Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix

Garcia-Frías, Javier; Zhong, Wei

doi:10.1109/lcomm.2003.813816

Cited by 181 publications

(122 citation statements)

References 9 publications

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“…For the network model, we assume a random geometric graph G(N, r) model typical for wireless ad-hoc or sensor networks, where N nodes are uniformly distributed over the unit square area and a node can reliably communicate only with the nodes in its transmission range r. In each simulation run, N P parity packets are created in the precoding phase, after which b(N + N P ) = bN I Raptor packets are produced and dispersed across the network during the LT coding phase. In the precoding phase, we apply a distributed version of R = 0.95 regular (4, 76) LDGM precode with the left degree d l = 4 and the right degree d r = 76 [14]. In the LT coding phase, weakened LT code degree distribution of maximum degree d max = 66 proposed for finite-length Raptor code design is used [2].…”

Section: Simulation Resultsmentioning

confidence: 99%

Raptor packets: A packet-centric approach to distributed raptor code design

Vukobratović

Stefanović

Stojaković

et al. 2009

2009 IEEE International Symposium on Information Theory

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Abstract-In this paper, we address the problem of distributed Raptor code design over information packets located across the network nodes. We propose a novel approach to this problem that consists of generating, encoding and dispersing Raptor packets across the network. Unlike recent node-centric proposals, where network nodes are responsible for collecting information packets and performing Raptor encoding, in the proposed packet-centric approach this task is assigned to Raptor packets. In a two-step encoding procedure that corresponds to precoding and LT-coding step of standard Raptor encoding, Raptor packets randomly traverse the network, collect and encode sufficient number of information packets following exactly a given degree distribution, and finish their paths in a random network node. The efficiency of the distributed Raptor coding scheme is confirmed by simulation results, where their performance is demonstrated to approach closely the performance of standard (centralized) Raptor codes.

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Section: Simulation Resultsmentioning

confidence: 99%

Raptor packets: A packet-centric approach to distributed raptor code design

Vukobratović

Stefanović

Stojaković

et al. 2009

2009 IEEE International Symposium on Information Theory

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“…Note that for the main and eavesdropper's channels the noise variances are different, hence the resulting optimal decoding rules are different. For the case of a binary symmetric channel with cross over probability p (14) where d H (y, c j i ) is the Hamming distance between the received vector y and the codeword c j i . In this case, the optimal decoding rule is obtained from (12) aŝ…”

Section: A Optimal Decodermentioning

confidence: 99%

“…Specifically, low density generator matrix (LDGM) codes introduced in [14] are systematic codes with generator matrices of the form G = [I k×k |P k×(n−k) ] where P is a sparse matrix. Hence, given one of G or H, the other can be obtained, and the binary Gaussian elimination can be used for the present setup with ease.…”

Section: ) Binary Gaussian Eliminationmentioning

confidence: 99%

Randomized Convolutional Codes for the Wiretap Channel

Nooraiepour¹,

Duman²

2017

IEEE Trans. Commun.

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Abstract-We study application of convolutional codes to the randomized encoding scheme introduced by Wyner as a way of confusing the eavesdropper over a wiretap channel. We describe optimal and practical sub-optimal decoders for the main and the eavesdropper's channels, and estimate the security gap, which is used as the main metric. The sub-optimal decoder works based on the trellis of the code generated by a convolutional code and its dual, where one encodes the data bits and the other encodes the random bits. By developing a code design metric, we describe how these two generators should be selected for optimal performance over a Gaussian wiretap channel. We also propose application of serially concatenated convolutional codes to this setup so as to reduce the resulting security gaps. Furthermore, we provide an analytical characterization of the system performance by extending existing lower and upper bounds for coded systems to the current randomized convolutional coding scenario. We illustrate our findings via extensive simulations and numerical examples, which show that the newly proposed coding scheme can outperform the other existing methods in the literature in terms of security gap.

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“…(When, after application of FEC, the bit error rate ceases to reduce with decreased Signal-to-Noise Ratio (SNR), an error floor is said to exist.) However, at least for a binary symmetric channel (BSC) it is has been analytically demonstrated [21] that concatenating two LDGM codes (applying one LDGM code after another) overcomes the onset of an error floor, while retaining LDGM's computational complexity, provided a belief-propagation (message-passing) decoding algorithm is employed. Later work [22] confirmed the findings of [21] for a Rayleigh channel and provides analysis on how best to configure LDGM codes.…”

Section: Ldgm Codesmentioning

confidence: 99%

Video over DSL with LDGM Codes for Interactive Applications

et al. 2016

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Digital Subscriber Line (DSL) network access is subject to error bursts, which, for interactive video, can introduce unacceptable latencies if video packets need to be re-sent. If the video packets are protected against errors with Forward Error Correction (FEC), calculation of the application-layer channel codes themselves may also introduce additional latency. This paper proposes Low-Density Generator Matrix (LDGM) codes rather than other popular codes because they are more suitable for interactive video streaming, not only for their computational simplicity but also for their licensing advantage. The paper demonstrates that a reduction of up to 4 dB in video distortion is achievable with LDGM Application Layer (AL) FEC. In addition, an extension to the LDGM scheme is demonstrated, which works by rearranging the columns of the parity check matrix so as to make it even more resilient to burst errors. Telemedicine and video conferencing are typical target applications.

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Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix

Cited by 181 publications

References 9 publications

Raptor packets: A packet-centric approach to distributed raptor code design

Raptor packets: A packet-centric approach to distributed raptor code design

Randomized Convolutional Codes for the Wiretap Channel

Video over DSL with LDGM Codes for Interactive Applications

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