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An improved upper bound on the redundancy of the optimal reversible variable length code (RVLC), is presented in terms of the largest symbol probability p1. The improvement is achieved for 2/9 < p1 < 1/4 and for 2/5 ≤ p1 ≤ 1/2. The bound guarantees that in these two regions, the redundancy of the optimal RVLC is less than 1 bit per symbol.
Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions the cake based on some...
We show that two essentially conditional linear inequalities for Shannon's entropies (including the Zhang-Yeung'97 conditional inequality) do not hold for asymptotically entropic points. This means that these inequalities are non-robust in a very strong sense. This result raises the question of the meaning of these inequalities and the validity of their use in practice-oriented applications.
In this paper, we introduce a 1-bit compressive sensing reconstruction algorithm that is not only robust against bit flips in the binary measurement vector, but also does not require a priori knowledge of the sparsity level of the signal to be reconstructed. Through numerical experiments, we show that our algorithm outperforms state-of-the-art reconstruction algorithms for the 1-bit compressive sensing...
The sparse representation problem of recovering an N dimensional sparse vector x from M < N linear observations y = Dx given dictionary D is considered. The standard approach is to let the elements of the dictionary be independent and identically distributed (IID) zero-mean Gaussian and minimize the l1-norm of x under the constraint y = Dx. In this paper, the performance of l1-reconstruction...
It is shown that the proposed lower bound by the authors in 2010 is greater than or equal to the BCH bound for any cyclic codes. Discussion of relationship between the proposed bound and the Hartmann-Zeng bound is also given. For these discussions three improved algorithms from the authors' algorithm are described.
We study the problem of multiple hypothesis testing (HT) in view of a rejection option. That model of HT has many different applications. Errors in testing of M hypotheses regarding the source distribution with an option of rejecting all those hypotheses are considered. The source is discrete and arbitrarily varying (AVS). The tradeoffs among error probability exponents/reliabilities associated with...
The recently introduced network equivalence results are used to create bit-pipe models that can replace multi-terminal channels within a discrete memoryless network. The goal is to create a set of simple “components” or “blocks” that can be substituted for the channel in such a way that the resulting network is capable of emulating the operation of the original one. We develop general upper and lower...
In a distributed storage system, codes for efficient repair of failed nodes has attracted significant recent research attention. Ideas from network coding and interference alignment have been used successfully to show bounds and construct coding schemes for efficient repair. In this article, we use ideas from classical algebraic codes to interpret the requirements of efficient repair as existence...
A new technique of designing spectral null codes with permutation sequences is presented. These new codes have nulls at sub-multiples of the frequency of the transmitted symbols and are also DC-free codes. The choice of the corresponding channel levels given to each transmitted symbols has guaranteed the elimination of the DC component at the lower frequencies and gave an advantage on the binary spectral...
In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from...
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