Notes on "Exact Decoding Probability Under Random Linear Network Coding"

Zhao, Xubo

doi:10.1109/lcomm.2012.041112.112564

Cited by 25 publications

(21 citation statements)

References 4 publications

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“…Then, under the independence assumption, we can compute the cdf for broadcast with telescopic codes, e.g. (8) with the resulting pmf in (9). f TB (t; N, 1 , .…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless, RLNC based techniques have the caveat of introducing overhead due to mainly two reasons in the coding process. First, retransmissions of linearly dependent packets occur due to the random selection of the coefficients [8], [9]. Second, in order to later perform decoding, the coding coefficients are appended to each coded packet before being sent through the network.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Overhead of Telescopic Codes in Network Coded Cooperation

Marcano

Heide

Lucani

et al. 2015

2015 IEEE 82nd Vehicular Technology Conference (VTC2015-Fall)

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Although Random Linear Network Coding (RLNC) has been shown to reduce the number of transmissions for multicast scenarios at large enough field sizes, there is an inherent signaling overhead to achieve these benefits. Traditionally, a larger field requires less transmissions but at the cost of a larger coding vector of coefficients. On the contrary, a lower field needs fewer bits to represent the coding coefficients, but has the drawback of requiring more transmissions to deliver the data due to a high probability of linear dependence while receiving the last packets. This work advocates for the use of telescopic network codes as a way to achieve low overhead for cooperation in multicast transmissions over mobile networks. The idea behind them is to design a field of a larger size as a composite of a previous with lower size in order to have arithmetics of the extended field as operations in the base field, hence, allowing the system to use different fields in a single generation. The resulting codes posses very low overhead by having a short coded packet representation besides keeping a low linearly dependent probability for the last packets. We provide an analytical framework that is supported by numerical results showing that is feasible to attain less than 3% total mean overhead instead of higher values with RLNC schemes in most of the considered cases achieving at least 1.5-2x gains.

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“…Then, under the independence assumption, we can compute the cdf for broadcast with telescopic codes, e.g. (8) with the resulting pmf in (9). f TB (t; N, 1 , .…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Overhead of Telescopic Codes in Network Coded Cooperation

Marcano

Heide

Lucani

et al. 2015

2015 IEEE 82nd Vehicular Technology Conference (VTC2015-Fall)

View full text Add to dashboard Cite

show abstract

“…For RLNC, this is not the case, since the occurrence of linearly-dependent coded packets is small, because all coding coefficients are used. Even for GF(2), the average amount of redundant packets for RLNC has been proven to be 1.6 packets after g have been transmitted [41,42], but less than the cases where sparse codes are utilized. Overall, we observe that there is a trade-off between goodput and linearly-dependent coded packets' transmission overhead.…”

Section: Encodingmentioning

confidence: 99%

On Goodput and Energy Measurements of Network Coding Schemes in the Raspberry Pi

et al. 2016

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Abstract:Given that next generation networks are expected to be populated by a large number of devices, there is a need for quick deployment and evaluation of alternative mechanisms to cope with the possible generated traffic in large-scale distributed data networks. In this sense, the Raspberry Pi has been a popular network node choice due to its reduced size, processing capabilities, low cost and its support by widely-used operating systems. For information transport, network coding is a new paradigm for fast and reliable data processing in networking and storage systems, which overcomes various limitations of state-of-the-art routing techniques. Therefore, in this work, we provide an in-depth performance evaluation of Random Linear Network Coding (RLNC)-based schemes for the Raspberry Pi Models 1 and 2, by showing the processing speed of the encoding and decoding operations and the corresponding energy consumption. Our results show that, in several scenarios, processing speeds of more than 80 Mbps in the Raspberry Pi Model 1 and 800 Mbps in the Raspberry Pi Model 2 are attainable. Moreover, we show that the processing energy per bit for network coding is below 1 nJ or even an order of magnitude less in these scenarios.

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“…Typically, the exact decoding probability under RLNC is derived in a fixed topology [11][12][13][14] . Trullols-Cruces et al [11] computed the exact probability that a receiver obtains N linearly independent packets among K N ≥ received packets, when the senders use RLNC over a Galois field.…”

Section: Introductionmentioning

confidence: 99%

“…This problem is equivalent to computing the probability that a N K × matrix has rank N , where each element is randomly selected from a Galois field with equal probability. Deriving the probability that this matrix has full rank in Theorem 1 [12] can be viewed as a special case of Theorem 1 [14] .…”

Section: Introductionmentioning

confidence: 99%

Exact decoding probability of random linear network coding for combinatorial networks

2015

Wuhan Univ. J. Nat. Sci.

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Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a (all) sink(s) represents the impact of major parameters, i.e., the size of field, the number of relays (and sinks) and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers' capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized.

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Notes on "Exact Decoding Probability Under Random Linear Network Coding"

Cited by 25 publications

References 4 publications

On the Overhead of Telescopic Codes in Network Coded Cooperation

On the Overhead of Telescopic Codes in Network Coded Cooperation

On Goodput and Energy Measurements of Network Coding Schemes in the Raspberry Pi

Exact decoding probability of random linear network coding for combinatorial networks

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