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signaling on the Gaussian channel","{\"openalex\":\"W2118111203\",\"doi\":\"10.1109/18.53734\"}","2026-05-22T04:54:07.423956548","2026-05-22T04:54:07.423958211","doi","10.1109/18.53734","arxivId","openalexId","W2118111203","abstractText","Signaling schemes for the Gaussian channel based on finite-dimensional lattices are considered. The signal constellation consists of all lattice points within a region R, and the shape of this region determines the average signal power. Spherical signal constellations minimize average signal power, and in the limit as N to infinity , the shape gain of the N-sphere over the N-cube approaches pi e/6 approximately=1.53 dB. A nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension. A signal constellation, Omega is partitioned into T subconstellations Omega /sub 0/, . . ., Omega /sub tau -1/ of equal size by scaling a basic region R. Signal points in the same subconstellation are used equiprobably, and a shaping code selects the subconstellation Omega /sub i/ with frequency f/sub i/. Shaping codes make it possible to achieve any desired fractional bit rate. The schemes presented are compared with equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. For comparable shape gain and constellation expansion ratio, the peak to average power ratio of the schemes presented is superior. Furthermore, a simple table lookup is all that is required to address points in the constellations. It is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework.< >","publishedDate","1990-07-01","publishedYear",1990,"venue","IEEE Transactions on Information Theory",262,"authors","keywords",[195,196,197],"pdfUrl","topVenue","Advanced Wireless Communication Techniques","Error Correcting Code Techniques","Cellular Automata and Applications","paper_W2104291851","Lossless image compression using integer to integer wavelet transforms","{\"openalex\":\"W2104291851\",\"doi\":\"10.1109/icip.1997.647983\"}","2026-05-21T09:56:28.207971739","2026-05-21T09:56:28.224194489","10.1109/icip.1997.647983","W2104291851","Invertible wavelet transforms that map integers to integers are important for lossless representations. We present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless image compression.","2002-11-23",2002,291,[210,211,212],"Image and Signal Denoising Methods","Advanced Data Compression Techniques","Advanced Image Fusion Techniques","paper_W2133866430","Z₄-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets","{\"openalex\":\"W2133866430\",\"doi\":\"10.1112/s0024611597000403\"}","2026-05-20T22:17:47.505991766","2026-05-20T22:19:13.184962525","10.1112/s0024611597000403","W2133866430","When m is odd, spreads in an orthogonal vector space of type Ω+(2m + 2,2) are related to binary Kerdock codes and extremal line-sets in 2m + 1 with prescribed angles. Spreads in a 2m-dimensional binary symplectic vector space are related to Kerdock codes over Z4 and extremal line-sets in \\CC 2 m with prescribed angles. These connections involve binary, real and complex geometry associated with extraspecial 2-groups. A geometric map from symplectic to orthogonal spreads is shown to induce the Gray map from a corresponding Z4-Kerdock code to its binary image. These geometric considerations lead to the construction, for any odd composite m, of large numbers of Z4-Kerdock codes. They also produce new Z4-linear Kerdock and Preparata codes. 1991 Mathematics Subject Classification: primary 94B60; secondary 51M15, 20C99.","1997-09-01",1997,"Proceedings of the London Mathematical Society",313,[226],"Coding theory and cryptography","paper_W2171843169","Modular andp-adic cyclic codes","{\"openalex\":\"W2171843169\",\"doi\":\"10.1007/bf01390768\"}","2026-05-20T10:52:26.212807781","2026-05-20T10:52:26.212883072","10.1007/bf01390768","W2171843169","1995-07-01",1995,"Designs Codes and Cryptography",336,[226,197,239],"Cooperative Communication and Network Coding","paper_W2091331782","Quantum Error Correction and Orthogonal Geometry","{\"arxiv\":\"quant-ph/9605005\",\"openalex\":\"W2091331782\",\"doi\":\"10.1103/physrevlett.78.405\"}","2026-05-14T20:54:01.313071282","2026-05-20T21:02:44.304753187","10.1103/physrevlett.78.405","quant-ph/9605005","W2091331782","A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.","1997-01-20","Physical Review Letters",831,[254,255,256],"https://arxiv.org/pdf/quant-ph/9605005","Quantum Computing Algorithms and Architecture","Quantum Information and Cryptography","Quantum-Dot Cellular Automata","paper_W2123457453","Sensitivity to Basis Mismatch in Compressed Sensing","{\"openalex\":\"W2123457453\",\"doi\":\"10.1109/tsp.2011.2112650\"}","2026-05-14T17:24:27.340700817","2026-05-21T21:57:15.191402958","10.1109/tsp.2011.2112650","W2123457453","The theory of compressed sensing suggests that successful inversion of an image of the physical world (broadly defined to include speech signals, radar/sonar returns, vibration records, sensor array snapshot vectors, 2-D images, and so on) for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis, provided that the image is sparse in an apriori known basis. For imaging problems in spectrum analysis, and passive and active radar/sonar, this basis is usually taken to be a DFT basis. However, in reality no physical field is sparse in the DFT basis or in any apriori known basis. No matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity. In this paper, we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases. We start by analyzing the effect of basis mismatch on the best k -term approximation error, which is central to providing exact sparse recovery guarantees. We establish achievable bounds for the l ₁ error of the best k -term approximation and show that these bounds grow linearly with the image (or grid) dimension and the mismatch level between the assumed and actual bases for sparsity. We then derive bounds, with similar growth behavior, for the basis pursuit l ₁ recovery error, indicating that the sparse recovery may suffer large errors in the presence of basis mismatch. Although, we present our results in the context of basis pursuit, our analysis applies to any sparse recovery principle that relies on the accuracy of best k -term approximations for its performance guarantees. We particularly highlight the problematic nature of basis mismatch in Fourier imaging, where spillage from off-grid DFT components turns a sparse representation into an incompressible one. We substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch, for problem sizes common to radar and sonar.","2011-02-11",2011,"IEEE Transactions on Signal Processing",912,[270,271,210],"Sparse and Compressive Sensing Techniques","Microwave Imaging and Scattering Analysis","paper_W1975358183","Wavelet Transforms That Map Integers to Integers","{\"openalex\":\"W1975358183\",\"doi\":\"10.1006/acha.1997.0238\"}","2026-05-14T12:24:26.423565453","2026-05-21T16:02:30.182019547","10.1006/acha.1997.0238","W1975358183","1998-07-01",1998,"Applied and Computational Harmonic Analysis",1084,[210,211],"paper_W2038681062","The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes","{\"openalex\":\"W2038681062\",\"doi\":\"10.1109/18.312154\"}","2026-05-14T07:37:31.262505041","2026-05-21T10:35:21.201390962","10.1109/18.312154","W2038681062","Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z/sub 4/ domain implies that the binary images have dual weight distributions. The Kerdock and \"Preparata\" codes are duals over Z/sub 4/-and the Nordstrom-Robinson code is self-dual-which explains why their weight distributions are dual to each other. The Kerdock and \"Preparata\" codes are Z/sub 4/-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z/sub 4/, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the \"Preparata\" code and a Hadamard-transform soft-decision decoding algorithm for the I(Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z/sub 4/, but extended Hamming codes of length n/spl ges/32 and the Golay code are not. Using Z/sub 4/-linearity, a new family of distance regular graphs are constructed on the cosets of the \"Preparata\" code.< >","1994-03-01",1994,1408,[226,296,239],"graph theory and CDMA systems","paper_W2167413626","Quantum error correction via codes over GF(4)","{\"openalex\":\"W2167413626\",\"doi\":\"10.1109/18.681315\"}","2026-05-14T05:26:15.225465423","2026-05-21T07:40:55.190430029","10.1109/18.681315","W2167413626","The problem of finding quantum error correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.",1796,[226,254,256],"paper_W2114207424","Good quantum error-correcting codes exist","{\"arxiv\":\"quant-ph/9512032\",\"openalex\":\"W2114207424\",\"doi\":\"10.1103/physreva.54.1098\"}","2026-05-14T03:25:06.340245981","2026-05-21T05:20:30.181656496","10.1103/physreva.54.1098","quant-ph/9512032","W2114207424","A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n=1-2${\\mathit{H}}_{2}$(2t/n) where ${\\mathit{H}}_{2}$(p) is the binary entropy function -p${\\mathrm{log}}_{2}$p-(1-p)${\\mathrm{log}}_{2}$(1-p). Upper bounds on this asymptotic rate are given. \\textcopyright{} 1996 The American Physical Society.","1996-08-01",1996,"Physical Review A",2544,[254,255,256],"https://arxiv.org/pdf/quant-ph/9512032",{"_59":323,"_61":324},[],[325],{"_64":326,"_66":327,"_68":328,"_70":329},1784607870415,{"_73":331,"_75":76,"_77":326,"_78":-5,"_79":26,"_80":26,"_81":26,"_82":-5,"_83":-5,"_84":85,"_35":86,"_87":88},[72,330],"[\"portal\",\"industries\"]","industries",[332,333,334,335,336,337,338,339,340,341,342,343],{"_15":405,"_29":406,"_31":-5,"_32":407,"_33":408,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":409,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":406,"_58":408},{"_15":401,"_29":402,"_31":-5,"_32":-5,"_33":403,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":404,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":402,"_58":403},{"_15":395,"_29":396,"_31":-5,"_32":397,"_33":398,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":399,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":396,"_58":398},{"_15":391,"_29":392,"_31":-5,"_32":-5,"_33":393,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":394,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":392,"_58":393},{"_15":387,"_29":388,"_31":-5,"_32":-5,"_33":389,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":390,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":388,"_58":389},{"_15":381,"_29":382,"_31":-5,"_32":383,"_33":384,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":385,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":382,"_58":384},{"_15":376,"_29":377,"_31":-5,"_32":-5,"_33":378,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":379,"_356":26,"_357":380,"_358":26,"_359":-5,"_57":377,"_58":378},{"_15":372,"_29":373,"_31":-5,"_32":-5,"_33":374,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":375,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":373,"_58":374},{"_15":368,"_29":369,"_31":-5,"_32":-5,"_33":370,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":371,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":369,"_58":370},{"_15":364,"_29":365,"_31":-5,"_32":-5,"_33":366,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":367,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":365,"_58":366},{"_15":360,"_29":361,"_31":-5,"_32":-5,"_33":362,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":363,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":361,"_58":362},{"_15":344,"_29":345,"_31":-5,"_32":-5,"_33":346,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":347,"_42":-5,"_44":-5,"_348":349,"_350":-5,"_351":76,"_352":353,"_354":355,"_356":26,"_357":85,"_358":26,"_359":-5,"_57":345,"_58":346},"tax_ind_smartphone","智能手机","Smartphone","manual","taxonomyType","INDUSTRY","code","level","parentId","tax_ind_root","path","科技行业/智能手机","sortOrder","isLeaf","entityCount","children","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算",true,"tax_ind_blockchain","区块链",[386],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[400],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[410,411],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_414":24},"SITE_BASE_URL"]

A.R. Calderbank 人物

A.R. Calderbank · 相关文章