Minimum distance upper bounds for 3-dimensional turbo codes using quadratic permutation polynomial interleavers

2008 ◽  
Author(s):  
Eirik Rosnes
Keyword(s):  
Turbo Codes ◽  
Minimum Distance ◽  
Upper Bounds ◽  
Permutation Polynomial ◽  
3 Dimensional

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

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 78
Author(s):  
Lucian Trifina ◽  
Daniela Tarniceriu ◽  
Jonghoon Ryu ◽  
Ana-Mirela Rotopanescu
Keyword(s):  
Upper Bound ◽  
Turbo Codes ◽  
Minimum Distance ◽  
Prime Numbers ◽  
Upper Bounds ◽  
The Other ◽  
Small Range ◽  
Generator Matrix ◽  
Fourth Degree ◽  
Minimum Distances

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.

Upper bounds on the minimum distance for turbo codes using CPP interleavers

2020 ◽  
Author(s):  
Lucian Trifina ◽  
Daniela Tarniceriu ◽  
Jonghoon Ryu ◽  
Ana-Mirela Rotopanescu
Keyword(s):  
Turbo Codes ◽  
Minimum Distance ◽  
Upper Bounds

Further upper bounds on the minimum distance for turbo codes using CPP interleavers

2020 ◽  
Vol 43 ◽  
pp. 101212
Author(s):  
Lucian Trifina ◽  
Daniela Tarniceriu ◽  
Jonghoon Ryu ◽  
Ana-Mirela Rotopanescu
Keyword(s):  
Turbo Codes ◽  
Minimum Distance ◽  
Upper Bounds

A New Upper Bound on the Minimum Distance of Turbo Codes

2004 ◽  
Vol 50 (12) ◽  
pp. 2985-2997 ◽  
Author(s):  
A. Perotti ◽  
S. Benedetto
Keyword(s):  
Upper Bound ◽  
Turbo Codes ◽  
Minimum Distance
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