Weight Distribution of Low-Density Parity-Check Codes

Di, Changyan; Richardson, Tanya; Urbanke, R.

doi:10.1109/tit.2006.883541

Cited by 163 publications

(171 citation statements)

References 15 publications

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“…(8,7) 0.00069 0.00468 0.00047 SPC (9,8) 0.00059 0.00145 0.00112 SPC (10,9) 0.00044 0.00124 SPC (11,10) 0.00244 0.00644 SPC (12,11) 0.98696 0.46560 SPC (13,12) 0.00748 0.52171 SPC (14,13) 0.00214 0.00202 SPC (15,14) 0.00054 0.00299 Ham. (15,11) 0.77169 0.69969 Threshold (by EXIT) 0.552 dB 0.567 dB 2.042 dB 2.059 dB 0.417 dB 0.429 dB perform as well as EE-DGLDPC code in the waterfall region, but it has a slightly a steeper error curve at higher SNRs. All three codes do not show error floors down to BER= 10 −7 .…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In addition, SCNs have more powerful error correcting capability than SPC codes, therefore GLDPC codes generally show better error floor behaviors than LDPC codes. One drawback of GLDPC codes is the so-called "rate loss under iterative decoding", which refers to the fact that GLDPC codes suffer from a certain degree of decoding threshold degradation under iterative decoding [15,16,36]. The rate loss issue is more prominent on sGLDPC codes, which can be addressed by (1) using hGLDPC codes, (2) generalizing GLDPC codes to DGLDPC codes, or (3) efficient puncturing, which will be discussed in Chapter 7.…”

Section: Gldpc Codesmentioning

confidence: 99%

“…Hamming (15,11) code is As an example for SVN node, Table 2.2 shows the { e g,h } of a SPC(6, 5) SVN node using systematic The { e g,h } of a SPC(6, 5) SVN node using systematic G comp . It should be noted that if G comp adopts another form, { e g,h } will be different, resulting in a different EXIT curve, which is not the case with SCN (i.e.…”

Section: Exit Chartsmentioning

confidence: 99%

“…i.e. CNs contain SPCs and SCNs using the same component code, typically the Hamming (15,11) code. In addition, if a SCN has degree n, we say it has n sockets; if there are l (l < n) edges connected to it, we say this SCN has (n − l) empty sockets and l sockets have been filled up.…”

Section: Extending Ace To Eace and The Modified Pegmentioning

confidence: 99%

“…In this experiment, rate-0.5 EE-DGLDPC codes are built according to the following optimized profiles, where SPC(5,4) codes (G comp matrix in systematic form) are used as SVNs and Hamming (15,11) as SCNs.…”

Section: Ee-dgldpc Codesmentioning

confidence: 99%

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Design of Finite-Length Generalized LDPC Codes

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Gldpc Codesmentioning

confidence: 99%

Section: Exit Chartsmentioning

confidence: 99%

Section: Extending Ace To Eace and The Modified Pegmentioning

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Section: Ee-dgldpc Codesmentioning

confidence: 99%

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2013

Wireless Communications

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Silver: Silent VOLE and Oblivious Transfer from Hardness of Decoding Structured LDPC Codes

Couteau

Rindal

Raghuraman

2021

Lecture Notes in Computer Science

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We put forth new protocols for oblivious transfer extension and vector OLE, called Silver, for SILent Vole and oblivious transfER. Silver offers extremely high performances: generating 10 million random OTs on one core of a standard laptop requires only 300ms of computation and 122KB of communication. This represents 37% less computation and ∼ 1300× less communication than the standard IKNP protocol, as well as ∼ 4× less computation and ∼ 14× less communication than the recent protocol of Yang et al. (CCS 2020). Silver is silent: after a one-time cheap interaction, two parties can store small seeds, from which they can later locally generate a large number of OTs while remaining offline. Neither IKNP nor Yang et al. enjoys this feature; compared to the best known silent OT extension protocol of Boyle et al. (CCS 2019), upon which we build up, Silver has 19× less computation, and the same communication. Due to its attractive efficiency features, Silver yields major efficiency improvements in numerous MPC protocols. Our approach is a radical departure from the standard paradigm for building MPC protocols, in that we do not attempt to base our constructions on a well-studied assumption. Rather, we follow an approach closer in spirit to the standard paradigm in the design of symmetric primitives: we identify a set of fundamental structural properties that allow us to withstand all known attacks, and put forth a candidate design, guided by our analysis. We also rely on extensive experimentations to analyze our candidate and experimentally validate their properties. In essence, our approach boils down to constructing new families of linear codes with (plausibly) high minimum distance and extremely low encoding time. While further analysis is of course welcomed in order to gain total confidence in the security of Silver, we hope and believe that initiating this approach to the design of MPC primitives will pave the way to new secure primitives with extremely attractive efficiency features.

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Weight Distribution of Low-Density Parity-Check Codes

Cited by 163 publications

References 15 publications

Design of Finite-Length Generalized LDPC Codes

Design of Finite-Length Generalized LDPC Codes

References

Silver: Silent VOLE and Oblivious Transfer from Hardness of Decoding Structured LDPC Codes

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