Related papers: Error Rates of Capacity-Achieving Codes Are Convex
Although kernel methods are widely used in many learning problems, they have poor scalability to large datasets. To address this problem, sketching and stochastic gradient methods are the most commonly used techniques to derive efficient…
Many neural network (NN) verification systems represent the network's input-output relation as a constraint program. Sound and complete, representations involve integer constraints, for simulating the activations. Recent works convexly…
Berlekamp and Zigangirov completely determined the capacity error function for binary error correcting codes with noiseless feedback. It is still an unsolved problem if the upper bound for the capacity error function in the non-binary case…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
In this paper, we study the probabilistic caching for an $N$-tier wireless heterogeneous network (HetNet) using stochastic geometry. A general and tractable expression of the successful delivery probability (SDP) is first derived. We then…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for…
A discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. An upper bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is…
Achievable error exponents for the one-way with noisy feedback and two-way AWGN channels are derived for the transmission of a finite number of messages $M$ using fixed block length $n$, under the almost sure (AS) and the expected block…
A strong converse theorem for channel capacity establishes that the error probability in any communication scheme for a given channel necessarily tends to one if the rate of communication exceeds the channel's capacity. Establishing such a…
When data is stored, compressed, or communicated through a media such as cable or air, sources of noise and other parameters such as EMI, crosstalk, and distance can considerably affect the reliability of these data. Error detection and…
Since the work of Polyanskiy, Poor and Verd\'u on the finite blocklength performance of capacity-achieving codes for discrete memoryless channels, many papers have attempted to find further results for more practically relevant channels.…
In this paper, we investigate network nest coded modulation schemes for multiple access relay channels. The performance of the distributed systems which are based on distributed convolutional codes with network coded modulation is…
This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a non-vanishing probability of error. The output distribution induced by an…
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…
This paper proposes a novel deep learning-based error correction coding scheme for AWGN channels under the constraint of one-bit quantization in the receivers. Specifically, it is first shown that the optimum error correction code that…
Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we…