2018
DOI: 10.24138/jcomss.v14i4.639
|View full text |Cite
|
Sign up to set email alerts
|

Low Complexity Rate Compatible Puncturing Patterns Design for LDPC Codes

Abstract: In contemporary digital communications design, two major challenges should be addressed: adaptability and flexibility. The system should be capable of flexible and efficient use of all available spectrums and should be adaptable to provide efficient support for the diverse set of service characteristics. These needs imply the necessity of limit-achieving and flexible channel coding techniques, to improve system reliability. Low Density Parity Check (LDPC) codes fit such requirements well, since they are capaci… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

1
12
0

Year Published

2018
2018
2021
2021

Publication Types

Select...
3
3

Relationship

2
4

Authors

Journals

citations
Cited by 8 publications
(13 citation statements)
references
References 44 publications
1
12
0
Order By: Relevance
“…Lemma As tfalse→normal∞, gsfalse(tfalse) becomes gsfalse(tfalse)=2thinmathspacej=2drρjWfalse(Ajzsfalse(tfalse)thinmathspacenormalezsfalse(tfalse)false) Proof When tfalse→normal∞, since, as shown in [9], the function ϕfalse(xfalse) has a rapid decrease in x , only the first terms of i=i1dlλiϕfalse(s+false(i1false)tfalse) are important in (1). Thus, we can simplify this sum to i=i1dlλiϕfalse(s+false(i1false)tfalse)=λi1ϕfalse(s+false(i11false)tfalse)+Ofalse(λi2ϕfalse(s+false(i21false)tfalse)false)being λi1 and λi2 the first and second non‐zero λi's, respectively, and observing that, in most practical cases, never λi2 is largely greater than λi1…”
Section: Upper Boundmentioning
confidence: 95%
See 1 more Smart Citation
“…Lemma As tfalse→normal∞, gsfalse(tfalse) becomes gsfalse(tfalse)=2thinmathspacej=2drρjWfalse(Ajzsfalse(tfalse)thinmathspacenormalezsfalse(tfalse)false) Proof When tfalse→normal∞, since, as shown in [9], the function ϕfalse(xfalse) has a rapid decrease in x , only the first terms of i=i1dlλiϕfalse(s+false(i1false)tfalse) are important in (1). Thus, we can simplify this sum to i=i1dlλiϕfalse(s+false(i1false)tfalse)=λi1ϕfalse(s+false(i11false)tfalse)+Ofalse(λi2ϕfalse(s+false(i21false)tfalse)false)being λi1 and λi2 the first and second non‐zero λi's, respectively, and observing that, in most practical cases, never λi2 is largely greater than λi1…”
Section: Upper Boundmentioning
confidence: 95%
“…In [7], an ‘ ad hoc ’ approximation by elementary functions is given (see (8) in [7]) for 0<x<10, which is explicitly invertible. A graph of ϕfalse(xfalse) may be found in [9], where the approximation of ϕfalse(xfalse) and its inverse were derived using the analysis outlined in [10].…”
Section: Low‐complexity Approximation Of the Exact Belief‐propagationmentioning
confidence: 99%
“…Possible future developments may consider the use of different coding schemes suitable for this application such as iteratively decoded low density parity check (LDPC) codes (see, e.g., [43]- [48]) or related structures, including irregular repeat-accumulate (IRA) codes [49], generalized IRA codes (see, e.g., [50]), tornado codes and protograph-based codes [26], turbo codes (see, e.g., [51]- [53]), serial and hybrid concatenated codes (see, e.g. [54]- [56]), concatenated turbo codes [57], and product codes (see, e.g., […”
Section: Conclusion and Open Problemsmentioning
confidence: 99%
“…Given a function δfalse(xfalse) approximating the true function ϕfalse(xfalse), its relative error in absolute value is defined as |εr|=|δfalse(xfalse)ϕfalse(xfalse)|ϕfalse(xfalse)where the true function ϕfalse(xfalse) has been computed through the normalMathematicafalse(Rfalse) statement, numerically approximating ϕfalse(xfalse), published in [4], which, for the computations of this Letter, has been refined to falsefalse{u,320,320falsefalse},thickmathspacethickmathspaceWorkingPrecision>40false]The same definition given in (8), with the appropriate substitutions, holds for the relative error in absolute value |εr|normalinv. of the inverse function δ1false(yfalse) approximating the inverse true function ϕ1false(yfalse).…”
Section: New Not Piecewise Defined Approximation Of ϕFalse(xfalse)mentioning
confidence: 99%
“…See its recent adoption, e.g. to get bounds on LDPC decoding thresholds in [3], rate‐compatible puncturing patterns for LDPC codes in [4], to obtain analytical bit‐error rate expressions in [5], and to design unequal error protection LDPC codes in [6].…”
Section: Introductionmentioning
confidence: 99%