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The minimum decoding delay for Convolutional Network Coding

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2010年第8期E93A卷 1518-1523页

作者： Guo, Wangmei Cai, Ning Xidian Univ State Key Lab ISN Xian 710071 Peoples R China

In this paper, we derive a lower bound on the minimum decoding delay for convolutional network codes, which provides us with a guide line in the performance of decoding delay for convolutional network code decoders. The lower bound can be achievable by the sequential decoder introduced by E. Erez and F. Feder. Then we discuss the relationship between the network topology and the minimum decoding delay. Finally, we illustrate our results by an example.

关键词： convolutional network coding minimum decoding delay sequential decoder

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The minimum decoding delay of maximum rate complex orthogonal space-time block codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2007年第8期53卷 2677-2684页

作者： Adams, Sarah Spence Karst, Nathaniel Pollack, Jonathan Franklin W Olin Coll Engn Needham MA 02492 USA

The growing demand for efficient wireless transmissions over fading channels motivated the development of space-time block codes. Space-time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum-likelihood decoding algorithm while achieving full transmit diversity. The two main research problems for these complex orthogonal space-time block codes (COSTBCs) have been to determine for any number of antennas the maximum rate and the minimum decoding delay for a maximum rate code. The maximum rate for COSTBCs was determined by Liang in 2003. This paper addresses the second fundamental problem by providing a tight lower bound on the decoding delay for maximum rate codes. It is shown that for a maximum rate COSTBC for 2m - 1 or 27m. antennas, a tight lower bound on decoding delay is r=((2m)(m-1)). This lower bound on decoding delay is achievable when the number of antennas is congruent to 0, 1, or 3 modulo 4. This paper also derives a tight lower bound on the number of variables required to construct a maximum rate COSTBC for any given number of antennas. Furthermore, it is shown that if a maximum rate COSTBC has a decoding delay of r where r < r <= 2r, then r = 2r. This is used to provide evidence that when the number of antennas is congruent to 2 modulo 4, the best achievable decoding delay is 2 ((2m)(m-1)).

关键词： generalized complex orthogonal design (GCOD) maximum rate minimum decoding delay multiple-input multiple-output (MIMO) space-time block code

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minimum Broadcast decoding delay for Generalized Instantly Decodable Network Coding

Minimum Broadcast Decoding Delay for Generalized Instantly D...

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IEEE Global Telecommunications Conference (GLOBECOM 2010)

作者： Sorour, Sameh Valaee, Shahrokh Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

ISBN: (纸本)9781424456383

In this paper, we introduce the concept of generalized instantly decodable network coding (G-IDNC) to further minimize decoding delay in wireless broadcast, compared to strict instantly decodable network coding (S-IDNC), studied in [1], [2]. G-IDNC loosens the strict instant decodability constraint in order to target more receivers while preserving the attractive properties of S-IDNC. We show that the minimum decoding delay problem for G-IDNC can be formulated as a maximum weight clique problem over a well structured graph. Since finding the maximum weight clique of a graph is NP-hard, we design a simple heuristic G-IDNC algorithm with sub-optimal performance. However, simulation results show that both proposed optimal and heuristic G-IDNC algorithms considerably outperform several other SIDNC and G-IDNC optimal and heuristic approaches.

关键词： Wireless Broadcast Network Coding minimum decoding delay Maximum Weight Clique Problem

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Novel Classes of Minimal delay and Low PAPR Rate 1/2 Complex Orthogonal Designs

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第4期57卷 2254-2262页

作者： Adams, Sarah Spence Davis, James Karst, Nathaniel Murugan, Mathav Kishore Lee, Bryce Crawford, Matthew Greeley, Caitlin Franklin W Olin Coll Engn Needham MA 02492 USA Univ Richmond Richmond VA 23173 USA Cornell Univ Ctr Appl Math Ithaca NY 14850 USA Indian Inst Technol Kharagpur 721302 W Bengal India

Complex orthogonal designs (CODs) of rate 1/2 have been considered recently for use in analog transmissions and as an alternative to maximum rate CODs due to the savings in decoding delay as the number of antennas increases. While algorithms have been developed to show that an upper bound on the minimum decoding delay for rate 1/2 CODs with n = 2m - 1 or n = 2m columns is nu(n) = 2(m-1) or nu(n) = 2(m), depending on the parity of n modulo 8, it remains open to determine the exact minimum delay. This paper shows that this bound nu(n) is also a lower bound on minimum decoding delay for a major class of rate 1/2 CODs, named balanced complex orthogonal designs (BCODs), and that this is the exact minimum decoding delay for most BCODs. These rate 1/2 codes are conjugation-separated and thus permit a linearized description of the transceiver signal. BCODs also display other combinatorial properties that are expected to be useful in implementation, such as having no linear processing. An elegant construction is provided for a class of rate 1/2 CODs that have no zero entries, effectively no irrational coefficients, no linear processing, and have each variable appearing exactly twice per column. The resulting codes meet the aforementioned bound on decoding delay in most cases. This class of CODs will be useful in practice due to their low peak-to-average power ratio (PAPR) and other desirable properties.

关键词： Complex orthogonal design minimum decoding delay multiple-input-multiple-output PAPR space-time block code

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A Lossy Graph Model for delay Reduction in Generalized Instantly Decodable Network Coding

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IEEE WIRELESS COMMUNICATIONS LETTERS 2014年第3期3卷 281-284页

作者： Douik, Ahmed Sorour, Sameh Al-Naffouri, Tareq Y. Alouini, Mohamed-Slim King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn CEMSE Div Thuwal Makkah Province Saudi Arabia KFUPM Dept Elect Engn Dhahran Eastern Provinc Saudi Arabia KAUST CEMSE Thuwal Makkah Province Saudi Arabia

The problem of minimizing the decoding delay in Generalized instantly decodable network coding (G-IDNC) for both perfect and lossy feedback scenarios is formulated as a maximum weight clique problem over the G-IDNC graph in [1]-[3]. In this letter, we introduce a new lossy G-IDNC graph (LG-IDNC) model to further minimize the decoding delay in lossy feedback scenarios. Whereas the G-IDNC graph represents only doubtless combinable packets, the LG-IDNC graph represents also uncertain packet combinations, arising from lossy feedback events, when the expected decoding delay of XORing them among themselves or with other certain packets is lower than that expected when sending these packets separately. We compare the decoding delay performance of LG-IDNC and G-IDNC graphs through extensive simulations. Numerical results show that our new LG-IDNC graph formulation outperforms the GIDNC graph formulation in all lossy feedback situations and achieves significant improvement in the decoding delay especially when the feedback erasure probability is higher than the packet erasure probability.

关键词： minimum decoding delay lossy feedback G-IDNC graph maximum weight clique problem

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delay Reduction in Lossy Intermittent Feedback for Generalized Instantly Decodable Network Coding

Delay Reduction in Lossy Intermittent Feedback for Generaliz...

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IEEE 9th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

作者： Douik, Ahmed Sorour, Sameh Alouini, Mohamed-Slim Al-Naffouri, Tareq Y. KAUST Thuwal Saudi Arabia

ISBN: (纸本)9781457720147

In this paper, we study the effect of lossy intermittent feedback loss events on the multicast decoding delay performance of generalized instantly decodable network coding. These feedback loss events create uncertainty at the sender about the reception statues of different receivers and thus uncertainty to accurately determine subsequent instantly decodable coded packets. To solve this problem, we first identify the different possibilities of uncertain packets at the sender and their probabilities. We then derive the expression of the mean decoding delay. We formulate the Generalized Instantly Decodable Network Coding (G-IDNC) minimum decoding delay problem as a maximum weight clique problem. Since finding the optimal solution is NP-hard, we design a variant of the algorithm employed in [1]. Our algorithm is compared to the two blind graph update proposed in [2] through extensive simulations. Results show that our algorithm outperforms the blind approaches in all the situations and achieves a tolerable degradation, against the perfect feedback, for large feedback loss period.

关键词： Multicast Channels Lossy Intermittent Feedback minimum decoding delay Maximum Weight Clique Problem

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