achievable information rates and Monte-Carlo simulations. We show significant performance gains compared to a single received sequence. In addition, we succeed in improving the performance of the aforementioned coding scheme by optimizing both the inner and outer codes.
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The Benjamini-Hochberg (BH) procedure is a celebrated method for multiple testing with false discovery rate (FDR) control. In this paper, we consider large-scale distributed networks where each node possesses a large number of p-values and the goal is to achieve the global BH performance in a communication-efficient manner. We propose that every node performs a local test with an adjusted test size according to the (estimated) global proportion of true null hypotheses. With suitable assumptions, our method is asymptotically equivalent to the global BH procedure. Motivated by this, we develop an algorithm for star networks where each node only needs to transmit an estimate of the (local) proportion of nulls and the (local) number of p-values to the center node; the center node then broadcasts a parameter (computed based on the global estimate and test size) to the local nodes. In the experiment section, we utilize existing estimators of the proportion of true nulls and consider various settings to evaluate the performance and robustness of our method.
The arboricity of a graph is the minimum number of forests required to cover all its edges. In this paper, we examine arboricity from a game-theoretic perspective and investigate cost-sharing in the minimum forest cover problem. We introduce the arboricity game as a cooperative cost game defined on a graph. The players are edges, and the cost of each coalition is the arboricity of the subgraph induced by the coalition. We study properties of the core and propose an efficient algorithm for computing the nucleolus when the core is not empty. In order to compute the nucleolus in the core, we introduce the prime partition which is built on the densest subgraph lattice. The prime partition decomposes the edge set of a graph into a partially ordered set defined from minimal densest minors and their invariant precedence relation. Moreover, edges from the same partition always have the same value in a core allocation. Consequently, when the core is not empty, the prime partition significantly reduces the number of variables and constraints required in the linear programs of Maschler's scheme and allows us to compute the nucleolus in polynomial time. Besides, the prime partition provides a graph decomposition analogous to the celebrated core decomposition and the density-friendly decomposition, which may be of independent interest.
The use of a large excess of service antennas brings a variety of performance benefits to distributed MIMO C-RAN, but the corresponding high fronthaul data loads can be problematic in practical systems with limited fronthaul capacity. In this work we propose the use of lossy dimension reduction, applied locally at each remote radio head (RRH), to reduce this fronthaul traffic. We first consider the uplink, and the case where each RRH applies a linear dimension reduction filter to its multi-antenna received signal vector. It is shown that under a joint mutual information criteria, the optimal dimension reduction filters are given by a variant of the conditional Karhunen-Loeve transform, with a stationary point found using block co-ordinate ascent. These filters are then modified such that each RRH can calculate its own dimension reduction filter in a decentralised manner, using knowledge only of its own instantaneous channel and network slow fading coefficients. We then show that in TDD systems these dimension reduction filters can be re-used as part of a two-stage reduced dimension downlink precoding scheme. Analysis and numerical results demonstrate that the proposed approach can significantly reduce both uplink and downlink fronthaul traffic whilst incurring very little loss in MIMO performance.
We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. In our achievability result, we decouple the reliability and privacy constraints, which are handled via source coding with quantum side information and universal hashing, respectively. Hence, we also establish that the multi-user coding problem under consideration can be handled solely via point-to-point coding techniques. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the solution, as well as new accelerated versions, using varying stepsizes. In addition, we propose distributed variants of these algorithms, which can be accelerated as well. While most existing results are ergodic, our nonergodic results significantly broaden our understanding of primal-dual optimization algorithms.
In this paper, we investigate a cell-free massive MIMO system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink spectral efficiency (SE) based on a two-layer decoding structure with maximum ratio (MR) or local minimum mean-square error (MMSE) combining applied in the first layer and optimal large-scale fading decoding method implemented in the second layer, respectively. To maximize the weighted sum SE, an uplink precoding structure based on an Iteratively Weighted sum-MMSE (I-WMMSE) algorithm using only channel statistics is proposed. Furthermore, with MR combining applied in the first layer, we derive novel achievable SE expressions and optimal precoding structures in closed-form. Numerical results validate our proposed results and show that the I-WMMSE precoding can achieve excellent sum SE performance.
As Deep Learning continues to drive a variety of applications in edge and cloud data centers, there is a growing trend towards building large accelerators with several sub-accelerator cores/chiplets. This work looks at the problem of supporting multi-tenancy on such accelerators. In particular, we focus on the problem of mapping jobs from several DNNs simultaneously on an accelerator. Given the extremely large search space, we formulate the search as an optimization problem and develop an optimization framework called M3E. In addition, we develop a specialized optimization algorithm called MAGMA with custom operators to enable structured sample-efficient exploration. We quantitatively compare MAGMA with several state-of-the-art methods, black-box optimization, and reinforcement learning methods across different accelerator settings (large/small accelerators) and different sub-accelerator configurations (homogeneous/heterogeneous), and observe MAGMA can consistently find better mappings.
This paper studies the adversarial torn-paper channel. This problem is motivated by applications in DNA data storage where the DNA strands that carry the information may break into smaller pieces that are received out of order. Our model extends the previously researched probabilistic setting to the worst-case. We develop code constructions for any parameters of the channel for which non-vanishing asymptotic rate is possible and show our constructions achieve optimal asymptotic rate while allowing for efficient encoding and decoding. Finally, we extend our results to related settings included multi-strand storage, presence of substitution errors, or incomplete coverage.
The ability to generate natural language sequences from source code snippets has a variety of applications such as code summarization, documentation, and retrieval. Sequence-to-sequence (seq2seq) models, adopted from neural machine translation (NMT), have achieved state-of-the-art performance on these tasks by treating source code as a sequence of tokens. We present ${\rm {\scriptsize CODE2SEQ}}$: an alternative approach that leverages the syntactic structure of programming languages to better encode source code. Our model represents a code snippet as the set of compositional paths in its abstract syntax tree (AST) and uses attention to select the relevant paths while decoding. We demonstrate the effectiveness of our approach for two tasks, two programming languages, and four datasets of up to $16$M examples. Our model significantly outperforms previous models that were specifically designed for programming languages, as well as state-of-the-art NMT models. An interactive online demo of our model is available at //code2seq.org. Our code, data and trained models are available at //github.com/tech-srl/code2seq.
Seam-cutting and seam-driven techniques have been proven effective for handling imperfect image series in image stitching. Generally, seam-driven is to utilize seam-cutting to find a best seam from one or finite alignment hypotheses based on a predefined seam quality metric. However, the quality metrics in most methods are defined to measure the average performance of the pixels on the seam without considering the relevance and variance among them. This may cause that the seam with the minimal measure is not optimal (perception-inconsistent) in human perception. In this paper, we propose a novel coarse-to-fine seam estimation method which applies the evaluation in a different way. For pixels on the seam, we develop a patch-point evaluation algorithm concentrating more on the correlation and variation of them. The evaluations are then used to recalculate the difference map of the overlapping region and reestimate a stitching seam. This evaluation-reestimation procedure iterates until the current seam changes negligibly comparing with the previous seams. Experiments show that our proposed method can finally find a nearly perception-consistent seam after several iterations, which outperforms the conventional seam-cutting and other seam-driven methods.
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