LE DEBRUITAGE DES IMAGES SONAR EN UTILISANT LA THEORIE DES ONDELETTES SORIN MOGA ET ALEXANDRU ISAR

LE DEBRUITAGE DES IMAGES SONAR EN UTILISANT LA

THEORIE DES ONDELETTES

SORIN MOGA ET ALEXANDRU ISAR

ISETc 2010, Timisoara, November 11, 2010

A Study of the Permutation SchemesUsed in Mobile Wireless Communications

Ioan Eugen Andor, Lucian Ardelean, Horia Baltă, Maria Kovaci, Marius Oltean and Alexandru Isar





Permutations: What for ?

- decorrelation

- spreading

noise

141 2 3 4 155 6 7 8 9 10 11 12 13

125 9 1 11 615 2 10 7 4 14 13 8 3

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Permutations: How?

- hard

- soft

1

input

2345678

2output

7541863

Berrou & others, 2004:(j) = (P*j + Q + 1) – N * int((P*j + Q + 1) / N), 0 j NQ=0 if j=0 mod 4,Q=int(N/2)+P1 if j=1 mod 4,Q=P2 if j=2 mod 4 andQ=int(N/2)+P3 if j=3 mod 4, where P=19, P1=376, P2=224, P3=600,

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Permutations in Encryption

99 124 119 123 242 107 111 197 48 1 103 43 254 215 171 118202 130 201 125 250 89 71 240173 212 162 175 156 164 114 192183 253 147 38 54 63 247 204 52 165 229 241 113 216 49 21 4 199 35 195 24 150 5 154 7 18 128 226 235 39 178 117 9 131 44 26 27 110 90 160 82 59 214 179 41 227 47 132 83 209 0 237 32 252 177 91106 203 190 57 74 76 88 207208 239 170 251 67 77 51 133 69 249 2 127 80 60 159 168 81 163 64 143 146 157 56 245188 182 218 33 16 255 243 210205 12 19 236 95 151 68 23196 167 126 61 100 93 25 115 96 129 79 220 34 42 44 136 70 238 184 20 222 94 11 219224 50 58 10 73 6 36 92194 211 172 98 145 149 228 121231 200 55 109 141 213 78 169108 86 244 234 101 122 174 8186 120 37 46 28 166 180 198232 221 116 31 75 189 139 138112 62 181 102 72 3 246 14 97 53 87 185 134 193 29 158225 248 152 17 105 217 42 148155 30 135 233 206 85 40 223140 161 137 13 191 230 66 104 65 153 45 15 176 84 187 22

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Permutations in WiMAX

• WiMAX uses OFDMA at the physical level• PERMUTATION = a way to allocate physical subcarriers to users• Result: physical resources (subcarriers) are mapped to logical

resources (subchannels)• Case of Study: DownLink PUSC 512• The available subcarriers are SPLIT in three segments• Every segment contains 140 subcarriers (data + pilots) • Frequency spreading: the 140 subcarriers are not adjacent in the

physical spectrum

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Example

• Pilots are different for odd/even symbols

• Guard band at the edge of the frequency band

• Segment0=120 Data+20 Pilots• The data subcarriers are split in 5

subchannels (5 subch x 24 subcarriers) = 120 subcarriers

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How it’s a subchannel composed ?

• The basic formula is:

• What physical subcarrier corresponds to the logical subcarrier k (k=0,…,23) from the logical subchannel s (s=0,…4) ?

• nk= (k+13s) mod 24• ps(j)=series obtained by shifting s times to the left the basic

permutation sequence• DLPermBase = an integer ranging from 0 to 31: is the one providing

randomness to the subchannel allocation • Ex. Subcarrier (3,2)=5*nk+[ps(nk mod 5)+0] mod 5 = 5 * 5 +3 = 28• Meaning: the logical subcarrier 3 from the logical subchannel 2 is

the 28th subcarrier available in the physical spectrum (out of the 120 allocated to segment 0).

• What is the reason behind…?

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Turbo-codes Permutations

û

DEC1

DI

DEC0

I I

Cha

nnel

Iex10

y1

y2

y0

LLR1

C1

C0

I

ux1

x2

x0

P

C1

Iex01

I

Interleaver :

Rectangular Random Decorrelation: minimum maximum

Spreading: maximum minimum

Berrou & others (2004): regular-random Crozier (2000): S-interleaver

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Distances Spectrum

Interleaving / de-interleaving : I I, with I = 1,2, ... N

-1 : I I, with -1( (i) ) = i, iIInterleaving distance: d(i, j) = i –j+ (i) – (j), i, j I, i j Minimum interleaving distance:

dmin = ji,dmin

jiIji,

ids(k)

k

700

600

500

400

300

200

100

00 400 800 1200 1600 2000

Distances Spectrum (DS), ids : J = 1, 2, ... , 2N Nids(k) = pairs number (i, j) I I for that d(i, j) = k

Spreading Degree (SD): sd = suppids(k) / ids(k) Jk

max

Random-interleaver DS:

-1

21

( - ) ( - )1 1 - -

k

x N

N x N k xids k x N k x N

C

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Frequencies’ Table

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Frequency positions DS

0 60 120 180 240 3000

30

60

90

120

150

0 60 120 180 240 3000

30

60

90

120

150no[d(i,j)=k]

d(i,j)=k

DS for the S-interleaver with S=13 and N=140

DS for the interleaver defined by the positions’ sequence of the 140 sub-carriers’ frequencies of a

BS segment

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Frequency positions DS

The DSs Parameters

Parameter S-interleaver Frequencies’ positionspermutation system

DL-PUSC

dmin

Dmax

smax

suppGN

1325395

2332.4526

140

3268121249

2.0579140

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Conclusions

- DL-PUSC permutation of the sub-carriers’ frequencies is very good. It minimizes the collision probability also for the case of mobile users, spreading the sub-carriers’ frequencies at an important distance;

-the fact that there are permutations with a higher spreading degree, lead us to the idea that this permutation can be improved. A more detailed analysis can leads to results more precise.

- the Turbo-codes permutations methods can be used to develop more performant methods for permutation of the sub-carriers’ frequencies in WiMAX.

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References

[1] H. Balta, S. El Assad, „Interleaving Distances Spectrum Comparison between Turcocodes Interleavers”, European Microwave Week, 10-15 September 2006, Manchester, UK;[2] S. Dolinar, and D. Divsalar, “Weight Distributions for Turbo Codes Using Random and Non-random Permutations”, TDA Progress Report 42-122, August 15, 1995.[3] IEEE 802.16e standard: "Air Interface for Fixed and Mobile Broadband Wireless Access Systems", December 2005;[4] D. Bojneagu, "The mapping of physical subcarriers to logical subchannels in OFDMA DL-PUSC 512 system", Alcatel-Lucent technical memo;[5] C. Berrou, Y. Saouter, C. Douillard, S. Kerouédan, and M. Jézéquel, “Designing good permutations for turbo codes: Toward a single model,” in Proc. IEEE Int. Conf. Commun., Paris, France, Jun. 2004, pp. 341–345.[6] S.N. Crozier, “New High-Spread High-Distance Interleavers for Turbo-Codes”, 20th Biennial Symposium on Communications, Kingston, Ontario, Canada, May 28-31, 2000, pp.3-7.

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LE DEBRUITAGE DES IMAGES SONAR EN UTILISANT LA THEORIE DES ONDELETTES SORIN MOGA ET ALEXANDRU ISAR