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This article continues the recent investigation of combinatorial joint source-channel coding. For the special case of a binary source and channel subject to distortion measured by Hamming distance, the lower (converse) bounds on achievable source distortion are improved for all values of channel noise. Operational duality between coding with bandwidth expansion factors ρ and 1 over ρ is established...
When transmitting information over a noisy channel, two approaches are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this paper we analyze a middle road, which we call a semiconstrained system. In...
This paper abstracts the unified problem of drug discovery and pathogen identification as an inhibitor-defective classification problem and learning of “association pattern” between the inhibitors and defectives. We refer to the “association graph” between the inhibitors and defectives as the Immune-Defectives Graph (IDG). Here, the expression of a defective might be inhibited by a subset of the inhibitors...
This paper offers a characterization of performance limits for classification and reconstruction of high-dimensional signals from noisy compressive measurements, in the presence of side information. We assume the signal of interest and the side information signal are drawn from a correlated mixture of distributions/components, where each component associated with a specific class label follows a Gaussian...
Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of...
Consider the problem of packing Hamming balls of a given relative radius subject to the constraint that they cover any point of the ambient Hamming space with multiplicity at most L. For odd L ≥ 3 an asymptotic upper bound on the rate of any such packing is proven. The resulting bound improves the best known bound (due to Blinovsky'1986) for rates below a certain threshold. The method is a superposition...
In this paper, we deal with the fixed-length lossy compression with the ϵ-fidelity criterion which is a kind of the distortion criterion such that the probability of exceeding a given distortion level is less than a given probability level. We give an achievability bound and a converse bound of the minimum number of codewords with this criterion. We show that our converse bound is tighter than that...
To formulate rewriting operations on flash memory, we extend Write-Once Memory (WOM) and introduce Erasable WOM (EWOM) which allows block erasures, and then we define codes to rewrite on them. To measure performances of EWOM codes, we introduce the rate tradeoff pair, which is derived from the sum rate. We give an outer bound of the region of the possible tradeoff pairs for a certain class of EWOM's...
A code design problem for memory devices with restricted state transitions is formulated as a combinatorial optimization problem that is called a subgraph domatic partition (subDP) problem. If any neighbor set of a given state transition graph contains all the colors, then the coloring is said to be valid. The goal of a subDP problem is to find the valid coloring that has the largest number of colors...
In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related. In this introductory work, the elements within the symmetric difference are related through the Hamming distance metric. Upper and lower bounds are derived on the minimum amount of information...
Nonergodic fading is a useful model for various wireless communication channels in both indoor and outdoor environments. With this model, a codeword is divided into multiple blocks such that fading is constant within a block and independent across blocks. Building on Poltyrev's work on infinite lattice constellations for the Gaussian channel, we derive a Poltyrev outage limit for lattice constellations...
The asynchronous-communication model is studied by means of i.i.d. codes and ML decoding. A random-coding bound to the joint probability of decoding and synchronization error is determined and used to recover the region of achievable information rates and asynchrony exponents.
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate R ∈ [0, 1]. An efficient interpolation-based decoding algorithm for this code construction is given which allows to correct insertions and deletions up to the normalized radius s (1 − ((1/h + h)/(h − s + 1))R), where h...
The problem of mismatched decoding with an additive metric q for a discrete memoryelss channel W is addressed. Two max-min multi-letter upper bounds on the mismatch capacity Cq(W) are derived. We further prove that if the average probability of error of a sequence of codebooks converges to zero sufficiently fast, then the rate of the code-sequence is upper bounded by the “product-space” improvement...
We construct the first class of permutation codes that are capable of correcting a burst of up to s unstable deletions, for general s. Efficient decoding algorithms are presented to show the correctness of our constructions.
Consider transmission of a polar code of block length N and rate R over a binary memoryless symmetric channel W with capacity I(W) and Bhattacharyya parameter Z(W) and let Pe be the error probability under successive cancellation decoding. Recall that in the error exponent regime, the channel W and R < I(W) are fixed, while Pe scales roughly as 2−√N. In the scaling exponent regime, the channel...
A well-known technique in assessing probabilities of rare events (used, e.g., in the sphere-packing bound), is that of finding a reference measure under which the event of interest has probability of order one and estimating the probability in question using the Kullback-Leibler divergence (KLD). A recent method has been proposed [2], that can be viewed as an extension of this idea in which the probability...
In this paper, we consider multiway relay networks with massive number of users. In this situation a fixed transmission scheduling is difficult to apply. We propose uncoordinated communications using the concept of coded slotted ALOHA (CSA), where simultaneous transmitted signals are detected using iterative demapping (IDM) algorithm to improve the success rate probability. We allow each user to transmit...
Caching is a viable solution for alleviating the severe capacity crunch in modern content centric wireless networks. Parts of popular files are pre-stored in users' cache memories such that at times of heavy demand, users can be served locally from their cache content thereby reducing the peak network load. In this work, we consider a central server assisted caching network where files are jointly...
This paper studies the fixed-error asymptotics of constant-composition codes for discrete memoryless channels. An achievable asymptotic expansion is derived with a third-order term that can be as high as 1/2 log n, while being lower when (i) a certain feasibility-decoding condition fails, or (ii) the channel is a sum channel. Converse bounds are used to provide conditions under which each of these...
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