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IEEE Transactions on Information Theory Publication Information
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-02-20 DOI: 10.1109/TIT.2025.3539816
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引用次数: 0
IEEE Transactions on Information Theory Information for Authors
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-02-20 DOI: 10.1109/TIT.2025.3539818
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引用次数: 0
Error Exponents for Entanglement Transformations From Degenerations
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-27 DOI: 10.1109/TIT.2025.3534327
Dávid Bugár;Péter Vrana
This paper explores the trade-off relation between the rate and the strong converse exponent for asymptotic LOCC transformations between pure multipartite states. Any single-copy probabilistic transformation between a pair of states implies that an asymptotic transformation at rate 1 is possible with an exponentially decreasing success probability. However, it is possible that an asymptotic transformation is feasible with nonzero probability, but there is no transformation between any finite number of copies with the same rate, even probabilistically. In such cases it is not known if the optimal success probability decreases exponentially or faster. A fundamental tool for showing the feasibility of an asymptotic transformation is degeneration. Any degeneration gives rise to a sequence of stochastic LOCC transformations from copies of the initial state plus a sublinear number of GHZ states to the same number of copies of the target state. These protocols involve parameters that can be freely chosen, but the choice affects the success probability. In this paper, we characterize an asymptotically optimal choice of the parameters and derive a single-letter expression for the error exponent of the resulting protocol. In particular, this implies an exponential lower bound on the success probability when the stochastic transformation arises from a degeneration.
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引用次数: 0
Bounds and Constructions of Quantum Locally Recoverable Codes From Quantum CSS Codes
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-24 DOI: 10.1109/TIT.2025.3533494
Gaojun Luo;Bocong Chen;Martianus Frederic Ezerman;San Ling
Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential application in quantum data storage. In this paper, we use classical LRCs to investigate quantum LRCs. We prove that the parameters of quantum LRCs are bounded by their classical counterparts. We deduce bounds on the parameters of quantum LRCs from bounds on the parameters of the classical ones. We establish a characterization of optimal pure quantum LRCs based on classical codes with specific properties. Using well-crafted classical LRCs as ingredients in the construction of quantum CSS codes, we offer the first construction of several families of optimal pure quantum LRCs.
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引用次数: 0
Generalized Regenerating Codes and Node Repair on Graphs
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-24 DOI: 10.1109/TIT.2025.3532625
Adway Patra;Alexander Barg
We consider regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the purpose of recovering the lost data. Compared to the standard setting, regenerating codes on graphs address two additional features. The repair information is moved across the network, and the cost of node repair is determined by the graphical distance from the helper nodes to the failed node. Accordingly, the helpers far away from the failed node may be expected to contribute less data for repair than the nodes in the neighborhood of that node. We analyze regenerating codes with nonuniform download for repair on graphs. Moreover, in the process of repair, the information moved from the helpers to the failed node may be combined through intermediate processing, reducing the repair bandwidth. We derive lower bounds for communication complexity of node repair on graphs, including repair schemes with nonuniform download and intermediate processing, and construct codes that attain these bounds. Additionally, some of the nodes may act as adversaries, introducing errors into the data moved in the network. For repair on graphs in the presence of adversarial nodes, we construct codes that support node repair and error correction in systematic nodes.
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引用次数: 0
Channel Coding With Mean and Variance Cost Constraints
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-24 DOI: 10.1109/TIT.2025.3533947
Adeel Mahmood;Aaron B. Wagner
We consider channel coding for discrete memoryless channels (DMCs) with a novel cost constraint that constrains both the mean and the variance of the cost of the codewords. We show that the maximum (asymptotically) achievable rate under the new cost formulation is equal to the capacity-cost function; in particular, the strong converse holds. We further characterize the optimal second-order coding rate of these cost-constrained codes; in particular, the optimal second-order coding rate is finite. We then show that the second-order coding performance is strictly improved with feedback using a new variation of timid/bold coding, significantly broadening the applicability of timid/bold coding schemes from unconstrained compound-dispersion channels to all cost-constrained channels. Equivalent results on the minimum average probability of error are also given.
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引用次数: 0
IEEE Transactions on Information Theory Information for Authors
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-23 DOI: 10.1109/TIT.2025.3527734
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引用次数: 0
IEEE Transactions on Information Theory Publication Information
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-23 DOI: 10.1109/TIT.2025.3527732
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引用次数: 0
Bounded-Degree Low-Rank Parity-Check Codes
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-22 DOI: 10.1109/TIT.2025.3532811
Ermes Franch;Chunlei Li
Low-rank parity-check (LRPC) codes are the rank-metric analogue of low-density parity-check codes and they found important applications in code-based cryptography. In this paper we investigate a sub-family of LRPC codes, which have a parity-check matrix defined over a subspace <inline-formula> <tex-math>${mathcal {V}}_{alpha,d}=langle 1,alpha, ldots, alpha ^{d-1} rangle _{mathbb {F}_{q}}subsetneq mathbb {F}_{q^{m}} $ </tex-math></inline-formula>, where <inline-formula> <tex-math>$mathbb {F}_{q^{m}}$ </tex-math></inline-formula> is the finite field of <inline-formula> <tex-math>$q^{m}$ </tex-math></inline-formula> elements, <inline-formula> <tex-math>$alpha in mathbb {F}_{q^{m}}$ </tex-math></inline-formula> is an element not in any proper subfield of <inline-formula> <tex-math>$mathbb {F}_{q^{m}}$ </tex-math></inline-formula>, and d is a positive integer significantly smaller than m. These codes are termed bounded-degree LRPC (BD-LRPC) codes. BD-LRPC codes are the same as the standard LRPC codes of density 2 when the degree <inline-formula> <tex-math>$d=2$ </tex-math></inline-formula>, while for degree <inline-formula> <tex-math>$dgt 2$ </tex-math></inline-formula> they constitute a proper subset of LRPC codes of density d. Exploiting the structure of <inline-formula> <tex-math>${mathcal {V}}_{alpha,d}$ </tex-math></inline-formula>, the BD-LRPC codes of degree d can uniquely correct errors of rank weight r when <inline-formula> <tex-math>$n-k geq r + u$ </tex-math></inline-formula> for certain <inline-formula> <tex-math>$u geq 1$ </tex-math></inline-formula>, in contrast to the condition <inline-formula> <tex-math>$n-kgeq dr$ </tex-math></inline-formula> required for the standard LRPC codes. This underscores the superior decoding capability of the BD-LRPC codes. Moreover, as the code length <inline-formula> <tex-math>$nrightarrow infty $ </tex-math></inline-formula>, when <inline-formula> <tex-math>$n/mrightarrow 0$ </tex-math></inline-formula>, the BD-LRPC codes with a code rate of <inline-formula> <tex-math>$R=k/n$ </tex-math></inline-formula> can be uniquely decodable with radius <inline-formula> <tex-math>$rho =r/n$ </tex-math></inline-formula> approaching the Singleton bound <inline-formula> <tex-math>$1-R$ </tex-math></inline-formula> by letting <inline-formula> <tex-math>$epsilon =u/nrightarrow 0$ </tex-math></inline-formula>; and when <inline-formula> <tex-math>$n/m$ </tex-math></inline-formula> is a constant, the BD-LRPC codes can have unique decoding radius <inline-formula> <tex-math>$rho = 1-R-epsilon $ </tex-math></inline-formula> for a small <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>, allowing for <inline-formula> <tex-math>$rho gt (1-R)/2$ </tex-math></inline-formula> with properly chosen parameters. This superior decoding capability is theoretically proved for the case <inline-formula> <tex-math>$d=2$ </tex-math></inline-formula> and confirmed by experimental results for <inline-formula> <tex-math>$dgt 2$ </
低秩奇偶校验(LRPC)码是低密度奇偶校验码的秩计量类似码,它们在基于密码的密码学中有着重要的应用。在本文中,我们研究了 LRPC 码的一个子系列,它的奇偶校验矩阵定义在一个子空间 ${mathcal {V}}_{alpha,d}=langle 1,alpha, ldots, alpha ^{d-1} rangle _mathbb {F}_{q}}subsetneq mathbb {F}_{q^{m}} 上。其中 $mathbb {F}_{q^{m}}$ 是包含 $q^{m}$ 元素的有限域,$alpha in mathbb {F}_{q^{m}}$ 是不在 $mathbb {F}_{q^{m}}$ 的任何适当子域中的元素,d 是明显小于 m 的正整数。当度为 $d=2$ 时,BD-LRPC 码与密度为 2 的标准 LRPC 码相同;而当度为 $dgt 2$ 时,它们构成了密度为 d 的 LRPC 码的一个适当子集。利用${mathcal {V}}_{alpha,d}$的结构,当$n-k geq r + u$为一定的$u geq 1$时,密度为d的BD-LRPC编码可以唯一地纠正秩权重为r的错误,而标准LRPC编码需要的条件是$n-k geq dr$。这凸显了 BD-LRPC 编码的卓越解码能力。此外,随着码长$nrightarrow infty$的增加,当$n/mrightarrow 0$时,让$epsilon =u/nrightarrow 0$,码率为$R=k/n$的BD-LRPC码可以唯一解码,半径为$rho =r/n$,接近单子约束1-R$;而当 $n/m$ 是一个常数时,BD-LRPC 编码在 $epsilon $ 很小时可以有独特的解码半径 $rho = 1-R-epsilon$,允许在正确选择参数的情况下达到 $rho gt (1-R)/2$ 。这种卓越的解码能力在理论上证明了 $d=2$ 的情况,并通过实验结果证实了 $dgt 2$ 的情况。
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引用次数: 0
Broadcast Channels With Heterogeneous Arrival and Decoding Deadlines: Second-Order Achievability
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2025-01-22 DOI: 10.1109/TIT.2025.3532649
Homa Nikbakht;Malcolm Egan;Jean-Marie Gorce;H. Vincent Poor
A standard assumption in the design of ultra-reliable low-latency communication systems is that the duration between message arrivals is larger than the number of channel uses before the decoding deadline. Nevertheless, this assumption fails when messages arrive rapidly and reliability constraints require that the number of channel uses exceed the time between arrivals. In this paper, we consider a broadcast setting in which a transmitter wishes to send two different messages to two receivers over Gaussian channels. Messages have different arrival times and decoding deadlines such that their transmission windows overlap. For this setting, we propose a coding scheme that exploits Marton’s coding strategy. We derive rigorous bounds on the achievable rate regions. Those bounds can be easily employed in point-to-point settings with one or multiple parallel channels. In the point-to-point setting with one or multiple parallel channels, the proposed achievability scheme is consistent with the normal approximation. In the broadcast setting, our scheme agrees with Marton’s strategy for sufficiently large numbers of channel uses and shows significant performance improvements over standard approaches based on time sharing for transmission of short packets.
超可靠低延迟通信系统设计中的一个标准假设是,信息到达之间的持续时间大于解码截止日期前的信道使用次数。然而,当信息快速到达,而可靠性约束要求信道使用次数超过信息到达间隔时间时,这一假设就失效了。在本文中,我们考虑了一种广播环境,即发送端希望通过高斯信道向两个接收端发送两个不同的信息。信息有不同的到达时间和解码期限,因此它们的传输窗口会重叠。针对这种情况,我们提出了一种利用 Marton 编码策略的编码方案。我们得出了可实现速率区域的严格界限。这些界限可以很容易地应用于具有一个或多个并行信道的点对点环境。在具有一个或多个并行信道的点对点环境中,所提出的可实现性方案与正常近似一致。在广播环境中,我们的方案在信道使用数量足够大的情况下与 Marton 的策略一致,与基于短数据包传输时间共享的标准方法相比,性能有显著提高。
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IEEE Transactions on Information Theory
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