We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the probability of error of mismatched decoding. The bound is shown to decay exponentially for coding rates smaller than a new upper bound to the mismatch capacity which is established in this paper. For rates higher than the new upper bound, the error probability is shown to be bounded away from zero. The new upper bound is shown to improve over previous upper bounds to the mismatch capacity.

We derive a sphere-packing error exponent for mismatched decoding over discrete memoryless channels. We find a lower bound to the probability of error of mismatched decoding that decays exponentially for coding rates smaller than a new upper bound to the mismatch capacity. For rates higher than the new upper bound, the error probability is shown to be bounded away from zero. The new upper bound is shown to improve over previous upper bounds to the mismatch capacity.

In this paper, we propose a new method to reconstruct a signal corrupted by noise where both signal and noise are sparse but in different domains. The main contribution of our algorithm is its low complexity; it has much lower run-time than most other algorithms. The reconstruction quality of our algorithm is both objectively (in terms of PSNR and SSIM) and subjectively better or comparable to other state-of-the-art algorithms. We provide a cost function for our problem, present an iterative method to find its local minimum, and provide the analysis of the algorithm. As an application of this problem, we apply our algorithm for Salt-and-Pepper noise (SPN) and Random-Valued Impulsive Noise (RVIN) removal from images and compare our results with other notable algorithms in the literature. Furthermore, we apply our algorithm for removing clicks from audio signals. Simulation results show that our algorithms are simple and fast, and it outperforms other state-of-the-art methods in terms of reconstruction quality and/or complexity.

We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error on the translated channel implies a mismatched-decoding error in the original channel. In particular, it is shown that if the rate exceeds the upper-bound, the probability of error tends to one exponentially when the block-length tends to infinity. We also show that the underlying optimization problem is a convex-concave problem and that an efficient iterative algorithm converges to the optimal solution. In addition, we show that, unlike achievable rates in the literature, the multiletter version of the bound cannot not improve. A number of examples are discussed throughout the paper.

We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error on the translated channel implies a mismatched-decoding error in the original channel. We show this bound recovers the binary-input binary-output mismatch capacity which is known to either be the channel capacity or zero. In addition, a strong converse is shown for this upper bound: if the rate exceeds the upper-bound, the probability of error tends to 1 exponentially when the block-length tends to infinity.

We revisit the problem of solving two-player zero-sum games in the decentralized setting. We propose a simple algorithmic framework that simultaneously achieves the best rates for honest regret as well as adversarial regret, and in addition resolves the open problem of removing the logarithmic terms in convergence to the value of the game. We achieve this goal in three steps. First, we provide a novel analysis of the optimistic mirror descent (OMD), showing that it can be modified to guarantee fast convergence for both honest regret and value of the game, when the players are playing collaboratively. Second, we propose a new algorithm, dubbed as robust optimistic mirror descent (ROMD), which attains optimal adversarial regret without knowing the time horizon beforehand. Finally, we propose a simple signaling scheme, which enables us to bridge OMD and ROMD to achieve the best of both worlds. Numerical examples are presented to support our theoretical claims and show that our non-adaptive ROMD algorithm can be competitive to OMD with adaptive step-size selection.

Adaptive thresholding methods have proved to yield a high signal‐to‐noise ratio (SNR) and fast convergence in sparse signal recovery. The robustness of a class of iterative sparse recovery algorithms, such as the iterative method with adaptive thresholding, has been found to outperform the state‐of‐art methods in respect of reconstruction quality, convergence speed, and sensitivity to noise. In this study, the authors introduce a new method for compressed sensing, using the sensing matrix and measurements. In our method, they iteratively threshold the signal and project the thresholded signal onto the translated null space of the sensing matrix. The threshold level is assigned adaptively. The results of the simulations reveal that the authors’ proposed method outperforms other methods in the signal reconstruction (in terms of the SNR). This performance advantage is noticeable when the number of available measurements approaches twice the sparsity number.