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Generalized Unequal Error Protection LT Codes for Progressive Data

Transmission

Suayb S. Arslan, Student Member, IEEE, Pamela C. Cosman, Fellow, IEEE,and Laurence B. Milstein, Fellow, IEEE

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Outline Introduction Background

UEP DF Code Designs UEP GENERALIZED LT (UEP GLT) CODING

Generalization of “weighted approach” Generalization of EWF codes

Progressive source transmission system description Optimization Numerical Results

Comparisons with the “weighted approach” Comparisons with UEP EWF codes

Conclusion

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Introduction(1/2)UEP(Unequal Error Protection)

Some source symbols are more important than others.

URT(Unequal Recovery Time) The more important section can be recovered earlier in

time.

UIT(Unequal Iteration Time) Evaluate system performance as a function of the iteration

index of the decoding algorithm.

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Introduction(2/2) Introduce a systematic degree-dependent selection concept.

Tailor the parameters of the proposed design to get dramatic improvements in expected distortion.

Apply the generalized LT codes to a progressive source and show that it has better UEP properties than other published results in the literature.

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BackgroundProgressive Source Coding

The beginning part of the bit stream is more important than the succeeding parts of the bit stream.

In progressive source transmission, it is of more concern to consider the decoded useful bits rather than the decoded total bits.

Fountain Codes

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UEP DF Code Designs(1/2)Weighted Approach

1) choose degree according to some degree distribution(DD). 2) for( i = 1 to i = )

A) choose the set from {,, …, } with probability . B) select input symbol uniformly from the set without

replacement. 3) XOR input symbols.

k source symbols = … , and = i j. | | = k is an integer, where 0 < < 1 and = 1.

7UEP DF Code Designs(2/2)Expanding Window Fountain Codes

1) randomly choose a window according to a window selection distribution(SD).—definition 3

2) LT coding is applied only to the bits contained in that window using a suitably chosen degree distribution.—definition 4

k source symbols = … , and = i j. | | = k is an integer, where 0 < < 1 and = 1.r embedded windows such that = .

8UEP GENERALIZED LT (UEP GLT) CODINGApply the degree-dependent selection idea to

provide increased UEP, URT and UIT properties. Generalization of “weighted approach” Generalization of EWF codes

9Generalization of “weighted approach”(1/3)

Parameter size = (r-1)k+k-1

: degree distribution vector

10Generalization of “w

eighted approach”(2/3)

11Generalization of “weighted approach”(3/3)The unequal protections achieved by allowing

coded symbols to make more edge connections with more important information sets.

It is beneficial to have low degree check nodes generally make edge connections with important information sets.

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Generalization of EWF codes

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Generalization of EWF codes

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Progressive source transmission system description

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Progressive source transmission system description

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Optimization(1/3)Design criterion

minimize the average distortion as equation (3).

To reduce the number of optimization parameters Choose SD to be an exponential function of the degree

number.

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Optimization(2/3)

Parameter size = (r-1)k+k-1

Parameter size = 3(r-1) +k-1

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Optimization(3/3)

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Numerical Results Use standard 512*512 Lena and 512*512 Goldhill images. B = 50000 bits Run all realization times 2 different values for k: k=100 and k=1000.

Set r = 2 and + = 1. Use the RSD with = c = 0.01.

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Comparisons with the “weighted approach”

21Comparisons with the “weighted approach”

22Comparisons with the “weighted approach”

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Comparisons with the “weighted approach”

24Comparisons with the “weighted approach”

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Comparisons with the “weighted approach”

26Comparisons with UEP EWF codesTruncated RSD [17]

[17] D. Sejdinovic, D. Vukobratovic, A. Doufexi, V. Senk and R. Piechocki, “Expanding window Fountain codes for Unequal Error Protection”, IEEE Trans. Commun., Vol. 57, No. 9, pp. 2510–2516, Sep. 2007.

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Comparisons with UEP EWF codes

GLTexp ： This scheme uses the Exponential SD with and optimizes the set { , } so that the proposed scheme achieves minimum distortion.

GLTexpOpt ： This scheme uses the Exponential SD with . It optimizes the set { , , , } so that the proposed scheme achieves minimum distortion.

GLTexpFullOpt ： This scheme uses the Exponential SD and optimizes the whole set of parameters { , , , , } so that the proposed scheme achieves minimum distortion.

As increasing the parameter space， we observe dramatic improvements in a progressive transmission scenario.

28Comparisons with UEP EWF codes

29Comparisons with UEP EWF codes