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Inner Code Assisted Parallel Concatenated Single Parity Check Codes

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2014年第Sup1期9卷 S44-S48页

作者： Izhar, Mohd Azri Mohd Fisal, Norsheila UTM Fac Elect Engn UTM MIMOS Ctr Excellence Johor Baharu 81310 Johor Malaysia

This paper proposes a novel coding scheme to improve the performance of multidimensional parallel concatenated single parity check (PCSPC) codes. The high error floor of PCSPC codes prevents clear turbo cliff to be seen in the bit-error rate (BER) performance. Based on the product accumulate type-I (PA-I) coding scheme, which adds serially an accumulator to the existing PCSPC code structure, our coding scheme considers a wide range of rate-1 recursive systematic convolutional (RSC) codes replacing the accumulator. The convergence behavior of the proposed iterative decoding is monitored and analyzed using an extrinsic information transfer (EXIT) chart. It has been revealed from the EXIT chart analysis that the proposed coding scheme has a lower convergence threshold than the PA-I coding scheme, especially when using a lower code rate PCSPC code as the outer code. For the 2D PCSPC(3,2) code with the code rate 0.5, the proposed coding scheme has a convergence threshold of 0.47 dB, whereas the convergence threshold of the PA-I coding scheme is 0.81 dB. The convergence threshold of the proposed coding scheme is closer to theoretical limit (0.28 dB away from the theoretical limit) than that of the PA-I coding scheme (0.62 dB away). However, for PCSPC codes with a higher code rate, the performance improvement of the proposed coding scheme with respect to the PA-I coding scheme becomes smaller. A series of simulations is carried out to investigate the performance of the proposed coding scheme, and the simulation results show that better performance is achieved by using the proposed coding scheme compared with the PA-I coding scheme. The simulation results show good consistency with the convergence threshold obtained from the EXIT chart, as the difference is only within 0.34 dB in all the evaluated cases. (c) 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

关键词： parallel concatenated single parity check codes product accumulate codes turbo codes single parity check codes channel coding coding theorem

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What is Shannon information?

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SYNTHESE 2016年第7期193卷 1983-2012页

作者： Lombardi, Olimpia Holik, Federico Vanni, Leonardo Univ Buenos Aires CONICET Buenos Aires DF Argentina Univ Nacl La Plata CONICET Buenos Aires DF Argentina Univ Buenos Aires Buenos Aires DF Argentina

Despite of its formal precision and its great many applications, Shannon's theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information are no longer rival, but different interpretations of a single formal concept.

关键词： Shannon entropy coding theorem Bit Epistemic interpretation Physical interpretation

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Quantum state merging and negative information

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COMMUNICATIONS IN MATHEMATICAL PHYSICS 2007年第1期269卷 107-136页

作者： Horodecki, Michal Oppenheim, Jonathan Winter, Andreas Univ Gdansk Inst Theoret Phys & Astrophys PL-80952 Gdansk Poland Univ Cambridge Dept Appl Math & Theoret Phys Cambridge England Univ Bristol Dept Math Bristol BS8 1TW Avon England

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.

关键词： coding theorem ENTANGLEMENT ENTROPY CHANNEL CAPACITY COMMUNICATION

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Hypothesis Testing for Arbitrarily Varying Source

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Acta Mathematica Sinica,English Series 1996年第1期12卷 33-39页

作者： Fu Fangwei Shen Shiyi Department of Mathematics Nankai University Tianjin, 300071 China Department of Mathematics Nankai University Tianjin China

Hypothesis testing for arbitrarily varying source (AVS), which is to decide between the two hypotheses for the varying behavior of the distribution of AVS, is considered in this paper. We determine the best asymptotic exponent of the second kind of error probability when the first kind of error probability is fixed. This result generalizes the well-known lemma of Stein in statistics. As a corollary, Strassen’s coding theorem for AVS is obtained.

关键词： Hypothesis testing Stein lemma Arbitrarily varying source coding theorem

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Capacity of a Noisy Function

Capacity of a Noisy Function

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IEEE Information Theory Workshop (ITW)

作者： Simon, Francois Telecom SudParis Inst TELECOM CITI F-91011 Evry France

ISBN: (纸本)9781424482641

This paper presents an extension of the memoryless channel coding theorem to noisy functions, i.e. unreliable computing devices without internal states. It is shown that the concepts of equivocation and capacity can be defined for noisy computations in the simple case of memoryless noisy functions. Capacity is the upper bound of input rates allowing reliable computation, i.e. decodability of noisy outputs into expected outputs. The proposed concepts are generalizations of these known for channels: the capacity of a noisy implementation of a bijective function has the same expression as the capacity of a communication channel. A lemma similar to Feinstein's one is stated and demonstrated. A model of reliable computation of a function thanks to a noisy device is proposed. A coding theorem is stated and demonstrated.

关键词： bijective function channel capacity channel coding coding theorem communication channel capacity decoding equivocation interference memoryless channel coding memoryless systems noisy function capacity noisy output decodability reliable computation telecommunication network reliability

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An Information Bottleneck Problem with Renyi's Entropy

An Information Bottleneck Problem with Renyi's Entropy

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IEEE International Symposium on Information Theory (ISIT)

作者： Weng, Jian-Jia Alajaji, Fady Linder, Tamas Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada

ISBN: (纸本)9781538682098

This paper considers an information bottleneck problem with the objective of obtaining a most informative representation of a hidden feature subject to a Renyi entropy complexity constraint. The optimal bottleneck trade-off between relevance (measured via Shannon's mutual information) and Renyi entropy cost is defined and an iterative algorithm for finding approximate solutions is provided. We also derive an operational characterization for the optimal trade-off by demonstrating that the optimal Renyi entropy-relevance trade-off is achievable by a simple time-sharing scalar coding scheme and that no coding scheme can provide better performance. Two examples where the optimal Shannon entropy-relevance trade-off can be exactly determined are further given.

关键词： Information bottleneck entropy-constrained optimization Renyi entropy coding theorem time-sharing

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Optimal coding for Randomized Kolmogorov Complexity and Its Applications 65

Optimal Coding for Randomized Kolmogorov Complexity and Its ...

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65th Symposium on Foundations of Computer Science

作者： Hirahara, Shuichi Lu, Zhenjian Nanashima, Mikito Natl Inst Informat Tokyo Japan Univ Warwick Coventry W Midlands England Tokyo Inst Technol Tokyo Japan

ISBN: (纸本)9798331516758;9798331516741

The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to obtaining fundamental results in average-case complexity, yet whether any samplable distribution admits a coding theorem for randomized time-bounded Kolmogorov complexity (rK(poly)) is open and a common bottleneck in the recent literature of meta-complexity. Previous works bypassed this issue by considering probabilistic Kolmogorov complexity (pK(poly)), in which public random bits are assumed to be available. In this paper, we present an efficient coding theorem for randomized Kolmogorov complexity under the non-existence of one-way functions, thereby removing the common bottleneck. This enables us to prove rK(poly) counterparts of virtually all the average-case results that were proved only for pK(poly), and enables the resolution of the following concrete open problems. 1) The existence of a one-way function is characterized by the failure of average-case symmetry of information for randomized time-bounded Kolmogorov complexity, as well as a conditional coding theorem for randomized time-bounded Kolmogorov complexity. This resolves the open problem of Hirahara, Ilango, Lu, Nanashima, and Oliveira (STOC'23). 2) Hirahara, Kabanets, Lu, and Oliveira (CCC'24) showed that randomized time-bounded Kolmogorov complexity admits search-to-decision reductions in the errorless average-case setting over any samplable distribution, and left open whether a similar result holds in the error-prone setting. We resolve this question affirmatively, and as a consequence, characterize the existence of a one-way function by the average-case hardness of computing rK(poly) with respect to an arbitrary samplable distribution, which is an rK(poly) analogue of the pK(poly) characterization of Liu and Pass (CRYPTO'23). The key technical lemma is that any d

关键词： Kolmogorov complexity coding theorem one-way functions symmetry of information meta-complexity

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Malleable coding with Fixed Segment Reuse

Malleable Coding with Fixed Segment Reuse

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IEEE International Symposium on Information Theory (ISIT)

作者： Kusuma, Julius Varshney, Lav R. Goyal, Vivek K. MIT Elect Res Lab Cambridge MA 02139 USA

ISBN: (纸本)9781457705953

In cloud computing, storage area networks, and remote backup storage, stored data is modified with updates from new versions. It is desirable for the data to not only be compressed but to also be easily modified during updates, since representing information and modifying the representation are both expensive. A malleable coding scheme considers both compression efficiency and ease of alteration, promoting codeword reuse. We examine the trade-off between compression efficiency and malleability cost-the difficulty of synchronizing compressed versions-measured as the length of a reused prefix portion. Through a coding theorem, the region of achievable rates and malleability is expressed as a single-letter optimization. Relationships to common information problems are also described.

关键词： Channel coding Decoding Entropy Markov processes Random variables Source coding cloud computing coding theorem data compression encoding fixed segment reuse malleable coding scheme optimisation remote backup storage single-letter optimization storage area networks

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On the Capacity and the Zero-Error Capacity of k-Resilient AND Anti-Collusion Codes

On the Capacity and the Zero-Error Capacity of <i>k</i>-Resi...

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IEEE Information Theory Workshop (ITW)

作者： Koga, Hiroki Univ Tsukuba Fac Engn Informat & Syst 1-1-1 Tennoudai Tsukuba Ibaraki 3058573 Japan

ISBN: (纸本)9781479959990

Embedding anti-collusion fingerprinting codes to digital contents enables us to protect the digital contents from piracy. Recently, Trappe et al. proposed an anti-collusion code (AND-ACC) such that all the illegal users are exactly detected from a binary sequence obtained from AND of all the codewords of the illegal users, where the number of the illegal users is assumed to be less than or equal to a constant k >= 2. In this paper we focus on the AND-ACC and analyze the number of codewords M with increasing the codeword length n for an arbitrarily fixed k >= 2. First, we define the zero-error capacity C-k* of the AND-ACC and give a lower and an upper bounds of C-k*. The lower bound of C-k* is obtained by using a lemma used in a coding theorem on the identification codes. In addition, we extend the AND-ACC to the case where negligible detection error is permitted. We define the capacity C k and give a lower and an upper bounds of C-k. These bounds are established by using techniques used for coding of a multiple-access channel.

关键词： encoding watermarking AND-ACC anticollusion fingerprinting codes codeword length coding theorem digital contents identification codes k-resilient AND anticollusion codes multiple-access channel zero-error capacity Bismuth Capacity planning Decoding Detectors Encoding Manganese Upper bound zero-error Digital content Upper bound Capacity planning Watermarking bismuth DEcoding manganese Multiple Access Channel coding Codes

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Robustness of Average-Case Meta-Complexity via Pseudorandomness 2022

Robustness of Average-Case Meta-Complexity via Pseudorandomn...

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54th Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Ilango, Rahul Ren, Hanlin Santhanam, Rahul MIT Cambridge MA 02139 USA Univ Oxford Oxford England Tsinghua Univ Beijing Peoples R China

ISBN: (纸本)9781450392648

We show broad equivalences in the average-case complexity of many different meta-complexity problems, including Kolmogorov complexity, time-bounded Kolmogorov complexity, and the Minimum Circuit Size Problem. These results hold for a wide range of parameters (various thresholds, approximation gaps, weak or strong average-case hardness, etc.) and complexity notions, showing the theory of meta-complexity is very robust in the average-case setting. Our results are shown by establishing new and generic connections between meta-complexity and the theory of pseudorandomness and one-way functions. Using these connections, we give the first unconditional characterization of one-way functions based on the average-case hardness of the Minimum Circuit Size Problem. We also give a surprising and clean characterization of one-way functions based on the average-case hardness of (the worst-case uncomputable) Kolmogorov complexity. Moreover, the latter is the first characterization of one-way functions based on the averagecase hardness of a fixed problem on any samplable distribution. We give various applications of these results to the foundations of cryptography and the theory of meta-complexity. For example, we show that the average-case hardness of deciding k-SAT or Clique on any samplable distribution of high enough entropy implies the existence of one-way functions. We also use our results to unconditionally solve various meta-complexity problems in CZK (computational zero-knowledge) on average, and give implications of our results for the classic question of proving NP-hardness for the Minimum Circuit Size Problem.

关键词： meta-complexity average-case complexity coding theorem minimum circuit size problem Kolmogorov complexity one-way functions

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