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The failures of iterative decoders for low-density parity-check (LDPC) codes on the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC) can be understood in terms of combinatorial objects known as trapping sets. In this paper, we derive a systematic method to identify the most relevant trapping sets for decoding over the BSC in the error floor region. We elaborate...
This is a tale of two linear programming decoders, namely channel coding linear programming decoding (CC-LPD) and compressed sensing linear programming decoding (CS-LPD). So far, they have evolved quite independently. The aim of the present paper is to show that there is a tight connection between, on the one hand, CS-LPD based on a zero-one measurement matrix over the reals and, on the other hand,...
We consider the compound capacity of polar codes under successive cancellation decoding for a collection of binary-input memoryless output-symmetric channels. By deriving a sequence of upper and lower bounds, we show that in general the compound capacity under successive decoding is strictly smaller than the unrestricted compound capacity.
Multilevel Reed-Solomon (RS) codes are powerful types of generalized concatenated codes which can improve the error-correcting capability of RS codes without resorting to large finite fields. The redundancy has to be non-uniformly distributed over the rows in order to maximize the minimum distance of multilevel RS codes. So the straightforward columnwise interleaving is not the efficient way of interleaving...
Detection of defective members of large populations has been widely studied in the statistics community under the name ??group testing??, a problem which dates back to World War II when it was suggested for syphilis screening. There, the main interest is to identify a small number of infected people among a large population using collective samples. In viral epidemics, one way to acquire collective...
We propose a new algorithm, called sequential sparse matching pursuit (SSMP), for solving sparse recovery problems. The algorithm provably recovers a k-sparse approximation to an arbitrary n-dimensional signal vector x from only O(k log(n/k)) linear measurements of x. The recovery process takes time that is only near-linear in n. Preliminary experiments indicate that the algorithm works well on synthetic...
Compressive sensing (CS) has developed as an enticing alternative to the traditional process of signal acquisition. For a length-N signal with sparsity K, merely M = O(K log N) ?? N random linear projections (measurements) can be used for robust reconstruction in polynomial time. Sparsity is a powerful and simple signal model; yet, richer models that impose additional structure on the sparse nonzeros...
Compressed sensing deals with the reconstruction of a high-dimensional signal from far fewer linear measurements, where the signal is known to admit a sparse representation in a certain linear space. The asymptotic scaling of the number of measurements needed for reconstruction as the dimension of the signal increases has been studied extensively. This work takes a fundamental perspective on the problem...
The problem of sparse signal recovery from a relatively small number of noisy measurements has been studied extensively in the recent literature on compressed sensing. However, the focus of those studies appears to be limited to the case of linear projections disturbed by Gaussian noise, and the sparse signal reconstruction problem is treated as linear regression with l1-norm regularization constraint...
We study the capacity of a class of deterministic discrete memoryless interference channels. Recent studies show that, in general, interference alignment is required to achieve capacity in interference channels. While interference alignment in general needs structured coding, we identify two scenarios where random coding achieves capacity and leads to single-letter capacity characterizations in deterministic...
This paper presents an achievable rate region for a 2-user Gaussian Z-interference channel with a noiseless and bidirectional digital communication link between the receivers. The region is achieved by utilizing the rate-splitting encoding technique, and the decode-and-forward and compress-and-forward strategies. In the very strong interference regime, the capacity region is achieved. In the weak...
Sufficient conditions required to achieve the interference-free capacity region of ergodic fading K-user interference channels (IFCs) are obtained. In particular, this capacity region is shown to be achieved when every receiver decodes all K transmitted messages such that the channel statistics and the water-filling power policies for all K (interference-free) links satisfy a set of K(K - 1) ergodic...
This paper develops a new achievable region for the K-user symmetric interference channel using algebraic interference alignment. Our scheme uses lattice codebooks to transform the interference channel into an equivalent noiseless discrete-alphabet additive interference channel. Subsequently, algebraic alignment schemes are used to characterize the achievable rates for this channel.
Cognitive radio methodologies have the potential to dramatically increase the throughput of wireless systems. Herein, control strategies which enable the superposition in time and frequency of primary and secondary user transmissions are explored in contrast to more traditional sensing approaches which only allow the secondary user to transmit when the primary user is idle. In this work, the optimal...
Hundreds of papers over the last two decades have studied the theory of distributed scheduling in wireless networks, including a number of them on stability or utility maximizing random access. Several publications in 2008 studied an adaptive CSMA that in theory can approach utility optimality without any message passing under a number of assumptions. This paper reports the results from the first...
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