
	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+x⁴+x³+x²+x+1

The circuit taps correspond to P(x) = (110011111).

Taps: (110011111) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 128 192 224 240 120 60 158 207 231 115 185 92 174 87 43 149 74 37 18 9 4 130 65 160 208 104 180 218 109 182 91 45 150 75 165 210 233 244 250 125 62 31 143 199 99 49 24 12 6 3 1

Period = 51 (autocorrelation)
Output =
100000001111001110101001000001011011010010111110001...

Sequence #3 (Starting with 2)

States: 2 129 64 32 16 136 68 162 81 40 148 202 229 242 249 124 190 223 111 55 27 13 134 195 225 112 184 220 110 183 219 237 118 187 221 238 119 59 29 14 135 67 33 144 72 164 82 41 20 10 5 2

Period = 51 (autocorrelation)
Output =
010000001000101001111101100001110110111011100001001...

Sequence #4 (Starting with 7)

States: 7 131 193 96 48 152 204 230 243 121 188 94 47 23 11 133 194 97 176 88 44 22 139 69 34 145 200 100 178 217 108 54 155 205 102 51 153 76 38 19 137 196 98 177 216 236 246 123 61 30 15 7

Period = 51 (autocorrelation)
Output =
111000001100111101000011010001001101100110010001101...

Sequence #5 (Starting with 8)

States: 8 132 66 161 80 168 84 42 21 138 197 226 113 56 28 142 71 163 209 232 116 58 157 206 103 179 89 172 214 107 181 90 173 86 171 85 170 213 106 53 154 77 166 211 105 52 26 141 70 35 17 8

Period = 51 (autocorrelation)
Output =
000100001010100011100010111001101011010101011001011...

Sequence #6 (Starting with 25)

States: 25 140 198 227 241 248 252 126 63 159 79 39 147 73 36 146 201 228 114 57 156 78 167 83 169 212 234 245 122 189 222 239 247 251 253 254 255 127 191 95 175 215 235 117 186 93 46 151 203 101 50 25

Period = 51 (autocorrelation)
Output =
100110001111110010010011100101011110111111110101110...

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 03:00:10 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...