
	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+x⁶+x⁵+x⁴+x+1

The circuit taps correspond to P(x) = (111110011).

Taps: (111110011) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 128 192 96 48 24 140 198 227 241 248 124 190 95 47 151 75 165 210 105 180 218 109 182 91 45 22 11 5 130 65 32 144 72 164 82 169 212 234 117 58 157 206 231 243 121 60 30 15 7 3 1

Period = 51 (autocorrelation)
Output =
100000001100011111010010110110100000100101011100111...

Sequence #3 (Starting with 2)

States: 2 129 64 160 80 40 148 74 37 18 9 132 194 225 112 184 220 238 119 187 221 110 183 219 237 118 59 29 14 135 195 97 176 216 236 246 251 125 62 159 79 167 83 41 20 138 69 34 17 8 4 2

Period = 51 (autocorrelation)
Output =
010000001010010000111011101101110000110111110010100...

Sequence #4 (Starting with 6)

States: 6 131 193 224 240 120 188 222 111 55 27 141 70 35 145 200 100 50 153 204 102 179 217 108 54 155 77 38 19 137 68 162 209 104 52 26 13 134 67 161 208 232 244 122 61 158 207 103 51 25 12 6

Period = 51 (autocorrelation)
Output =
011000001111011000100110011011001000101100001011110...

Sequence #5 (Starting with 10)

States: 10 133 66 33 16 136 196 98 177 88 44 150 203 101 178 89 172 86 171 85 170 213 106 181 90 173 214 107 53 154 205 230 115 185 92 46 23 139 197 226 113 56 28 142 71 163 81 168 84 42 21 10

Period = 51 (autocorrelation)
Output =
010100001000110100110101010110101100111010001110001...

Sequence #6 (Starting with 31)

States: 31 143 199 99 49 152 76 166 211 233 116 186 93 174 215 235 245 250 253 254 255 127 191 223 239 247 123 189 94 175 87 43 149 202 229 114 57 156 78 39 147 73 36 146 201 228 242 249 252 126 63 31

Period = 51 (autocorrelation)
Output =
111110001100101110101111111101111010100111001001001...

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 00:42:17 ADT Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...