CommunicationsSequences

This Julia package provides functions to generate data sequences that are frequently used in digital communications.

• Linear shift-register sequences
• Barker sequences
• Golay complementary sequences
• Zadoff-Chu sequences
• Frank sequences
• Other sequences?
• Expand documentation
• Improve tests

LFSR sequences are implemented as stateful, infinite iterators. The sequence is defined by the feedback taps, specified in Fibonacci notation, from largest to smallest degree. The package pre-defines feedback taps for maximum-length sequences of degrees 2 to 24. While the LFSR produces boolean output by default, it is possible to define arbitrary outputs.

Example:

# Instantiate an LFSR iterator with taps (10, 7, 5)
l = LFSR((10, 7, 5))

# Instantiate a maximum-length LFSR iterator with period 2^16-1
l = LFSR(lfsrtaps[16])

# Specify the outputs to be 1.0 and -1.0
l = LFSR(lfsrtaps[16], mapping = (1.0, -1.0))

# Obtain the first 20 values of the sequence
first(l, 20)

# Obtain the next 20 values -- recall that the iterator is stateful
first(l, 20)

The iterator is quite fast. On an IceLake i5 laptop:

using BenchmarkTools
l = LFSR(lfsrtaps[16], mapping = (1.0, -1.0))
@btime iterate($l, nothing)

results in

  15.192 ns (0 allocations: 0 bytes)

or almost 66 million iterations per second.

Barker sequences (or "codes"), being quite short, are provided as tuples that can be accessed from a dictionary. For example,

barker["7"]

returns the tuple

(1, 1, 1, -1, -1, 1, -1)

The full list of sequences and their keys is:

    "2a" => (1, 1)
    "2b" => (1, -1)
    "3"  => (1, 1, -1)
    "4a" => (1, 1, -1, 1)
    "4b" => (1, 1, 1, -1)
    "5"  => (1, 1, 1, -1, 1)
    "7"  => (1, 1, 1, -1, -1, 1, -1)
    "11" => (1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1)
    "13" => (1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1 , 1)