A Logarithmic Upper Bound on the Minimum Distance of Turbo Codes

2004 ◽  
Vol 50 (8) ◽  
pp. 1692-1710 ◽  
Author(s):  
M. Breiling
Keyword(s):  
Upper Bound ◽  
Turbo Codes ◽  
Minimum Distance

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

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 bound on the minimum distance of turbo codes

2001 ◽  
Vol 49 (5) ◽  
pp. 808-815 ◽  
Author(s):  
M. Breiling ◽  
J.B. Huber
Keyword(s):  
Upper Bound ◽  
Turbo Codes ◽  
Minimum Distance

scholarly journals Minimum Symbol Error Probability MIMO Design under the Per-Antenna Power Constraint

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Enoch Lu ◽  
I.-Tai Lu
Keyword(s):  
Upper Bound ◽  
Error Probability ◽  
Minimum Distance ◽  
Necessary Conditions ◽  
Mimo Systems ◽  
Symbol Error Probability ◽  
Power Constraint ◽  
Rank One ◽  
Single User ◽  
Numerical Approaches

Approximate minimum symbol error probability transceiver design of single user MIMO systems under the practical per-antenna power constraint is considered. The upper bound of a lower bound on the minimum distance between the symbol hypotheses is established. Necessary conditions and structures of the transmit covariance matrix for reaching the upper bound are discussed. Three numerical approaches (rank zero, rank one, and permutation) for obtaining the optimum precoder are proposed. When the upper bound is reached, the resulting design is optimum. When the upper bound is not reached, a numerical fix is used. The approach is very simple and can be of practical use.

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