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Optimal Codes in the Class of 2-Bit delay Decodable Codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第1期71卷 797-832页

作者： Hashimoto, Kengo Iwata, Ken-Ichi Univ Fukui Dept Informat Sci Fukui 9108507 Japan

For an integer k >= 0 , k-bit delay decodable code-tuples are source codes that use a finite number of code tables and allow a decoding delay of at most k bits. It is known that the class of k-bit delay decodable code-tuples can achieve a better average codeword length than Huffman codes for k >= 2 . However, it is generally challenging to find an optimal k-bit delay decodable code-tuple (i.e., a k-bit delay decodable code-tuple achieving the optimal average codeword length among all k-bit delay decodable code-tuples) because the class of k-bit delay decodable code-tuples is a comprehensive and flexible class containing a variety of source code consisting of any finite number of code tables. AIFV (almost instantaneous fixed-to-variable length) codes are 2-bit delay decodable code-tuples consisting of two code tables satisfying certain constraints. This paper proves that the class of AIFV codes always contains an optimal 2-bit delay decodable code-tuple for any given source distribution. Thus, we can find an optimal 2-bit delay decodable code-tuple in the class of 2-bit delay decodable code-tuples by considering only the class of AIFV codes, which is a very restricted subclass compared to the whole class of 2-bit delay decodable code-tuples.

关键词： Codes delays decoding Symbols Arithmetic Source coding Probability distribution Iterative decoding Indexes Redundancy Data compression source coding decoding delay average codeword length code-tuples AIFV codes

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Lightweight Instantly Decodable Network Coding: Performance Analysis and Algorithm Design

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IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第1期73卷 317-331页

作者： Su, Rina Sun, Qifu Tyler Wang, Le Liu, Shaoteng Zhang, Zhongshan Song, Linqi Beijing Inst Technol Sch Cyberspace Sci & Technol Beijing 100081 Peoples R China Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 100083 Peoples R China Huawei Technol Co Ltd Network Technol Lab Shenzhen 518129 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China City Univ Hong Kong Shenzhen Res Inst Shenzhen 518057 Peoples R China

We consider broadcasting a block of data packets to multiple users via instantly decodable network coding (IDNC) under the semi-online feedback transmission mode. In this paper, we first introduce a new class of IDNC schemes called lightweight IDNC, tailored for wireless broadcast with stringent computational load at the receiver end. Unlike traditional IDNC that may encode a larger number of original packets together, lightweight IDNC limits each coded packet to a combination of at most two original packets. Explicit lower bounds of the total completion delay as well as the decoding delay are respectively obtained for arbitrary lightweight IDNC schemes. We further investigate the number of transmission rounds as another performance metric, and explicitly characterize its distribution and expectation. The characterizations apply to arbitrary partition-based IDNC schemes, including the lightweight IDNC schemes considered in this paper. A new efficient algorithm is also proposed to construct lightweight IDNC schemes which grants the original packets with lower coding opportunity a higher priority to be encoded. Numerical analyses demonstrate that the lightweight IDNC schemes constructed by the new algorithm not only achieve lower completion and decoding delays in comparison with the ones constructed by the existing algorithm but also adhere closely to theoretical lower bounds, demonstrating their efficiency and practical utility.

关键词： Receivers delays decoding Heuristic algorithms Encoding Wireless communication Network coding Wireless broadcast instantly decodable network coding lightweight completion delay decoding delay transmission rounds

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On the criteria for designing complex orthogonal space-time block codes

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Science China(Information Sciences) 2016年第8期59卷 153-163页

作者： Haibin KAN Xiaodong LIU Guangyue HAN School of Computer Science Fudan University Shanghai Key Laboratory of Intelligent Information Processing Fudan University Department of Mathematics University of Hong Kong

A complex orthogonal design(COD) used in space-time block codes is a kind of combinatorial design. It has been well studied because it has a fast maximum-likelihood decoding algorithm and achieves full diversity. When designing CODs, there are seven characteristics that should be considered, which include code rate, decoding delay, transceiver signal linearization, peak-to-average power ratio, etc. In this paper, we study the relationships among these design criteria. We prove that the maximum rate of generalized CODs(GCODs)that meet the last five criteria is 1/2. Moreover, we present a new method to construct GCODs based on *** this method on balanced complex orthogonal designs(BCODs), we obtain a novel class of GCODs that performs almost perfectly with respect to all the seven properties.

关键词： space-time block code complex orthogonal design decoding delay transceiver signal linearization peak-to-average power ratio(PAPR)

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delay Reduction for Instantly Decodable Network Codes With Lossy Feedback Channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第12期71卷 6821-6833页

作者： Mei, Zhonghui Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing 210003 Peoples R China

In this paper, we study the decoding delay reduction problem for instantly decodable network coding (IDNC) with lossy feedback channels. In order to characterize the uncertainty of the reception state due to erasure feedback, we develop a statistical model of the state feedback matrix, whose elements are employed to indicate the likelihood of the reception status evaluated by the sender. The statistical model of the state feedback matrix can be updated according to the Markov model. With the established statistical model of the state feedback matrix, we build the statistical model of the IDNC graph, which can be used to indicate the likelihood of the coding opportunities among the vertices in the IDNC graph. The decoding delay reduction problem can be formulated as a maximum weight clique (MWC) problem. We develop two heuristic algorithms to solve the MWC problem, namely the maximum weight vertex (MWV) search and the approximate maximum weight path based MWV (A-MWP-MWV) search. Simulation results show that our proposed scheme based on statistical reception status model outperforms the scheme which keeps the reception state unchanged due to lossy feedback in estimating the reception status, and A-MWP-MWV outperforms MWV in solving the MWC problem without increasing additional complexity.

关键词： Instantly decodable network coding lossy feedback decoding delay maximum weight clique problem

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Construction of Low delay Maximal Rate Single-Symbol Decodable Distributed STBC with Channel Phase Information

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Transactions of Nanjing University of Aeronautics and Astronautics 2016年第6期33卷 -页

作者： Chen Junsheng Zhang Xiaofei Shu Feng Wang Jianxin College of Information Engineering Yangzhou University School of Electronic and Optical Engineering Nanjing University of Science and Technology College of Electronic and Information Engineering Nanjing University of Aeronautics and Astronautics National Mobile Communications Research Laboratory Southeast University

Exploiting the source-to-relay channel phase information at the relays can increase the rate upper-bound of distributed orthogonal space-time block codes(STBC)from 2/K to 1/2,where Kis the number of *** technique is known as distributed orthogonal space-time block codes with channel phase information(DOSTBC-CPI).However,the decoding delay of existing DOSTBC-CPIs is not ***,based on the rate of 1/2 balanced complex orthogonal design(COD),an algorithm is provided to construct a maximal rate DOSTBC-CPI with only half the decoding delay of existing *** results show that the proposed method exhibits lower symbol error rate than the existing DOSTBC-CPIs.

关键词： distributed STBC channel phase information decoding delay single-symbol decoding

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On the maximality of languages with combined types of code properties

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THEORETICAL COMPUTER SCIENCE 2014年第C期550卷 79-89页

作者： Kari, Lila Konstantinidis, Stavros Kopecki, Steffen Univ Western Ontario London ON Canada St Marys Univ Halifax NS B3H 3C3 Canada

We consider the decision problem of whether or not a given regular language is maximal with respect to certain combined types of code properties. In the recent past, there have been a few formal methods for defining code properties, such as the trajectory-based type of codes and the transducer-based type of codes, that allow one to decide the maximality problem, including the case where maximality is tested with respect to combined properties within these formal methods. The property of "deciphering delay 1", also known as decoding delay 1, is not known to be definable with these methods, but it is known that the maximality of this property alone is decidable for regular languages. Here, we consider the problem of deciding maximality of a regular language with respect to deciphering delay 1 and a transducer-based property, such as suffix code, overlap-free language, and error-detection properties. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Code properties Deciphering delay decoding delay Decidable Maximal codes Syntactic monoids

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Improved NSC decoding algorithm for polar codes based on multi-in-one neural network

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COMPUTERS & ELECTRICAL ENGINEERING 2020年 86卷

作者： Wang, Xiumin Li, Jun Wu, Zhuoting He, Jinlong Zhang, Yue Shan, Liang China Jiliang Univ Coll Informat Engn CN-310018 Hangzhou Zhejiang Peoples R China Nanjing Univ Informat Sci & Technol Binjiang Coll CN-214105 Wuxi Jiangsu Peoples R China Univ Leicester Dept Engn Aerosp & Computat Engn ACE Res Grp Leicester LE1 7RH Leics England

Neural network-based decoding algorithms have potential value to be researched in the field of polar codes due to their low decoding latency. The neural successive cancellation (NSC) algorithm, combining deep learning and successive cancellation (SC) algorithm of polar codes, was proposed to reduce the latency of decoding. In terms of overall latency, the NSC algorithm does not fully consider the parallel decoding of special nodes in SC decoding tree, which limits the reduction of system delay to a certain extent. In this paper, we propose a multi-in-one neural simplified successive cancellation (MIO-NSSC) decoding algorithm for polar codes based on deep learning. The proposed MIO-NSSC algorithm, which is suitable for general nodes, mainly improves the existing fast simplified successive cancellation (FSSC) and the NSC algorithms to obtain a multi-in-one neural network instead of multiple neural networks in the NSC algorithm by using a new training strategy. Through applying the FSSC algorithm to a special node, the decoding delay of the proposed algorithm is further reduced. The experimental results demonstrate that the proposed MIO-NSSC algorithm can achieve significant latency reduction and resource consumption efficiency improvement compared with the NSC algorithm. The latency of the proposed MIO-NSSC decoding algorithm is about 21% lower than that of the NSC algorithm, and approximately seven neural networks are saved compared with the NSC algorithm. Furthermore, the MIO-NSSC algorithm can reduce the computational complexity without loss of performance. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Polar codes Neural networks decoding delay Neural successive cancellation Simplified successive cancellation

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Feedback-Based Online Network Coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第10期63卷 6628-6649页

作者： Sundararajan, Jay Kumar Shah, Devavrat Medard, Muriel Sadeghi, Parastoo MIT 77 Massachusetts Ave Cambridge MA 02139 USA Qualcomm Res San Diego CA 92121 USA MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA Australian Natl Univ Canberra ACT 2601 Australia

Current approaches to the practical implementation of network coding are batch-based, and often do not use feedback, except possibly to signal completion of a file download. In this paper, the various benefits of using feedback in a network coded system are studied. It is shown that network coding can be performed in a completely online manner, without the need for batches or generations, and that such online operation does not affect the throughput. Although these ideas are presented in a single-hop packet erasure broadcast setting, they naturally extend to more general lossy networks, which employ network coding in the presence of feedback. The impact of feedback on sender-side queue size and receiver-side decoding delay is studied in an asymptotic sense as the traffic load approaches capacity. Different notions of decoding delay are considered, including an order-sensitive notion, which assumes that packets are useful only when delivered in order. Strategies for adaptive coding based on feedback are presented. Our scheme achieves throughput optimality and asymptotically optimal sender queue size and is conjectured to achieve asymptotically optimal in-order delivery delay for any number of receivers. This paper may be viewed as a natural extension of Automatic Repeat reQuest to coded networks.

关键词： ARQ decoding delay network coding

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Fountain-Coding Aided Secure Transmission With delay and Content Awareness

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2020年第7期69卷 7992-7997页

作者： Sun, Li Huang, Dantong Swindlehurst, A. Lee Xi An Jiao Tong Univ Sch Informat & Commun Engn Xian 710049 Peoples R China Zhejiang Lab Hangzhou 311121 Peoples R China Univ Calif Irvine Ctr Pervas Commun & Comp Irvine CA 92697 USA

Fountain coding is a new paradigm for enhancing wireless communications security. In this paper, we investigate how to dynamically construct the fountain code to prevent information leakage and reduce the decoding delay at the legitimate receiver. To be specific, a method is developed to determine how many source packets should be used and which source packets should be chosen to participate in the fountain coding process, taking into account the channel quality, delay constraint, as well as the priorities of various source packets. We also apply the proposed scheme to practical image transmission, and demonstrate the advantages of our scheme via numerical simulations.

关键词： delays decoding Receivers Channel coding Wireless communication Security Physical layer security fountain code decoding delay image transmission

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On decoding of DVR-based linear network codes

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2015年第6期26卷 527-542页

作者： Sun, Qifu Tyler Li, Shuo-Yen Robert Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 100083 Peoples R China Univ Elect Sci & Technol China Chengdu 610054 Peoples R China

The conventional theory of linear network coding (LNC) is only over acyclic networks. Convolutional network coding (CNC) applies to all networks. It is also a form of LNC, but the linearity is w.r.t. the ring of rational power series rather than the field of data symbols. CNC has been generalized to LNC w.r.t. any discrete valuation ring (DVR) in order for flexibility in applications. For a causal DVR-based code, all possible source-generated messages form a free module, while incoming coding vectors to a receiver span the received submodule. An existing time-invariant decoding algorithm is at a delay equal to the largest valuation among all invariant factors of the received submodule. This intrinsic algebraic attribute is herein proved to be the optimal decoding delay. Meanwhile, time-variant decoding is formulated. The meaning of time-invariant decoding delay gets a new interpretation through being a special case of the time-variant counterpart. The optimal delay turns out to be the same for time-variant decoding, but the decoding algorithm is more flexible in terms of decodability check and decoding matrix design. All results apply, in particular, to CNC.

关键词： Linear network coding Discrete valuation ring Cyclic networks decoding delay Time-variant decoding

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