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On the Weight Hierarchy of Product Codes
Designs, Codes and Cryptography, 2004In this paper the generalization of a formula concerning to product codes with more than two components is given. Especially the generalization of the Wei-Yang formula to the product codes with an arbitrary number of components is given and proven. This is done by using some definitions, theorems, propositions and an example.
Conchita Martínez-Pérez +1 more
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Improved Code Shortening for Block and Product Codes
2006 IEEE 63rd Vehicular Technology Conference, 2006Code shortening is commonly performed in practice but its analytical decoding performance is not well understood. In this letter, we present tight bounds for estimating the weight enumerator and hence BER (bit error rate) performance of linear shortened and shortened-extended block/product codes operating in AWGN and Rayleigh fading channels.
Kai Ching Lim, Yong Liang Guan 0001
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IEEE Transactions on Broadcasting, 2006
In this paper, a turbo-product-coded, quadrature-vestigial-sideband (QVSB), digital modulation and coding scheme are presented. This scheme is more complex than the VSB modulation and coding format employed for high-definition television; and it achieves spectral-efficiency performance within 4 to 5dB of the Shannon-Bound, with relatively conservative ...
John Poklemba, David Wenzel
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In this paper, a turbo-product-coded, quadrature-vestigial-sideband (QVSB), digital modulation and coding scheme are presented. This scheme is more complex than the VSB modulation and coding format employed for high-definition television; and it achieves spectral-efficiency performance within 4 to 5dB of the Shannon-Bound, with relatively conservative ...
John Poklemba, David Wenzel
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Combinatorica, 2007
What is the maximum possible number, f3(n), of vectors of length n over {0,1,2} such that the Hamming distance between every two is even? What is the maximum possible number, g3(n), of vectors in {0,1,2}n such that the Hamming distance between every two is odd?
Noga Alon, Eyal Lubetzky
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What is the maximum possible number, f3(n), of vectors of length n over {0,1,2} such that the Hamming distance between every two is even? What is the maximum possible number, g3(n), of vectors in {0,1,2}n such that the Hamming distance between every two is odd?
Noga Alon, Eyal Lubetzky
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Analog decoding of product codes
Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494), 2002A design approach is presented for soft-decision decoding of block product codes ("block turbo codes") using analog computation with MOS devices. Application of analog decoding to large code sizes is also considered with the introduction of serial analog interfaces and pipeline schedules.
Chris Winstead +3 more
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Concatenated codes, matrix-product codes and their schur product [PDF]
, 2021 The aim of thesis is two-fold. Firstly, we introduce concatenated codes, matrixproduct codes and elaborate on their relation. It is known that a matrix-product code can be seen as a concatenated code. We give a proof of this fact. Conversely, we show how a particular concatenated code can be viewed as a matrix-product code.
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On products of graphs for LDPC codes
Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674), 2004The notion of product block codes, whose generator matrix is the tensor product of the constituent generator matrices, is well established. Typically, they have good performance and a decoding algorithm with complexity on the order of the complexity of the decoding algorithms of the constituent codes.
Jun Xu 0004, Shu Lin 0001, Ian F. Blake
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Quantum Information Processing, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Product codes and the singleton bound
1994Minimum distance is not always the most determinant factor to acheive high performance for error correction. Of course the knowledge of the whole weight distribution of the code is more accurate than the knowledge of the mere minimum distance, and the phenomenon amplifies for a high noise level.
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