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Journal articles on the topic 'Uniquely decodable code'

Author: Grafiati

Published: 6 September 2023

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1

Austrin, Per, Petteri Kaski, Mikko Koivisto, and Jesper Nederlof. "Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs." IEEE Transactions on Information Theory 64, no. 2 (February 2018): 1368–73. http://dx.doi.org/10.1109/tit.2017.2688378.

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2

Külekci, Muhammed Oğuzhan, and Yasin Öztürk. "Applications of Non-Uniquely Decodable Codes to Privacy-Preserving High-Entropy Data Representation." Algorithms 12, no. 4 (April 17, 2019): 78. http://dx.doi.org/10.3390/a12040078.

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Non-uniquely-decodable (non-UD) codes can be defined as the codes that cannot be uniquely decoded without additional disambiguation information. These are mainly the class of non–prefix–free codes, where a code-word can be a prefix of other(s), and thus, the code-word boundary information is essential for correct decoding. Due to their inherent unique decodability problem, such non-UD codes have not received much attention except a few studies, in which using compressed data structures to represent the disambiguation information efficiently had been previously proposed. It had been shown before that the compression ratio can get quite close to Huffman/Arithmetic codes with an additional capability of providing direct access in compressed data, which is a missing feature in the regular Huffman codes. In this study we investigate non-UD codes in another dimension addressing the privacy of the high-entropy data. We particularly focus on such massive volumes, where typical examples are encoded video or similar multimedia files. Representation of such a volume with non–UD coding creates two elements as the disambiguation information and the payload, where decoding the original data from these elements becomes hard when one of them is missing. We make use of this observation for privacy concerns. and study the space consumption as well as the hardness of that decoding. We conclude that non-uniquely-decodable codes can be an alternative to selective encryption schemes that aim to secure only part of the data when data is huge. We provide a freely available software implementation of the proposed scheme as well.

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3

Kulhandjian, Michel, Claude D’Amours, and Hovannes Kulhandjian. "Multiway Physical-Layer Network Coding via Uniquely Decodable Codes." Wireless Communications and Mobile Computing 2018 (June 28, 2018): 1–8. http://dx.doi.org/10.1155/2018/2034870.

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We focus on a multiway relay channel (MWRC) network where two or more users simultaneously exchange information with each other through the help of a relay node. We propose for the first time to apply ternary uniquely decodable (UD) code sets that we have developed to allow each user to uniquely recover the information bits from the noisy channel environment. One of the key features of the proposed scheme is that it utilizes a very simple decoding algorithm, which requires only a few logical comparisons. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder is almost as good as the maximum-likelihood (ML) decoder. In addition to that through simulations, we show that the proposed scheme can significantly improve the sum-rate capacity, which in turn can potentially improve overall throughput, as it needs only two time slots (TSs) to exchange information compared to the conventional methods.

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4

Woryna, Adam. "On the set of uniquely decodable codes with a given sequence of code word lengths." Discrete Mathematics 340, no. 2 (February 2017): 51–57. http://dx.doi.org/10.1016/j.disc.2016.08.013.

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5

van den Braak, P. C., and H. van Tilborg. "A family of good uniquely decodable code pairs for the two-access binary adder channel." IEEE Transactions on Information Theory 31, no. 1 (January 1985): 3–9. http://dx.doi.org/10.1109/tit.1985.1057004.

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6

Romashchenko, Andrei, Alexander Shen, and Marius Zimand. "27 Open Problems in Kolmogorov Complexity." ACM SIGACT News 52, no. 4 (December 20, 2021): 31–54. http://dx.doi.org/10.1145/3510382.3510389.

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This formula can be informally read as follows: the ith messagemi brings us log(1=pi) "bits of information" (whatever this means), and appears with frequency pi, so H is the expected amount of information provided by one random message (one sample of the random variable). Moreover, we can construct an optimal uniquely decodable code that requires about H (at most H + 1, to be exact) bits per message on average, and it encodes the ith message by approximately log(1=pi) bits, following the natural idea to use short codewords for frequent messages. This fits well the informal reading of the formula given above, and it is tempting to say that the ith message "contains log(1=pi) bits of information." Shannon himself succumbed to this temptation [46, p. 399] when he wrote about entropy estimates and considers Basic English and James Joyces's book "Finnegan's Wake" as two extreme examples of high and low redundancy in English texts. But, strictly speaking, one can speak only of entropies of random variables, not of their individual values, and "Finnegan's Wake" is not a random variable, just a specific string. Can we define the amount of information in individual objects?

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7

Vanroose, P., and E. C. van der Meulen. "Uniquely decodable codes for deterministic relay channels." IEEE Transactions on Information Theory 38, no. 4 (July 1992): 1203–12. http://dx.doi.org/10.1109/18.144701.

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8

Li, Yatian, Tianwen Geng, and Shijie Gao. "Improve the throughput of M-to-1 free-space optical systems by employing uniquely decodable codes." Chinese Optics Letters 21, no. 3 (2023): 030603. http://dx.doi.org/10.3788/col202321.030603.

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9

Singh, Amiya, Poonam Singh, Arash Amini, and Farokh Marvasti. "Set of uniquely decodable codes for overloaded synchronous CDMA." IET Communications 10, no. 10 (July 1, 2016): 1236–45. http://dx.doi.org/10.1049/iet-com.2015.0819.

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10

Ni, J., and B. Honary. "System state-independent-unique-decodable CCMA codes." IEE Proceedings I Communications, Speech and Vision 140, no. 3 (1993): 185. http://dx.doi.org/10.1049/ip-i-2.1993.0028.

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11

SHARMA, R., P. GUPTA, and R. K. TUTEJA. "LOWER BOUNDS ON $L^t_{1:1}(D)$ IN TERMS OF RENYI ENTROPY." Tamkang Journal of Mathematics 22, no. 4 (December 1, 1991): 335–42. http://dx.doi.org/10.5556/j.tkjm.22.1991.4622.

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In this paper we obtain the lower bounds for the exponentiated mean codeword length (as defined by Campbell [4]) for one-one codes of size $D$ by using the functions which represent possible transformations from one-one codes of size $D$ to uniquely decodable codes.

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12

Mashayekhi, Omid, and Farokh Marvasti. "Uniquely Decodable Codes with Fast Decoder for Overloaded Synchronous CDMA Systems." IEEE Transactions on Communications 60, no. 11 (November 2012): 3145–49. http://dx.doi.org/10.1109/tcomm.2012.081012.110178.

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13

Ahlswede, R., and V. B. Balakirsky. "Construction of uniquely decodable codes for the two-user binary adder channel." IEEE Transactions on Information Theory 45, no. 1 (1999): 326–30. http://dx.doi.org/10.1109/18.746834.

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14

Yu, Qi-Yue, Ya-Tian Li, Wei-Xiao Meng, and Wei Xiang. "Uniquely Decodable Codes for Physical-Layer Network Coding in Wireless Cooperative Communications." IEEE Systems Journal 13, no. 4 (December 2019): 3956–67. http://dx.doi.org/10.1109/jsyst.2019.2891785.

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15

Woryna, Adam. "On the ratio of prefix codes to all uniquely decodable codes with a given length distribution." Discrete Applied Mathematics 244 (July 2018): 205–13. http://dx.doi.org/10.1016/j.dam.2018.02.026.

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16

Bross, S. I., and I. F. Blake. "Upper bound for uniquely decodable codes in a binary input N-user adder channel." IEEE Transactions on Information Theory 44, no. 1 (1998): 334–40. http://dx.doi.org/10.1109/18.651062.

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17

Yu, Qi-Yue, Wei-Xiao Meng, and Shu Lin. "Packet Loss Recovery Scheme with Uniquely-Decodable Codes for Streaming Multimedia over P2P Networks." IEEE Journal on Selected Areas in Communications 31, no. 9 (September 2013): 142–54. http://dx.doi.org/10.1109/jsac.2013.sup.0513013.

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18

Shin, Jae Kyun, and S. Krishnamurty. "On Identification and Canonical Numbering of Pin-Jointed Kinematic Chains." Journal of Mechanical Design 116, no. 1 (March 1, 1994): 182–88. http://dx.doi.org/10.1115/1.2919344.

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This paper deals with the development of a standard code for the unique representation of pin-jointed kinematic chains based on graph theory. Salient features of this method include the development of an efficient and robust algorithm for the identification of isomorphism in kinematic chains; the formulation of a unified procedure for the analysis of symmetry in kinematic chains; and the utilization of symmetry in the coding process resulting in the unique well-arranged numbering of the links. This method is not restricted to simple jointed kinematic chains only, and it can be applied to any kinematic chain which can be represented as simple graphs including open jointed and multiple jointed chains. In addition, the method is decodable as the original chain can be reconstructed unambiguously from the code values associated with the chains.

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19

Kiviluoto, Lasse, and Patric R. J. Ostergard. "New Uniquely Decodable Codes for the $T$-User Binary Adder Channel With $3 \le T \le 5$." IEEE Transactions on Information Theory 53, no. 3 (March 2007): 1219–20. http://dx.doi.org/10.1109/tit.2006.890692.

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20

Xu, Jie, Zhiyong Zheng, Kun Tian, and Man Chen. "Two properties of prefix codes and uniquely decodable codes." Designs, Codes and Cryptography, June 20, 2023. http://dx.doi.org/10.1007/s10623-023-01253-1.

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