The limitation of permutation polynomial interleavers for turbo codes and a scheme for dithering permutation polynomials

Ryu, Jonghoon; Trifina, Lucian; Balta, Horia

doi:10.1016/j.aeue.2015.06.007

Cited by 12 publications

(5 citation statements)

References 9 publications

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“…Thus, the 4-PPs established in Theorem 1 always allow a PLPP representation with D eq = 4 LPPs. Therefore, from Table 2 in [19] it results that the tightest upper bound derived in [19] is equal to 52. Thus, the upper bound of 36, derived in Theorem 1, is much tighter.…”

Section: Remarksmentioning

confidence: 93%

“…Table 15 shows some CPPs and 4-PPs with optimum minimum distance for several LTE interleaver lengths of the form given in (5). We note that for all these 4-PPs we have D eq = 4, and thus, the best upper bound derived in [19] is equal to 52. Minimum distances (d min ) and corresponding multiplicities (N d min ), spread factors (D), nonlinearity degrees (ζ), and refined nonlinearity degrees (ζ ) for each CPP and each 4-PP are also given in Table 15.…”

Section: Remarksmentioning

confidence: 99%

“…In this subsection, we make some remarks regarding the upper bounds on the minimum distance derived in [19] and those on the minimum distance derived in this paper. From Lemma 3.2 and Table 2 in [19], it results that an upper bound on minimum distance for turbo codes with any degree PP interleavers is equal to 36 in the following conditions:…”

Section: Remarksmentioning

confidence: 99%

“…In [15], upper bounds of the minimum distance for turbo codes with QPP interleavers and different interleaver lengths were obtained. Some upper bounds for PP interleavers of any degree were obtained in [19]. Recently, some results regarding upper bounds of the minimum distance for turbo codes with cubic permutation polynomial (CPP) interleavers have been acquired [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Lengths for Which Fourth Degree PP Interleavers Lead to Weaker Performances Compared to Quadratic and Cubic PP Interleavers

Trifina

Tărniceriu

Ryu

et al. 2020

Entropy

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In this paper, we obtain upper bounds on the minimum distance for turbo codes using fourth degree permutation polynomial (4-PP) interleavers of a specific interleaver length and classical turbo codes of nominal 1/3 coding rate, with two recursive systematic convolutional component codes with generator matrix G = [ 1 , 15 / 13 ] . The interleaver lengths are of the form 16 Ψ or 48 Ψ , where Ψ is a product of different prime numbers greater than three. Some coefficient restrictions are applied when for a prime p i ∣ Ψ , condition 3 ∤ ( p i − 1 ) is fulfilled. Two upper bounds are obtained for different classes of 4-PP coefficients. For a 4-PP f 4 x 4 + f 3 x 3 + f 2 x 2 + f 1 x ( mod 16 k L Ψ ) , k L ∈ { 1 , 3 } , the upper bound of 28 is obtained when the coefficient f 3 of the equivalent 4-permutation polynomials (PPs) fulfills f 3 ∈ { 0 , 4 Ψ } or when f 3 ∈ { 2 Ψ , 6 Ψ } and f 2 ∈ { ( 4 k L − 1 ) · Ψ , ( 8 k L − 1 ) · Ψ } , k L ∈ { 1 , 3 } , for any values of the other coefficients. The upper bound of 36 is obtained when the coefficient f 3 of the equivalent 4-PPs fulfills f 3 ∈ { 2 Ψ , 6 Ψ } and f 2 ∈ { ( 2 k L − 1 ) · Ψ , ( 6 k L − 1 ) · Ψ } , k L ∈ { 1 , 3 } , for any values of the other coefficients. Thus, the task of finding out good 4-PP interleavers of the previous mentioned lengths is highly facilitated by this result because of the small range required for coefficients f 4 , f 3 and f 2 . It was also proven, by means of nonlinearity degree, that for the considered inteleaver lengths, cubic PPs and quadratic PPs with optimum minimum distances lead to better error rate performances compared to 4-PPs with optimum minimum distances.

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Section: Remarksmentioning

confidence: 93%

Section: Remarksmentioning

confidence: 99%

Section: Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lengths for Which Fourth Degree PP Interleavers Lead to Weaker Performances Compared to Quadratic and Cubic PP Interleavers

Trifina

Tărniceriu

Ryu

et al. 2020

Entropy

Self Cite

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“…In essence, Dither adds uniformly distributed noise that is not correlated with the collected signal at the input of the ADC [13][14][15], which can break the correlation between the input signal and the sampling frequency and reduce the accumulation of erroneous codewords [16][17][18]. Then, the noise is subtracted from the output [19] to improve the spurious-free dynamic range (SFDR) of the ADC as much as possible without influencing other performance indicators [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a new chaotic system and its application in ADC

Shen¹,

Zou²,

Zhang³

et al. 2022

Phys. Scr.

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The improvement of Analog-to-Digital Converter (ADC) performance is crucial to improve the data quality of the signal acquisition system. Therefore, based on the dithering technology, combined with the chaotic system, the study designs and analyses a novel method to improve the Spurious-Free dynamic range (SFDR) of the ADC. First, a new five-dimensional chaotic system is proposed in this paper. The chaotic characteristics and dynamic behavior of the new system have been deeply analysed. The analysis methods mainly consist of the Lyapunov exponent, bifurcation diagram, power spectrum and sample entropy. The corresponding simulation model has been developed in Simulink, and the simulation results prove the reality and feasibility of the new chaotic system. Second, the random number homogenization universal algorithm is used to modify the amplitude of the chaotic sequences generated by the new chaotic system. The uniformity and correlation analysis prove that the Dither signal has strong uniformity and randomness. Third, a behaviour-level simulation model of the pipeline ADC is built; then, the narrowband, broadband and different amplitude Dither signals are added to verify the improvement effect for the dynamic performance of the ADC. The experimental results demonstrate that the designed method can improve the SFDR of the ADC by 10.37 dBc, which effectively eliminates the harmonic energy and improves the dynamic performance of the ADC.

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Minimum Distance of Turbo Codes with Permutation Polynomial-Based Interleavers

Trifina

Tărniceriu

2018

Permutation Polynomial Interleavers for Turbo Codes

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The limitation of permutation polynomial interleavers for turbo codes and a scheme for dithering permutation polynomials

Cited by 12 publications

References 9 publications

Lengths for Which Fourth Degree PP Interleavers Lead to Weaker Performances Compared to Quadratic and Cubic PP Interleavers

Lengths for Which Fourth Degree PP Interleavers Lead to Weaker Performances Compared to Quadratic and Cubic PP Interleavers

Dynamical analysis of a new chaotic system and its application in ADC

Minimum Distance of Turbo Codes with Permutation Polynomial-Based Interleavers

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