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Recently, two novel matrices whose some entries are not syndromes and other entries are known syndromes have been presented to generate weak-locator polynomials needed in decoding the ternary quadratic residue code of length 61. This paper proposes a new unknown syndrome calculation for a class of cyclic codes and a completely algebraic decoding of the (23, 11, 9) ternary quadratic residue code up...
In this paper, a novel reversible data hiding by using Reed-Solomon (RS) code is proposed for efficient transmission in encryption image. To increase the recovery of data from encrypted image, RS codes are used to encode messages, and then the code words can be embedded into encrypted image according to encryption key. After receiving embedding the code words, the receiver firstly decrypts the encrypted...
The major challenge for the development of Turbo-Code decoders for the 3GPP LTE/LTE-A standard is the support of very high code rates while achieving a high throughput with a low decoding latency. For high code rates the decoding process can oscillate, i.e. although the decoder converges to a valid code word in the nth half-iteration, the code word after the n+1th half iteration can be invalid again...
In this paper, we initiate the study of networked stabilization via a MIMO communication scheme between the controller and the plant. Specifically, the communication system is modeled as a MIMO transceiver, which consists of three parts: an encoder, a MIMO channel, and a decoder. In the spirit of MIMO communication, the number of SISO subchannels in the transceiver is often greater than the number...
Skew polynomials are elements of a noncommutative ring that, in recent years, have found applications in coding theory and cryptography. Skew polynomials have a well-defined evaluation map. This map leads to the definition of a class of codes called Generalized Skew-Evaluation codes that contains Gabidulin codes as a special case as well as other related codes with additional desirable properties...
In this work, we present a multiple server fingerprint verification scheme that provides enhanced template security by eliminating several known vulnerabilities of the fuzzy vault scheme. We secure templates from adversarial attacks in honest-but-curious server scenarios by utilizing commutative encryption in which the raw fingerprint template is never used in matching or storage. In this system,...
This paper proposes an improved Logarithmic Maximum A Posteriori (Log-MAP) algorithm for Turbo decoding in the Third Generation Partnership Project Long Term Evolution (3GPP LTE). In the proposed algorithm, we exploit the understanding of polynomial regression function to approximately compute the logarithm term (also called correction function) in the Jacobian logarithmic function. The goal is to...
The partial-inverse approach is further developed to decoding interleaved Reed-Solomon codes and subfield-evaluation codes beyond half the minimum distance. The resulting decoding algorithm is new, and its decoding capability is shown to be state-of-the-art.
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 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...
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and decoding algorithms. In this paper we consider such cyclic codes. We provide constructions of optimal cyclic codes for which their codewords do not have full length...
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...
Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proven, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to prove...
Fire codes are cyclic codes generated by the product of two polynomials: a binomial that characterizes the code's guaranteed burst correcting capability and an irreducible polynomial that characterizes the code length. However, the true burst correcting capability of a Fire code may exceed its guaranteed burst correcting capability. The true burst correcting capability of primitive Fire codes, in...
The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We show that the column sum rank parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several column distance properties and introduce a new family of convolutional codes that maximize the column...
We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kopparty. We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions. We also give a complexity estimate of the associated encoding algorithm.
In 2002, Wong-Wang-Wing presented a verifiable redistributing secret shares protocol, where the new parties must have been honest. They used Feldman's Verifiable Secret Sharing scheme, which assumed that the discrete logarithm is hard. In 2013, Nojoumian and Stinson presented information-theoretically (unconditionally) secure schemes under assumption that at most t out of 4t+1 parties are actively...
This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first propose a robust reconstruction for polynomials from erroneous residues when the degrees of all residue errors are small, namely robust Chinese Remainder Theorem (CRT) for polynomials. It basically says that a polynomial can be reconstructed from erroneous residues such that the degree of the reconstruction...
An interpolation-based list decoding algorithm for ℓ-quasi-cyclic codes over finite fields is developed and its guaranteed decoding radius for ℓ-phased burst errors is proven. It is also shown that for this error model and for certain parameter ranges, this new approach is advantageous over existing schemes.
A sum-network is a directed acyclic network in which all terminal nodes demand the ‘sum’ of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. Our main result is that unlike a multiple unicast network, the coding...
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