def make_non_differential_constellation(m, gray_coded):
side = int(pow(m, 0.5))
if (not isinstance(m, int) or m < 4 or not is_power_of_four(m)):
raise ValueError("m must be a power of 4 integer.")
# Each symbol holds k bits.
k = int(log(m) / log(2.0))
if gray_coded:
# Number rows and columns using gray codes.
gcs = gray_code(side)
# Get inverse gray codes.
i_gcs = mod_codes.invert_code(gcs)
else:
i_gcs = range(0, side)
# The distance between points is found.
step = 2.0/(side-1)
gc_to_x = [-1 + i_gcs[gc]*step for gc in range(0, side)]
# First k/2 bits determine x position.
# Following k/2 bits determine y position.
const_map = []
for i in range(m):
y = gc_to_x[get_bits(i, 0, k/2)]
x = gc_to_x[get_bits(i, k/2, k/2)]
const_map.append(complex(x,y))
return const_map
def make_differential_constellation(m, gray_coded):
"""
Create a constellation with m possible symbols where m must be
a power of 4.
Points are laid out in a square grid.
Bits referring to the quadrant are differentilly encoded,
remaining bits are gray coded.
"""
sqrtm = pow(m, 0.5)
if (not isinstance(m, int) or m < 4 or not is_power_of_four(m)):
raise ValueError("m must be a power of 4 integer.")
# Each symbol holds k bits.
k = int(log(m) / log(2.0))
# First create a constellation for one quadrant containing m/4 points.
# The quadrant has 'side' points along each side of a quadrant.
side = int(sqrtm/2)
if gray_coded:
# Number rows and columns using gray codes.
gcs = gray_code(side)
# Get inverse gray codes.
i_gcs = dict([(v, key) for key, v in enumerate(gcs)])
else:
i_gcs = dict([(i, i) for i in range(0, side)])
# The distance between points is found.
step = 1/(side-0.5)
gc_to_x = [(i_gcs[gc]+0.5)*step for gc in range(0, side)]
# Takes the (x, y) location of the point with the quadrant along
# with the quadrant number. (x, y) are integers referring to which
# point within the quadrant it is.
# A complex number representing this location of this point is returned.
def get_c(gc_x, gc_y, quad):
if quad == 0:
return complex(gc_to_x[gc_x], gc_to_x[gc_y])
if quad == 1:
return complex(-gc_to_x[gc_y], gc_to_x[gc_x])
if quad == 2:
return complex(-gc_to_x[gc_x], -gc_to_x[gc_y])
if quad == 3:
return complex(gc_to_x[gc_y], -gc_to_x[gc_x])
raise StandardError("Impossible!")
# First two bits determine quadrant.
# Next (k-2)/2 bits determine x position.
# Following (k-2)/2 bits determine y position.
# How x and y relate to real and imag depends on quadrant (see get_c function).
const_map = []
for i in range(m):
y = get_bits(i, 0, (k-2)/2)
x = get_bits(i, (k-2)/2, (k-2)/2)
quad = get_bits(i, k-2, 2)
const_map.append(get_c(x, y, quad))
return const_map
