Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction of error patterns beyond half the minimum distance, provided that the errors in the received signal occur in bursts. In this work, collaborative decoding of interleaved Reed-Solomon codes by multi-sequence shift-register synthesis is considered and analyzed. Based on the framework of interleaved Reed-Solomon codes, concatenated code designs are investigated, which are obtained by interleaving several Reed-Solomon codes, and concatenating them with an inner block code.

In this paper, a new approach for decoding lowrate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. Unlike the Sudan algorithm published in 1997, this new approach is based on multi-sequence shiftregister synthesis, which makes it easy to understand and simple to implement. The computational complexity of this shift-register based algorithm is of the same order as the complexity of the well-known Berlekamp-Massey algorithm. Moreover, the error correcting radius coincides with the error correcting radius of the original Sudan algorithm, and the practical decoding performance observed on a q-ary symmetric channel (QSC) is virtually identical to the decoding performance of the Sudan algorithm. Bounds for the failure and error probability as well as for the QSC decoding performance of the new algorithm are derived, and the performance is illustrated by means of examples.Index Terms-Reed-Solomon codes, decoding beyond half the minimum distance, Interleaved Reed-Solomon codes, multisequence shift-register synthesis,

Different transforms used in binding a secret key to correlated physical-identifier outputs are compared. Decorrelation efficiency is the metric used to determine transforms that give highly-uncorrelated outputs. Scalar quantizers are applied to transform outputs to extract uniformly distributed bit sequences to which secret keys are bound. A set of transforms that perform well in terms of the decorrelation efficiency is applied to ring oscillator (RO) outputs to improve the uniqueness and reliability of extracted bit sequences, to reduce the hardware area and information leakage about the key and RO outputs, and to maximize the secret-key length. Low-complexity error-correction codes are proposed to illustrate two complete key-binding systems with perfect secrecy, and better secret-key and privacy-leakage rates than existing methods. A reference hardware implementation is also provided to demonstrate that the transform-coding approach occupies a small hardware area.There are multiple key-generation, or generated-secret (GS), and key-binding, or chosen-secret (CS), methods to reconstruct secret keys from noisy PUF outputs, where the key is generated from the PUF outputs or bound to them, respectively. Code-offset fuzzy extractors [9] are examples of key-generation methods and the fuzzy commitment scheme [10] is a key-binding method. Code constructions based on Wyner-Ziv (WZ) coding are illustrated in [11] to asymptotically achieve the information-theoretic limits for the GS and CS models. These constructions might have high complexity, which is undesired for, e.g., IoT applications. In addition, since a key should be stored in a secure database for both models, it is more practical to allow a trusted entity to choose the secret key bound to a PUF output. Thus, in this paper, we aim at further improving reliability, privacy, secrecy, and hardware cost performance of a transform-coding algorithm, explained next, that is applied to PUF outputs in combination with the fuzzy commitment scheme.PUFs have similar features to biometric identifiers like fingerprints. Both identifier types have correlated and noisy outputs due to surrounding environmental conditions [12]. Correlation in PUF outputs leaks information about the secret key, which causes secrecy leakage, and about the PUF output, causing privacy leakage [13][14][15]. Moreover, noise reduces reliability of PUF outputs and error-correction codes are needed to satisfy the reliability requirements. The transform-coding approach [16,17] in combination with a set of scalar quantizers has made its way into secret-key binding with continuous-output biometric and physical identifiers, as they allow reducing the output correlation and adjusting the effective noise at the PUF output. For instance, the discrete cosine transform (DCT) is the building block in [17] to generate a uniformly distributed bit sequence from RO outputs under varying environmental conditions. Efficient post-processing steps are applied to obtain more reliable PUF outputs rather than changing the har...

So far, in the area of Random Linear Network Coding, attention has been given to the so-called one-shot network coding, meaning that the network is used just once to propagate the information. In contrast, one can use the network more than once to spread redundancy over different shots. In this paper, we propose rank metric convolutional codes for this purpose. The framework we present is slightly more general than the one which can be found in the literature. We introduce a rank distance, which is suitable for convolutional codes, and derive a new Singleton-like upper bound. Codes achieving this bound are called Maximum Rank Distance (MRD) convolutional codes. Finally, we prove that this bound is optimal by showing a concrete construction of a family of MRD convolutional codes.

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For many algebraic codes the main part of decoding can be reduced to row reduction of a module basis, enabling general, flexible and highly efficient algorithms. Inspired by this, we develop an approach of transforming matrices over skew polynomial rings into certain normal forms. We apply this to solve generalised shift register problems, or Padé approximations, over skew polynomial rings which occur in error and erasure decoding -Interleaved Gabidulin codes. We obtain an algorithm with complexity O( µ 2 ) where µ measures the size of the input problem. Further, we show how to listdecode Mahdavifar-Vardy subspace codes in O( r 2 m 2 ) time, where m is a parameter proportional to the dimension of the codewords' ambient space and r is the dimension of the received subspace.