
	ECE4253 Digital Communications

	Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Linear Recursive Sequence Generator

Shift registers with feedback essentially divide polynomials to create distinctive binary sequences.

This online tool draws and analyzes digital circuits which generate Linear Recursive Sequences (LRS) based on a defining polynomial P(x). The circuit shown below is traced through all possible states. Maximum length sequences are identified. The autocorrelation of each sequence can also be checked (maximum 1023 bits).

Fibonacci Implementation

alternate configuration Fibonacci

Circuit based on P(x) = x⁸+x⁴+x³+x+1

The circuit taps correspond to P(x) = (100011011).

Taps: (100011011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 128 64 32 16 136 196 98 177 88 44 150 75 165 210 105 52 154 205 102 179 217 236 246 123 61 158 207 231 115 185 220 110 55 155 77 38 147 201 100 50 25 140 198 227 113 56 28 14 7 3 1

Period = 51 (autocorrelation)
Output =
100000001000110100101100110111100111011001001100011...

Sequence #3 (Starting with 2)

States: 2 129 192 96 48 152 76 166 211 233 116 186 221 238 119 187 93 174 87 171 213 106 53 26 141 70 163 81 40 148 202 101 178 89 172 214 107 181 90 173 86 43 149 74 37 146 73 36 18 9 4 2

Period = 51 (autocorrelation)
Output =
010000001100101110111010101100010100110101101010010...

Sequence #4 (Starting with 5)

States: 5 130 193 224 112 184 92 46 23 139 197 226 241 120 60 30 143 199 99 49 24 12 134 195 97 176 216 108 182 91 45 22 11 133 194 225 240 248 124 62 159 79 167 83 169 84 170 85 42 21 10 5

Period = 51 (autocorrelation)
Output =
101000001110100011110001100001101101000011111001010...

Sequence #5 (Starting with 6)

States: 6 131 65 160 80 168 212 234 117 58 157 206 103 51 153 204 230 243 249 252 126 191 95 47 151 203 229 242 121 188 94 175 215 235 245 122 189 222 239 247 251 125 190 223 111 183 219 109 54 27 13 6

Period = 51 (autocorrelation)
Output =
011000001010111001100111111010011110101111011111011...

Sequence #6 (Starting with 8)

States: 8 132 66 161 208 232 244 250 253 254 255 127 63 31 15 135 67 33 144 200 228 114 57 156 78 39 19 137 68 34 145 72 164 82 41 20 138 69 162 209 104 180 218 237 118 59 29 142 71 35 17 8

Period = 51 (autocorrelation)
Output =
000100001011111111000010011100100010010100010110111...

See a detailed analysis and State Table for this circuit.

Specify the taps for your sequence

Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates.


2024-04-29 02:33:25 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...