
	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+x⁷+x³+x+1

The circuit taps correspond to P(x) = (110001011).

Taps: (110001011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 128 192 224 240 248 124 190 223 111 183 219 109 54 155 77 38 147 201 228 242 121 60 158 207 103 51 25 12 134 67 33 144 200 100 50 153 204 102 179 217 236 118 187 93 46 23 11 133 66 161 80 40 148 202 229 114 185 220 110 55 27 141 198 99 49 152 76 166 83 41 20 10 5 130 65 160 208 232 116 58 29 14 7 3 1

Period = 85 (autocorrelation)
Output =
1000000011111011011001001111001100001001100110111010000101001110
110001100101000001011...

Sequence #3 (Starting with 2)

States: 2 129 64 32 16 8 132 194 97 176 216 108 182 91 173 214 107 181 90 45 22 139 69 162 81 168 84 42 21 138 197 98 177 88 172 86 171 85 170 213 106 53 154 205 230 115 57 28 142 199 227 241 120 188 94 47 151 203 101 178 89 44 150 75 165 82 169 212 234 245 122 61 30 15 135 195 225 112 56 156 78 39 19 9 4 2

Period = 85 (autocorrelation)
Output =
0100000010000110110101101000101010001101010101100111000111101001
101001010111100001110...

Sequence #4 (Starting with 6)

States: 6 131 193 96 48 24 140 70 163 209 104 180 218 237 246 123 189 222 239 119 59 157 206 231 243 249 252 126 63 159 79 167 211 233 244 250 253 254 255 127 191 95 175 87 43 149 74 37 146 73 36 18 137 196 226 113 184 92 174 215 235 117 186 221 238 247 251 125 62 31 143 71 35 17 136 68 34 145 72 164 210 105 52 26 13 6

Period = 85 (autocorrelation)
Output =
0110000011000101101111011100111111001011111111010100100100011101
011101111100010001001...

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.


2024-04-28 20:45:23 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...