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Design of a Synthesisable ReedSolomon
"... error correction, verilog, synthesis, synthesisable, hardware, ECC, Galois field In this report we describe the design of a ReedSolomon error correction core that supports errors and erasures decoding. In a second report HPL2001125 we describe the verification of this core. The core consists of s ..."
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of separate encoder and decoder blocks that can be operated independently, each with symbol wide data paths. These blocks have sufficient throughput to handle backtoback codewords, and the overall latency is typically less than two codewords. The design is expressed in the Verilog hardware description
CollusionSecure Fingerprinting for Digital Data
 IEEE Transactions on Information Theory
, 1996
"... This paper discusses methods for assigning codewords for the purpose of fingerprinting digital data (e.g., software, documents, and images). Fingerprinting consists of uniquely marking and registering each copy of the data. This marking allows a distributor to detect any unauthorized copy and trac ..."
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Cited by 347 (1 self)
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This paper discusses methods for assigning codewords for the purpose of fingerprinting digital data (e.g., software, documents, and images). Fingerprinting consists of uniquely marking and registering each copy of the data. This marking allows a distributor to detect any unauthorized copy
On the locality of codeword symbols
 IEEE Trans. Inform. Theory
, 2012
"... Consider a linear [n, k, d]q code C. We say that that ith coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small redundancy, low locality for information coordinates, large dis ..."
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Cited by 48 (1 self)
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the bound as optimal. We prove some structure theorems about optimal codes, which are particularly strong for small distances. This gives a fairly complete picture of the tradeoffs between codewords length, worstcase distance and locality of information symbols. We then consider the locality of parity
1 On the Locality of Codeword Symbols
"... Abstract—Consider a linear [n, k, d]q code C. We say that that ith coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small redundancy, low locality for information coordinates, ..."
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to codes attaining the bound as optimal. We prove some structure theorems about optimal codes, which are particularly strong for small distances. This gives a fairly complete picture of the tradeoffs between codewords length, worstcase distance and locality of information symbols. We then consider
Codeword distinguishability in minimum diversity decoding
 JOURNAL OF DISCRETE MATHEMATICAL SCIENCES AND CRYPTOGRAPHY
, 2005
"... We retake a codingtheoretic notion which goes back to Cl. Shannon: codeword distinguishability. This notion is standard in zeroerror information theory, but its bearing is definitely wider and it may help to better understand new forms of coding, as we argue below. In our approach, the underlyin ..."
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Cited by 4 (4 self)
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We retake a codingtheoretic notion which goes back to Cl. Shannon: codeword distinguishability. This notion is standard in zeroerror information theory, but its bearing is definitely wider and it may help to better understand new forms of coding, as we argue below. In our approach
Characterizations of pseudocodewords of LDPC codes
, 2005
"... An important property of highperformance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graphbased algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient ..."
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Cited by 12 (1 self)
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An important property of highperformance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graphbased algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so called fundamental cone in Euclidean space which is a function of a given parity check matrix of a code, rather than of the code itself. We give a number of properties of this fundamental cone derived from its connection to unramified covers of the graphical models on which the decoding algorithms operate. For the class of cycle codes, these developments naturally lead to a characterization of the fundamental polytope as the Newton polytope of the Hashimoto edge zeta function of the underlying graph.
Symmetries of Codeword Stabilized Quantum Codes ∗
"... Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical errorcorrecting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general fr ..."
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Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical errorcorrecting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general
Pseudocodewords of cycle codes via zeta functions
 Journal of Pragmatics
, 2004
"... Abstract — Cycle codes are a special case of lowdensity paritycheck (LDPC) codes and as such can be decoded using an iterative messagepassing decoding algorithm on the associated Tanner graph. The existence of pseudocodewords is known to cause the decoding algorithm to fail in certain instances. ..."
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Cited by 17 (7 self)
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Abstract — Cycle codes are a special case of lowdensity paritycheck (LDPC) codes and as such can be decoded using an iterative messagepassing decoding algorithm on the associated Tanner graph. The existence of pseudocodewords is known to cause the decoding algorithm to fail in certain instances
SemiSupervised Clustering via Learnt Codeword Distances
"... This paper focuses on semisupervised clustering, where the goal is to cluster a set of datapoints given a set of similar/dissimilar examples. These examples provide instancelevel equivalence/inequivalence constraints (e.g., similar pairs belong to the same cluster while dissimilar pairs belong t ..."
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Cited by 4 (2 self)
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by the instancelevel constraints. Inspired by the success of recent bagofwords models, we utilize codewords (or visualwords) as building blocks. Our proposed technique learns nonparametric distance metrics over codewords from these equivalence (and optionally, inequivalence) constraints, which we
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