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This paper uses extrinsic-information-transfer (EXIT)-function analysis employing the reciprocal channel approximation (RCA) to obtain optimal LDPC code degree distributions for initial hard decoding (one-bit quantization of the channel output) and for decoding with the soft information provided by additional reads in both SLC (two-level cell) and MLC (four-level-cell) Flash memory. These results...
Non-binary low-density parity-check (LDPC) codes are linear block codes defined by the sparse parity-check matrix over finite fields. The weight distribution is a significant factor to evaluate error floors of LDPC codes. In this paper, we propose a probabilistic method for estimating the low part of the weight distribution of non-binary LDPC codes. Using the proposed method, we can estimate the low...
The Extended Min-Sum (EMS) algorithm for non-binary low-density parity-check (LDPC) defined over an alphabet of size q operates on truncated messages of length q′ to achieve a complexity of the order q′2. In contrast, Walsh-Hadamard (WH) transform based iterative decoders achieve a complexity of the order q log q, which is much larger for q′ ≪ q. In this paper, we demonstrate that considerable savings...
A trellis code constructed by concatenating a delay processor and a signal mapper to a convolutional code with a short constraint length can be regarded as a convolutional code with a large constraint length. We can obtain a close upper bound and a close lower bound for such a code. In this paper, we use this code structure to construct low-density parity check convolutional codes which are 4-cycles...
Entanglement-assisted quantum error-correcting (EAQEC) codes, a wider class of stabilizer codes, allow us to construct quantum error-correcting codes from arbitrary classical codes with the help of ebits, i.e. maximally entangled quantum states. However, in the construction of EAQEC codes, it is desirable to use as small number of ebits as possible because of the high cost in the preparation of those...
Recently a variety of lattices called low density lattices codes (LDLC) have been studied because they can be decoded efficiently using belief propagation, and can be seen as a Euclidean space codes analogue to low density parity check codes (LDPC). Previous LDLC lattice designs, like Latin square, are based on high-complexity computer search to eliminate 4-cycles. Array codes have been used to construct...
Raptor codes are the first class of fountain codes with linear time encoding and decoding. These codes are recommended in standards such as Third Generation Partnership Project (3GPP) and digital video broadcasting. RaptorQ codes are an extension to Raptor codes, having better coding efficiency and flexibility. Standard Raptor and RaptorQ codes are systematic with equal error protection of the data...
In this paper, generalized pseudo-cyclic (GPC) codes are proposed and their basic properties are investigated. Generator polynomial matrices of GPC codes are constructively defined and thereby a dimension formula for GPC codes is provided. While a pseudo-cyclic code is equal to an ideal of the ring which consists of polynomials modulo a fixed polynomial, a GPC code is equal to a submodule of the direct...
Mobile devices have multiple network interfaces, some of which have security weaknesses, yet are used for sensitive data despite the risk of eavesdropping. We describe a data-splitting approach which, by design, maps exactly to a wiretap channel, thereby offering information theoretic security. Being based on the deletion channel, it perfectly hides block boundaries from the eavesdropper, which enhances...
In this work we investigate codes in Zn2m that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter t. We will show upper bounds on these cross codes, derive constructions for linear codes and respective decoding algorithm. The constructions (and decoding algorithms) are given for length n = 2 and n = 3, but for general m and t.
In this paper, we propose a graph-based construction method for distributed data storage codes design. Relations among storage cost, repair cost and repair outage (probability where repair fails) are obtained in terms of the structural properties of the underlying graph. As a result, our approach can simplify the code design problem. Tradeoffs among different system parameters are also obtained.
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