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Weight enumerators of self-dual quantum codes 自双量子编码的权重枚举器
arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03576
Yin Chen, Shan Ren
{"title":"Weight enumerators of self-dual quantum codes","authors":"Yin Chen, Shan Ren","doi":"arxiv-2409.03576","DOIUrl":"https://doi.org/arxiv-2409.03576","url":null,"abstract":"We use algebraic invariant theory to study three weight enumerators of\u0000self-dual quantum codes over finite fields. We show that the weight enumerators\u0000of self-dual quantum codes can be expressed algebraically by two polynomials\u0000and the double weight enumerators of self-dual quantum codes can be expressed\u0000algebraically by five polynomials. We also explicitly compute the complete\u0000weight enumerators of some special self-dual quantum codes. Our approach avoids\u0000applying the well-known Molien's formula and demonstrates the potential of\u0000employing invariant theory to compute weight enumerators of quantum codes.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Robust End-to-End Image Transmission with Residual Learning 利用残差学习实现稳健的端到端图像传输
arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03243
Cenk M. Yetis
{"title":"Robust End-to-End Image Transmission with Residual Learning","authors":"Cenk M. Yetis","doi":"arxiv-2409.03243","DOIUrl":"https://doi.org/arxiv-2409.03243","url":null,"abstract":"Recently, deep learning (DL) based image transmission at the physical layer\u0000(PL) has become a rising trend due to its ability to significantly outperform\u0000conventional separation-based digital transmissions. However, implementing\u0000solutions at the PL requires a major shift in established standards, such as\u0000those in cellular communications. Application layer (AL) solutions present a\u0000more feasible and standards-compliant alternative. In this work, we propose a\u0000layered image transmission scheme at the AL that is robust to end-to-end (E2E)\u0000channel errors. The base layer transmits a coarse image, while the enhancement\u0000layer transmits the residual between the original and coarse images. By mapping\u0000the residual image into a latent representation that aligns with the structure\u0000of the E2E channel, our proposed solution demonstrates high robustness to E2E\u0000channel errors.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fundamentals of Energy-Efficient Wireless Links: Optimal Ratios and Scaling Behaviors 高能效无线链路基础：最佳比率和扩展行为
arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03436
Anders Enqvist, Özlem Tuğfe Demir, Cicek Cavdar, Emil Björnson
{"title":"Fundamentals of Energy-Efficient Wireless Links: Optimal Ratios and Scaling Behaviors","authors":"Anders Enqvist, Özlem Tuğfe Demir, Cicek Cavdar, Emil Björnson","doi":"arxiv-2409.03436","DOIUrl":"https://doi.org/arxiv-2409.03436","url":null,"abstract":"In this paper, we examine the energy efficiency (EE) of a base station (BS)\u0000with multiple antennas. We use a state-of-the-art power consumption model,\u0000taking into account the passive and active parts of the transceiver circuitry,\u0000including the effects of radiated power, signal processing, and passive\u0000consumption. The paper treats the transmit power, bandwidth, and number of\u0000antennas as the optimization variables. We provide novel closed-form solutions\u0000for the optimal ratios of power per unit bandwidth and power per transmit\u0000antenna. We present a novel algorithm that jointly optimizes these variables to\u0000achieve maximum EE, while fulfilling constraints on the variable ranges. We\u0000also discover a new relationship between the radiated power and the passive\u0000transceiver power consumption. We provide analytical insight into whether using\u0000maximum power or bandwidth is optimal and how many antennas a BS should\u0000utilize.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise 多变量高斯源与加性噪声互信息的次模性
arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03541
George Crowley, Inaki Esnaola
{"title":"Submodularity of Mutual Information for Multivariate Gaussian Sources with Additive Noise","authors":"George Crowley, Inaki Esnaola","doi":"arxiv-2409.03541","DOIUrl":"https://doi.org/arxiv-2409.03541","url":null,"abstract":"Sensor placement approaches in networks often involve using\u0000information-theoretic measures such as entropy and mutual information. We prove\u0000that mutual information abides by submodularity and is non-decreasing when\u0000considering the mutual information between the states of the network and a\u0000subset of $k$ nodes subjected to additive white Gaussian noise. We prove this\u0000under the assumption that the states follow a non-degenerate multivariate\u0000Gaussian distribution.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"297 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Neural Entropy 神经熵
arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03817
Akhil Premkumar
{"title":"Neural Entropy","authors":"Akhil Premkumar","doi":"arxiv-2409.03817","DOIUrl":"https://doi.org/arxiv-2409.03817","url":null,"abstract":"We examine the connection between deep learning and information theory\u0000through the paradigm of diffusion models. Using well-established principles\u0000from non-equilibrium thermodynamics we can characterize the amount of\u0000information required to reverse a diffusive process. Neural networks store this\u0000information and operate in a manner reminiscent of Maxwell's demon during the\u0000generative stage. We illustrate this cycle using a novel diffusion scheme we\u0000call the entropy matching model, wherein the information conveyed to the\u0000network during training exactly corresponds to the entropy that must be negated\u0000during reversal. We demonstrate that this entropy can be used to analyze the\u0000encoding efficiency and storage capacity of the network. This conceptual\u0000picture blends elements of stochastic optimal control, thermodynamics,\u0000information theory, and optimal transport, and raises the prospect of applying\u0000diffusion models as a test bench to understand neural networks.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hemispherical Antenna Array Architecture for High-Altitude Platform Stations (HAPS) for Uniform Capacity Provision 用于高空平台站 (HAPS) 的半球形天线阵列架构，以提供统一容量
arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03474
Omid Abbasi, Halim Yanikomeroglu, Georges Kaddoum
{"title":"Hemispherical Antenna Array Architecture for High-Altitude Platform Stations (HAPS) for Uniform Capacity Provision","authors":"Omid Abbasi, Halim Yanikomeroglu, Georges Kaddoum","doi":"arxiv-2409.03474","DOIUrl":"https://doi.org/arxiv-2409.03474","url":null,"abstract":"In this paper, we present a novel hemispherical antenna array (HAA) designed\u0000for high-altitude platform stations (HAPS). A significant limitation of\u0000traditional rectangular antenna arrays for HAPS is that their antenna elements\u0000are oriented downward, resulting in low gains for distant users. Cylindrical\u0000antenna arrays were introduced to mitigate this drawback; however, their\u0000antenna elements face the horizon leading to suboptimal gains for users located\u0000beneath the HAPS. To address these challenges, in this study, we introduce our\u0000HAA. An HAA's antenna elements are strategically distributed across the surface\u0000of a hemisphere to ensure that each user is directly aligned with specific\u0000antenna elements. To maximize users minimum signal-to-interference-plus-noise\u0000ratio (SINR), we formulate an optimization problem. After performing analog\u0000beamforming, we introduce an antenna selection algorithm and show that this\u0000method achieves optimality when a substantial number of antenna elements are\u0000selected for each user. Additionally, we employ the bisection method to\u0000determine the optimal power allocation for each user. Our simulation results\u0000convincingly demonstrate that the proposed HAA outperforms the conventional\u0000arrays, and provides uniform rates across the entire coverage area. With a\u0000$20~mathrm{MHz}$ communication bandwidth, and a $50~mathrm{dBm}$ total power,\u0000the proposed approach reaches sum rates of $14~mathrm{Gbps}$.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization 高斯率失真感知编码和熵约束标量量化
arXiv - MATH - Information Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02388
Li Xie, Liangyan Li, Jun Chen, Lei Yu, Zhongshan Zhang
{"title":"Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization","authors":"Li Xie, Liangyan Li, Jun Chen, Lei Yu, Zhongshan Zhang","doi":"arxiv-2409.02388","DOIUrl":"https://doi.org/arxiv-2409.02388","url":null,"abstract":"This paper investigates the best known bounds on the quadratic Gaussian\u0000distortion-rate-perception function with limited common randomness for the\u0000Kullback-Leibler divergence-based perception measure, as well as their\u0000counterparts for the squared Wasserstein-2 distance-based perception measure,\u0000recently established by Xie et al. These bounds are shown to be nondegenerate\u0000in the sense that they cannot be deduced from each other via a refined version\u0000of Talagrand's transportation inequality. On the other hand, an improved lower\u0000bound is established when the perception measure is given by the squared\u0000Wasserstein-2 distance. In addition, it is revealed by exploiting the\u0000connection between rate-distortion-perception coding and entropy-constrained\u0000scalar quantization that all the aforementioned bounds are generally not tight\u0000in the weak perception constraint regime.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Successive-Cancellation Flip Decoding of Polar Codes Under Fixed Channel-Production Rate 固定信道生产率下极性编码的逐次消隐翻转解码
arXiv - MATH - Information Theory Pub Date : 2024-09-04 DOI: arxiv-2409.03051
Ilshat Sagitov, Charles Pillet, Pascal Giard
{"title":"Successive-Cancellation Flip Decoding of Polar Codes Under Fixed Channel-Production Rate","authors":"Ilshat Sagitov, Charles Pillet, Pascal Giard","doi":"arxiv-2409.03051","DOIUrl":"https://doi.org/arxiv-2409.03051","url":null,"abstract":"Polar codes are a class of error-correcting codes that provably achieve the\u0000capacity of practical channels under the low-complexity successive-cancellation\u0000flip (SCF) decoding algorithm. However, the SCF decoding algorithm has a\u0000variable execution time with a high (worst-case) decoding latency. This\u0000characteristic poses a challenge to the design of receivers that have to\u0000operate at fixed data rates. In this work, we propose a multi-threshold\u0000mechanism that restrains the delay of a SCF decoder depending on the state of\u0000the buffer to avoid overflow. We show that the proposed mechanism provides\u0000better error-correction performance compared to a straightforward\u0000codeword-dropping mechanism at the cost of a small increase in complexity. In\u0000the region of interest for wireless communications, the proposed mechanism can\u0000prevent buffer overflow while operating with a fixed channel-production rate\u0000that is 1.125 times lower than the rate associated to a single decoding trial.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Group Information Geometry Approach for Ultra-Massive MIMO Signal Detection 超大质量多输入多输出信号检测的群信息几何方法
arXiv - MATH - Information Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02616
Jiyuan Yang, Yan Chen, Xiqi Gao, Xiang-Gen Xia, Dirk Slock
{"title":"Group Information Geometry Approach for Ultra-Massive MIMO Signal Detection","authors":"Jiyuan Yang, Yan Chen, Xiqi Gao, Xiang-Gen Xia, Dirk Slock","doi":"arxiv-2409.02616","DOIUrl":"https://doi.org/arxiv-2409.02616","url":null,"abstract":"We propose a group information geometry approach (GIGA) for ultra-massive\u0000multiple-input multiple-output (MIMO) signal detection. The signal detection\u0000task is framed as computing the approximate marginals of the a posteriori\u0000distribution of the transmitted data symbols of all users. With the approximate\u0000marginals, we perform the maximization of the {textsl{a posteriori}} marginals\u0000(MPM) detection to recover the symbol of each user. Based on the information\u0000geometry theory and the grouping of the components of the received signal,\u0000three types of manifolds are constructed and the approximate a posteriori\u0000marginals are obtained through m-projections. The Berry-Esseen theorem is\u0000introduced to offer an approximate calculation of the m-projection, while its\u0000direct calculation is exponentially complex. In most cases, more groups, less\u0000complexity of GIGA. However, when the number of groups exceeds a certain\u0000threshold, the complexity of GIGA starts to increase. Simulation results\u0000confirm that the proposed GIGA achieves better bit error rate (BER) performance\u0000within a small number of iterations, which demonstrates that it can serve as an\u0000efficient detection method in ultra-massive MIMO systems.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Key Compression Limits for $k$-Minimum Value Sketches k$ 最小值草图的密钥压缩限制
arXiv - MATH - Information Theory Pub Date : 2024-09-04 DOI: arxiv-2409.02852
Charlie Dickens, Eric Bax, Alexander Saydakov
{"title":"Key Compression Limits for $k$-Minimum Value Sketches","authors":"Charlie Dickens, Eric Bax, Alexander Saydakov","doi":"arxiv-2409.02852","DOIUrl":"https://doi.org/arxiv-2409.02852","url":null,"abstract":"The $k$-Minimum Values (kmv) data sketch algorithm stores the $k$ least hash\u0000keys generated by hashing the items in a dataset. We show that compression\u0000based on ordering the keys and encoding successive differences can offer\u0000$O(log n)$ bits per key in expected storage savings, where $n$ is the number\u0000of unique values in the data set. We also show that $O(log n)$ expected bits\u0000saved per key is optimal for any form of compression for the $k$ least of $n$\u0000random values -- that the encoding method is near-optimal among all methods to\u0000encode a kmv sketch. We present a practical method to perform that\u0000compression, show that it is computationally efficient, and demonstrate that\u0000its average savings in practice is within about five percent of the theoretical\u0000minimum based on entropy. We verify that our method outperforms off-the-shelf\u0000compression methods, and we demonstrate that it is practical, using real and\u0000synthetic data.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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