Erasure Codes with a Banded Structure for Hybrid Iterative-ML Decoding

Soro, Alexandre; Cunche, Mathieu; Lacan, Jérôme; Roca, Vincent

doi:10.1109/glocom.2009.5426098

Cited by 4 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is well known that the complexity of the GE algorithm can be reduced if the system matrix is structured in some specific way. For instance, the use of a band structure to reduce the ML decoding complexity has been studied in [11] and [10]. In this section, we show that the parity check matrix of QC-LDPC codes features such a "hidden" band structure, that allows for considerably reducing the complexity of ML decoding with standard GE.…”

Section: Pseudo-band Matrix Transformation and ML Decoding Complmentioning

confidence: 92%

Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

Cunche

Savin

Roca

2010

2010 International Symposium on Information Theory &Amp; Its Applications

Self Cite

View full text Add to dashboard Cite

In this paper, we show that over the binary erasure channel, Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding. We demonstrate that the quasicyclic structure of the parity-check matrix can be advantageously used in order to significantly reduce the complexity of the ML decoding. This is achieved by a simple row/column permutation that transforms a QC matrix into a pseudo-band form. Based on this approach, we propose a class of QC-LDPC codes with almost ideal error correction performance under the ML decoding, while the required number of row/symbol operations scales as k √ k, where k is the number of source symbols. I. PROBLEM POSITION AND RELATED WORKSIn modern communication systems, data is often transmitted as independent packets. These packets can be subject to losses (erasures) caused by bad channel conditions, intermittent connectivity, congested routers, or failures. If solutions based on the retransmission of lost packets are possible (ARQ, Automatic Repeat Requests), they are not always suitable (e.g. broadcasting), nor possible (no return link, e.g. satellite communications). In such cases Forward Error Correction (FEC) schemes represent the foremost alternative. These schemes rely on erasure codes operating either at the transport or the application layer of the communication system, which are able to recover lost data thanks to the transmission of redundant (repair) packets.In the family of error-correcting codes, a prominent role is played by Low-Density Parity-Check (LDPC) codes. They feature a linear complexity iterative (IT) decoding, and can be optimized for a broad class of channels, with asymptotically performance close to the theoretical Shannon limit. Although iterative and maximum likelihood (ML) are equivalent for cycle-free codes, for a given finite code (with cycles) the gap between their performance can be significant. Hence, ML decoding has been recently considered in order to improve the correction capacity of LDPC codes over the binary erasure channel (BEC) for short to moderate code-length. This comes at a cost in the decoding complexity; however, efficient ML decoding algorithms with reduced complexity have been proposed over the last few years [1].Before discussing the complexity of the ML decoding, let us first consider the complexity of the encoding process. Encoding a systematic LDPC code is equivalent to solving a linear system H p P = H s S, where H = (H s , H p ) is the paritycheck matrix of the code, and S and P denote respectively This work was supported by the French ANR grant No 2006 TCOM 019 (CAPRI-FEC project).the sequences of source and parity bits. This can be done by Gaussian elimination (GE), whose complexity 1 , expressed as the number of row operations 2 , is expected to scale as k 2 , where k denotes the number of source bits. However, it has been shown in [9] that the GE can take advantage of the sparseness of the parity check matrix, and it can be efficiently performed in O((gk) 2 ) row/symbol operations, where g is called the...

show abstract

Section: Pseudo-band Matrix Transformation and ML Decoding Complmentioning

confidence: 92%

Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

Cunche

Savin

Roca

2010

2010 International Symposium on Information Theory &Amp; Its Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, as we detail in Section IV, the definition of the encoding window used in our paper is not the same as in [20] due to the different goal of our work. Other related approaches based on the concept of encoding window can be found in [21], [22]. However, as in [20], both papers consider a simple source-receiver scenario and do not consider recombinations at the network nodes.…”

Section: Related Workmentioning

confidence: 99%

“…In detail, [21] proposes an LDPC scheme that aims at minimizing the memory accesses during encoding, but the properties of the code are shown for very large block sizes and windows, which would be an issue for multimedia applications. In [22], a class of LDPC codes with a hybrid iterative/maximum likelihood decoding scheme is presented, where the generator matrix is designed to have a banded structure so to reduce the maximum likelihood decoding complexity. Therefore, to the best of our knowledge, our work is the first to leverage the concept of encoding window to solve the problem of preserving the decoding complexity through the recombinations at the network nodes, which is the main novelty of our work.…”

Section: Related Workmentioning

confidence: 99%

Band Codes for Energy-Efficient Network Coding With Application to P2P Mobile Streaming

Fiandrotti

Bioglio

Grangetto

et al. 2014

IEEE Trans. Multimedia

View full text Add to dashboard Cite

A key problem in network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments. Controlling and hence limiting such factors has always been an important but elusive research goal, since the packet degree distribution, which is the main factor driving the complexity, is altered in a non-deterministic way by the random recombinations at the network nodes. In this paper we tackle this problem with a new approach and propose Band Codes (BC), a novel class of network codes specifically designed to preserve the packet degree distribution during packet encoding, recombination and decoding. BC are random codes over GF(2) that exhibit low decoding complexity, feature limited and controlled degree distribution by construction, and hence allow to effectively apply NC even in energy-constrained scenarios. In particular, in this paper we motivate and describe our new design and provide a thorough analysis of its performance.We provide numerical simulations of the BC performance in order to validate the analysis and assess the overhead of BC with respect to a conventional random NC scheme. Moreover, experiment in a realworld application, namely peer-to-peer mobile media streaming using a random-push protocol, show that BC reduce the decoding complexity by a factor of two with negligible increase of the encoding overhead, paving the way for the application of NC to power-constrained devices.

show abstract

“…To compute the latter value, we count the number of times a received packet is subtracted from an encoded packet and the number of operations needed to invert the matrices. The method used is similar to [11]. Please note that one operation represents a linear combination of two vectors, as this is the most complex component of an operation; we neglect the multiplication of a vector by a scalar and the size of the vector as these are simple operations.…”

Section: Evaluation Of Code Complexitymentioning

confidence: 99%

Memory and complexity analysis of on-the-fly coding schemes for multimedia multicast communications

Smith

Lochin

Lacan

2012

2012 IEEE International Conference on Communications (ICC)

Self Cite

View full text Add to dashboard Cite

A new class of erasure codes for delay-constraint applications, called on-the-fly coding, have recently been introduced for their improvements in terms of recovery delay and achievable capacity. Despite their promising characteristics, little is known about the complexity of the systematic and non-systematic variants of this code, notably for live multicast transmission of multimedia content which is their ideal use case. Our paper aims to fill this gap and targets specifically the metrics relevant to mobile receivers with limited resources: buffer size requirements and computation complexity of the receiver. As our contribution, we evaluate both code variants on uniform and bursty erasure channels. Results obtained are unequivocal and demonstrate that the systematic codes outperform the nonsystematic ones, in terms of both the buffer occupancy and computation overhead.

show abstract

Erasure Codes with a Banded Structure for Hybrid Iterative-ML Decoding

Cited by 4 publications

References 15 publications

Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

Band Codes for Energy-Efficient Network Coding With Application to P2P Mobile Streaming

Memory and complexity analysis of on-the-fly coding schemes for multimedia multicast communications

Contact Info

Product

Resources

About