A new multiple-input multiple-output (MIMO) receiver scheme for practical binary codes is proposed that provides consistent gains over conventional linear receivers. We first develop a practical successive integer for...
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A new multiple-input multiple-output (MIMO) receiver scheme for practical binary codes is proposed that provides consistent gains over conventional linear receivers. We first develop a practical successive integer forcing (IF) scheme based on practical binary codes rather than lattice codes. We then present the successive cancellation integer forcing (SC-IF) scheme, which combines and enhances successive IF and minimum mean squared error successive interference cancellation (MMSE-SIC). In this scheme, the receiver first decides whether individual decoding or IF sum decoding is appropriate for each data stream, and then conducts successive IF sum decoding only for selected streams while decoding the remaining streams using MMSE-SIC. The proposed SC-IF methodology mitigates the performance loss caused by mismatched IF filtering in fading channels, while attenuating the noise amplification caused by MMSE filtering. Extensive link-level simulations demonstrate that the proposed successive IF significantly improves the basic IF, and the SC-IF improves both the successive IF and MMSE-SIC, offering uniform improvements over conventional linear receivers for most channel correlation and variation parameters and modulation orders at comparable computational costs. These results illustrate the viability of SC-IF as a fundamental building block for high-performance MIMO receivers in 5G-Advanced and/or subsequent-generation communication systems.
Let K(n, 1) denote the minimal cardinality of a binary code of length n and covering radius one. Blass and Litsyn proved a lower bound for K (n, 1) in the case n equivalent to 5 (mod6). We give a simplification of the...
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Let K(n, 1) denote the minimal cardinality of a binary code of length n and covering radius one. Blass and Litsyn proved a lower bound for K (n, 1) in the case n equivalent to 5 (mod6). We give a simplification of the proof, which yields a slightly better result.
The binary code spanned by the rows of the point byblock incidence matrix of a Steiner triple system STS(v)is studied. A sufficient condition for such a code to containa unique equivalence class of STS(v)'s of max...
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The binary code spanned by the rows of the point byblock incidence matrix of a Steiner triple system STS(v)is studied. A sufficient condition for such a code to containa unique equivalence class of STS(v)'s of maximalrank within the code is proved. The code of the classical Steinertriple system defined by the lines in PG(n-1,2)(n3), or AG(n,3) (n3) is shown to contain exactly v codewordsof weight r=(v-1)/2, hence the system is characterizedby its code. In addition, the code of the projective STS(2n-1)is characterized as the unique (up to equivalence) binary linearcode with the given parameters and weight distribution. In general,the number of STS(v)'s contained in the code dependson the geometry of the codewords of weight r. Itis demonstrated that the ovals and hyperovals of the definingSTS(v) play a crucial role in this geometry. Thisrelation is utilized for the construction of some infinite classesof Steiner triple systems without ovals.
Asymptotic covering properties of families of binary codes are studied. A Gaussian approximation to the weight distribution of translates for codes of high strength is used. From this an upper bound on the covering ra...
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Asymptotic covering properties of families of binary codes are studied. A Gaussian approximation to the weight distribution of translates for codes of high strength is used. From this an upper bound on the covering radius of these codes is deduced. Applications include Reed-Muller codes, quadratic residue codes, and BCH codes. Sufficient conditions for a family of codes to have best possible covering radius (asymptotically perfect codes) are derived.
Hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the Hamming space. Hashing has proven a valuable tool for large-scale informat...
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Hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the Hamming space. Hashing has proven a valuable tool for large-scale information retrieval. We propose a column generation based binary code learning framework for data-dependent hash function learning. Given a set of triplets that encode the pairwise similarity comparison information, our column generation based method learns hash functions that preserve the relative comparison relations within the large-margin learning framework. Our method iteratively learns the best hash functions during the column generation procedure. Existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest-multivariate performance measures such as the AUC and NDCG. Our column generation based method can be further generalized from the triplet loss to a general structured learning based framework that allows one to directly optimize multivariate performance measures. For optimizing general ranking measures, the resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. We use a combination of column generation and cutting-plane techniques to solve the optimization problem. To speed-up the training we further explore stage-wise training and propose to optimize a simplified NDCG loss for efficient inference. We demonstrate the generality of our method by applying it to ranking prediction and image retrieval, and show that it outperforms several state-of-the-art hashing methods.
In the manufacture of oligo arrays for DNA hybridization experiments, manufacturing defects must be detected and their position determined. The design of manufacturing protocols for such oligo arrays leads to a combin...
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In the manufacture of oligo arrays for DNA hybridization experiments, manufacturing defects must be detected and their position determined. The design of manufacturing protocols for such oligo arrays leads to a combinatorial problem, requiring certain binary codes which have an additional balance property Constructions using block designs and packings for these codes, within a range of interest in a practical manufacturing application, are developed. The focus is on equireplicate codes, constant weight codes in which every bit position is a one equally often.
By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T(n) for any n greater than or equal to 5. (C) 2003 Elsevier Ltd....
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By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T(n) for any n greater than or equal to 5. (C) 2003 Elsevier Ltd. All rights reserved.
The stabilizers of the minimum-weight codewords of dual binary codes obtained from the strongly regular graphs T(n) defined by the primitive rank-3 action of the alternating groups A(n) where n >= 5, on ohm((2)), t...
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The stabilizers of the minimum-weight codewords of dual binary codes obtained from the strongly regular graphs T(n) defined by the primitive rank-3 action of the alternating groups A(n) where n >= 5, on ohm((2)), the set of duads of ohm = (1, 2,..., n), are examined. (c) 2005 Elsevier Ltd. All rights reserved.
A binary code C subset of or equal to F-2(n) with M codewords is called an (n, M, r, mu) multiple covering of the farthest-off points (MCF) if the Hamming spheres of radius r centered at the codewords cover the whole ...
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A binary code C subset of or equal to F-2(n) with M codewords is called an (n, M, r, mu) multiple covering of the farthest-off points (MCF) if the Hamming spheres of radius r centered at the codewords cover the whole space F-2(n) and every x is an element of F-2(n) such that d(x,C) = r is covered by at least mu codewords. The minimum possible cardinality F(n, r, mu) of such a code is studied and tables of upper bounds on F(n, r, mu) for n less than or equal to 16,r less than or equal to 4,mu less than or equal to 4 are given.
The determination of bounds for A(n, d, w), the maximum possible number of binary vectors of length n, weight w, and pairwise Hamming distance no less than d, is a classic problem in coding theory. Such sets of vector...
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The determination of bounds for A(n, d, w), the maximum possible number of binary vectors of length n, weight w, and pairwise Hamming distance no less than d, is a classic problem in coding theory. Such sets of vectors have many applications. A description is given of how the problem can be used in a first-year undergraduate computational mathematics class as a challenging alternative to more traditional problems, and thus provide motivation for programming with loops and arrays, and the investigation of computational efficiency. Some new results, obtained by a fast implementation of a lexicographic approach, are also presented.
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