Design of small rate, close to ideal, GLDPC-staircase AL-FEC codes for the erasure channel

2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Sayadi³

2012

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Reed Solomon RS(n, k) codes are Maximum Distance Separable (MDS) ideal codes that can be put into a systematic form, which makes them well suited to many situations. In this work we consider use-cases that rely on a software RS codec and for which the code is not fixed. This means that the application potentially uses a different RS(n, k) code each time, and this code needs to be built dynamically. A lightweight code creation scheme is therefore highly desirable, otherwise this stage would negatively impact the encoding and decoding times. Constructing such an RS code is equivalent to constructing its systematic generator matrix. Using the classic Vandermonde matrix approach to that purpose is feasible but adds significant complexity. In this paper we propose an alternative solution, based on Hankel matrices as the base matrix. We prove theoretically and experimentally that the code construction time and the number of operations performed to build the target RS code are largely in favor of the Hankel approach, which can be between 3.5 to 157 times faster than the Vandermonde approach, depending on the (n, k) parameters.

Section: Introductionmentioning

confidence: 94%

Complexity comparison of the use of Vandermonde versus Hankel matrices to build systematic MDS Reed-Solomon codes

2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Sayadi³

2012

Self Cite

“…As shown in [14], GLDPC-Staircase codes exhibit excellent performances under hybrid decoding over the BEC, both for large and very small objects, and both in terms of average performance and low error floor. For instance, with a source block of size K = 1 000 symbols (resp.…”

Section: Gldpc-staircase Performancementioning

confidence: 99%

“…1 Several additional benefits are detailed in [14], like their small rate feature (a large number of repair symbols can be produced, in an incremental way, on demand, while keeping excellent performances) and their major flexibility (the GLDPC-Staircase behavior can be tuned to look more like MDS codes or LDPC-Staircase codes). It makes it possible to adapt to the exact use-case and channel conditions (e.g.…”

Section: Gldpc-staircase Performancementioning

confidence: 99%

“…each repair symbol depends on the previous repair symbol because of the staircase structure of the LDPC code); and (3) the extra-repair symbols generated by RS codes. For the reasons detailed in [14] (i.e. improved performance under ML decoding compared to an irregular distribution), we assume that all the check nodes have the same number, E, of extra-repair symbols.…”

Section: Gldpc-staircase Code Constructionmentioning

confidence: 99%

“…GLDPC-Staircase (N G , K) codes [9] [14] can be represented by a Tanner graph (Fig. 1) with the following meaning: that has the interesting property that the first repair symbol is also equal to the XOR sum of the source symbols.…”

Section: Gldpc-staircase Code Constructionmentioning

confidence: 99%

See 2 more Smart Citations

Optimization with exit functions of GLDPC-Staircase codes for the BEC

Savin

2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

et al. 2012

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In a previous work we introduced the Generalized LDPCStaircase codes for the Binary Erasure Channel, based on LDPC-Staircase codes and Reed Solomon as component codes. In this paper we perform an asymptotic analysis, in terms of EXtrinsic Information Transfer functions and we derive an upper bound of the ML decoding threshold based on the area theorem. We use this analysis to study the impact of the internal LDPC-Staircase code rate on the performance, and show that the proposed Generalized LDPC-Staircase codes closely approach the channel capacity, with only a small number (E = 2, 3) of extra-repair symbols per check node.

Impacts of the packet scheduling on the performance of erasure codes: Methodology and application to GLDPC-Staircase codes

2015 European Conference on Networks and Communications (EuCNC)

Sayadi³

2015

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Content broadcasting over wireless networks heavily relies on Application-Level FEC codes to improve transmission robustness in front of channel erasures. Because they operate in the higher layers of the protocol stack, they benefit from a lot of flexibility. In particular, since streaming applications and bulk transfer applications have different constraints, different packet scheduling strategies may be used by the sender, offering different trade-offs between decoding latency and long erasure burst protection. This work tries to find the best packet scheduling scheme(s) at a sender for a given type of AL-FEC codes.The contributions are twofold: first we define a methodology to measure the impacts of packet scheduling on AL-FEC performance, both under ITerative (IT) and Maximum Likelihood (ML) decoding, for a large set of channels; then we apply this methodology to GLDPC-Staircase codes, an extension of LDPC-Staircase codes using Reed Solomon codes as inner codes. In previous works we showed that these codes have erasure recovery performance close to ideals codes when packets are transmitted in a random order. In this work we show that these codes perform extremely well when sending source packets sequentially first (a key requirement to keep latency minimum with streaming applications) and then extra-repair packets followed by LDPC repair packets, both in a random order. 1