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raptor.py
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raptor.py
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import constants
import param_gen
import networkx
import matrix
import primes
import math
import copy
from octet_array import octet_array
from schedule import Schedule
class RaptorQ(object):
def __init__(self, symbols):
self.K = symbols.k
self.symbols = symbols
#Tuples are (K',J(K'),S(K'),H(K'),W(K'))
for (self.KP, self.J, self.S, self.H, self.W) in constants.sys_indices:
if self.KP >= self.K:
break
self.L = self.KP + self.S + self.H
self.P = self.L - self.W
self.P1 = primes.next(self.P)
self.U = self.P - self.H
self.B = self.W - self.S
self.current_id = 0
def next(self):
sym_id, ret_sym = self.current_id, self.encode(self.current_id)
self.current_id += 1
return sym_id, ret_sym
def encode(self, X):
d, a, b, d1, a1, b1 = param_gen.tuples(self, X)
result = copy.deepcopy(self.i_symbols[b])
for j in xrange(1,d):
b = (b + a) % self.W
result = result ^ self.i_symbols[b]
while b1 >= self.P:
b1 = (b1+a1) % self.P1
result = result ^ self.i_symbols[self.W+b1]
for j in xrange(1, d1):
b1 = (b1 + a1) % self.P1
while b1 >= self.P:
b1 = (b1+a1) % self.P1
result = result ^ self.i_symbols[self.W+b1]
return result
def calculate_i_symbols(self):
self.a = self.gen_a()
schedule = self.create_schedule()
D = self.calculate_d()
for beta, xor_row, target_row in schedule.ops:
new_row = matrix.multiply_octet_by_row(beta, D[xor_row])
if target_row != None:
D[target_row] ^= new_row
else:
D[xor_row] = new_row
self.i_symbols = [None]*self.L
for i in xrange(self.L):
self.i_symbols[schedule.c[i]] = D[schedule.d[i]]
def calculate_d(self):
d = []
symbolsize = self.symbols.symbolsize*8
for i in xrange(self.S+self.H):
ba = octet_array(symbolsize)
ba.setall(0)
d.append(ba)
for i, symbol in self.symbols:
d.append(octet_array(copy.deepcopy(symbol)))
return d
def create_schedule(self):
n = len(self.symbols)
m = self.S + self.H + n
self.X = copy.deepcopy(self.a)
i = 0
u = self.P
c = range(self.L)
d = range(m)
self.X = copy.deepcopy(self.a)
schedule = Schedule(self.L, m)
schedule_X = Schedule(self.L, m)
#CHECK OUT RIGHT ABOVE SECTION 5.4.2.3
#EFFICIENCY CAN IMPROVE WHEN YOU DONT APPLY ROW OPS TILL THEY"RE CHOSEN IN DECODER
while (i + u) < self.L:
r, rows_with_r = self.rows_in_v_with_min_r(self.a, m, i, u)
if r == 0:
raise Exception("Unable to decode. No nonzero row to choose from v")
#Separate hdpc and non_hdpc rows. Non hdpc should always be handled first
non_hdpc_rows = []
hdpc_rows = []
for row_index in rows_with_r:
if row_index<self.S or row_index>=(self.S+self.H):
non_hdpc_rows.append(row_index)
else:
hdpc_rows.append(row_index)
# If r is two and we have non_hdpc rows then use the graph to find row, otherwise choose any row
# If r is not two choose row with minimum original degree
if r == 2:
if len(non_hdpc_rows) > 0:
chosen_row_index = self.choose_row_from_graph(self.a, m, i, u, non_hdpc_rows)
else:
chosen_row_index = rows_with_r[0]
else:
if len(non_hdpc_rows) > 0:
chosen_row_index = self.choose_min_degree_row(self.a, m, i, u, non_hdpc_rows)
else:
chosen_row_index = self.choose_min_degree_row(self.a, m, i, u, rows_with_r)
self.exchange_row(self.a, i, chosen_row_index, schedule)
self.exchange_row(self.X, i, chosen_row_index, schedule_X)
#Reorder columns, 1 non-zero followed by 0's then r-1 non-zeros
ba = self.a[i].get(i)
if ba.count() == 0:
for col in xrange(self.L-u):
ba = self.a[i].get(col)
if ba.count() > 0:
self.exchange_column(self.a, i, col, schedule)
self.exchange_column(self.X, i, col, schedule_X)
back_col = (self.L-u)-1
front_col = i+1
while front_col < back_col:
front_ba = self.a[i].get(front_col)
while front_ba.count() == 0 and front_col < back_col:
front_col += 1
front_ba = self.a[i].get(front_col)
back_ba = self.a[i].get(back_col)
while back_ba.count() > 0 and back_col > front_col:
back_col -= 1
back_ba = self.a[i].get(back_col)
if front_col < back_col:
self.exchange_column(self.a, front_col, back_col, schedule)
self.exchange_column(self.X, front_col, back_col, schedule_X)
chosen_entry = self.a[i].get(i)
chosen_val = chosen_entry.val()#param_gen.int_from_ba(chosen_entry)
for row_index in xrange(i+1, m):
curr_entry = self.a[row_index].get(i)
curr_val = curr_entry.val()#param_gen.int_from_ba(curr_entry)
if curr_val != 0:
beta = matrix.divide_octet(curr_entry, chosen_entry)
self.xor_row(self.a, beta, i, row_index, schedule)
if chosen_val > 1:
beta = matrix.divide_octet(octet_array('10000000'), chosen_entry)
self.multiply_row(self.a, beta, i, schedule)
i += 1
u += (r-1)
#Discard rows/columns of X
#So we're i x i matrix in lower triangular form
del self.X[i:]
for row in self.X:
del row[i*8:]
#GAUSSIAN ON U_LOWER
for col_index in xrange(i, self.L):
pivot_ba = self.a[col_index].get(col_index)
pivot_val = pivot_ba.val()# param_gen.int_from_ba(pivot_ba)
if pivot_val == 0:
for row_index in xrange(col_index+1, m):
pivot_ba = self.a[row_index].get(col_index)
pivot_val = pivot_ba.val()#param_gen.int_from_ba(pivot_ba)
if pivot_val > 0:
self.exchange_row(self.a, col_index, row_index, schedule)
if pivot_val == 0:
raise Exception("U lower is of less rank than %s." % u)
if pivot_val != 1:
entry_inv = matrix.inverse_octet(pivot_ba)
self.multiply_row(self.a, entry_inv, col_index, schedule)
pivot_ba = self.a[col_index].get(col_index)
for row_index in xrange(col_index+1, m):
curr_entry = self.a[row_index][col_index*8: (col_index+1)*8]
curr_val = curr_entry.val()#param_gen.int_from_ba(curr_entry)
if curr_val != 0:
beta = octet_array('10000000')
if curr_val > 1:
beta = matrix.divide_octet(curr_entry, pivot_ba)
self.xor_row(self.a, beta, col_index, row_index, schedule)
# U Lower should now be in upper triangular form. now attack the top
for col_index in xrange(self.L - 1, self.L - u - 1, -1):
pivot_ba = self.a[col_index].get(col_index)
pivot_val = pivot_ba.val()#param_gen.int_from_ba(pivot_ba)
for row_index in xrange(i, col_index):
curr_ba = self.a[row_index].get(col_index)
curr_val = curr_ba.val()#param_gen.int_from_ba(curr_ba)
if curr_val != 0:
beta = octet_array('10000000')
if curr_val > 1:
beta = matrix.divide_octet(curr_ba, pivot_ba)
self.xor_row(self.a, beta, col_index, row_index, schedule)
#GAUSSIAN ON U_LOWER DONE
# Discard any rows left after l
del self.a[self.L:]
#Multiply X by A to make U_Upper sparse. this means top-left of A is X
#new_top_a = matrix.octet_mat_multiply_bit(self.X, self.a[:i])
#for row_index in xrange(len(new_top_a)):
# self.a[row_index] = new_top_a[row_index]
#Zero out U_Upper with multiples of the identity
for row_index in xrange(i):
for col_index in xrange(i, self.L):
curr_ba = self.a[row_index].get(col_index)
curr_val = curr_ba.val()#param_gen.int_from_ba(curr_ba)
if curr_val != 0:
self.xor_row(self.a, curr_ba, col_index, row_index, schedule)
#Make the rest of A be the identity matrix
'''
for j in xrange(0, i):
curr_ba = self.a[j][j*8:(j+1)*8]
curr_val = curr_ba.val()#param_gen.int_from_ba(curr_ba)
if curr_val != 1:
curr_inv = matrix.inverse_octet_ba(curr_ba)
self.multiply_row(self.a, curr_inv, j, schedule)
curr_ba = self.a[j][j*8:(j+1)*8]
for l in xrange(0, j):
curr_ba = self.a[j][l*8:(l+1)*8]
curr_val = curr_ba.val()#param_gen.int_from_ba(curr_ba)
if curr_val != 0:
pivot_ba = self.a[l][l*8:(l+1)*8]
self.xor_row(self.a, curr_ba, l, j, schedule)
'''
return schedule
@classmethod
def xor_row(cls, a, beta, r1, r2, schedule):
"""
XORS r2 into r1 and records the operation
within the schedule
Arguments:
a -- List of l sized bitarrays
beta -- bitarray indicating multiplier with row r1
r1 -- Integer source row id
r2 -- Integer target row id
schedule -- Schedule to record the operation in
"""
# XOR r2 of a into r1 of a
new_row = matrix.multiply_octet_by_row(beta, a[r1])
a[r2] ^= new_row
# Schedule the xor
schedule.xor(beta, r1, r2)
@classmethod
def multiply_row(cls, a, beta, r1, schedule):
"""
Multiplies A[r1] by beta and records in schedule
Beta must be bitarray
Arguments:
beta -- Integer indicating multiplier with row r1
r1 -- Integer indicating target row
"""
a[r1] = matrix.multiply_octet_by_row(beta, a[r1])
#Schedule the multiply
schedule.multiply(beta, r1)
@classmethod
def exchange_column(cls, a, c1, c2, schedule):
"""
Exchanges column c1 of a with column c2 of a and records the operation
in the schedule
Arguments:
a -- List of bit arrays representing a
c1 -- Integer first column id
c2 -- Integer second column id
schedule -- Schedule of operations performed upon a
"""
# Exchange the columns c1 and c2 in a
for i in xrange(len(a)):
temp = a[i].get(c1)
a[i].set(c1, a[i].get(c2))
a[i].set(c2, temp)
# Record the operation
schedule.exchange_column(c1, c2)
@classmethod
def exchange_row(cls, a, r1, r2, schedule):
"""
Exchanges row r1 of a with row r2 of a and records the operation
in the schedule
Arguments:
a -- list of bitarrays representing a
r1 -- Integer id of first row to exchange
r2 -- Integer id of second row to exchange
schedule -- Schedule to record the operation in
"""
# Exchange r1 with r2 of a
temp = a[r1]
a[r1] = a[r2]
a[r2] = temp
# Record the operation
schedule.exchange_row(r1, r2)
def choose_min_degree_row(self, a, m, i, u, rows_with_r):
"""
Chooses a minimum degree row out of rows with r
Arguments:
a -- List of bitarrays representing matrix a
m -- Integer n + s + h(a should have m rows)
i -- Integer representing the i'th iteration in reducing matrix V
u -- Integer representing number of columns in matix U
rows_with_r -- List of row columns sharing the same number of ones
in matrix V
"""
# Calculate number of non-zero entries in columns of amongst V.
all_degrees = {}
for column in xrange(i, self.L - u):
all_degrees[column] = []
for row in xrange(i, m):
octet_ba = a[row].get(column)
if octet_ba.count() > 0:
all_degrees[column].append(row)
# Degrees contains only columns that contain one of the rows in question
degrees = {}
for row in rows_with_r:
for col in all_degrees:
if row in all_degrees[col]:
degrees[col] = all_degrees[col]
# Find minimum column
min_degree = m + 1
min_column = None
for column in degrees:
if not (len(degrees[column]) == 0):
if len(degrees[column]) < min_degree:
min_degree = len(degrees[column])
min_column = degrees[column]
# Return first row of min column that is among rows_with_r
for row in min_column:
if row in rows_with_r:
return row
def choose_row_from_graph(self, a, m, i, u, graph_rows):
"""
Builds a graph from rows where rows are edges and columns are vertices.
Then chooses the first edge from the largest component
Arguments:
a -- List of bitarrays representing matrix A
m -- Integer total number of rows in A
i -- Integer representing i'th iteration of reducing V
u -- Integer representing number of columns in u
rows_with_r -- List of row indexes that share the same number of ones
in V
"""
#find rows with exactly 2 non-zero entries
graph = networkx.Graph()
for row in graph_rows:
vertices = []
for vertex in xrange(i, self.L - u):
if a[row][vertex*8]:
vertices.append(vertex)
v1, v2 = tuple(vertices)
graph.add_edge(v1, v2, row_index=row)
# Calculate components in graph
components = networkx.connected_component_subgraphs(graph)
# Find the max component
max_component = None
max_size = 0
for c in components:
edges = c.edges(data=True)
if len(edges) > max_size:
max_component = edges
max_size = len(edges)
_, _, data = max_component[0]
row = data['row_index']
return row
def rows_in_v_with_min_r(self, a, m, i, u):
"""
Returns a tuple with the minimum number of 1s in a row in v
and the indexes of the rows containing that number of 1s
Arguments:
a -- List of bitarrays representing the matrix A
m -- Integer total number of rows in A
i -- Integer indicating i'th iteration of reducing V in A
u -- Integer number of columns in matrix U
Returns tuple (minimum r, list of rows with minimum r)
"""
# Find minimum number of ones in a row in sub matrix v.
min_r = None
rows_with_min_r = []
for row_index in xrange(i, m):
v_row = a[row_index]
# let r be the number of ones in a row in v
r = 0
for col_index in xrange(i, self.L-u):
ba = v_row.get(col_index)
if ba.count() > 0:
r += 1
# Ignore rows
if r == 0:
continue
if min_r is None or r < min_r:
min_r = r
rows_with_min_r = [row_index]
elif r == min_r:
rows_with_min_r.append(row_index)
return min_r, rows_with_min_r
def gen_a(self):
'''
Produces matrix A which is used to create intermediate symbols.
A look like the following
+---------------------+
S |ldpc,1 | I_S | ldpc,2|
+---------------------+
H |hdpc | I_H |
+---------------------+
| | (Should have height equal to
KP |g_enc | number of symbols we're given)
+---------------------+
'''
#These have the identity matries built into
#them so all we have to do is put them together
ldpc = self.gen_ldpc()
hdpc = self.gen_hdpc_IH()
g_enc = self.gen_g_enc()
return (ldpc + hdpc + g_enc)
def gen_g_enc(self):
'''
Creates the g_enc matrix. Bottom part of A.
Basically, use the tuples to find indices of C values that
will be xor'd together during encoding for each value of i (ESI).
i corresponds to rows and the indices correspond to columns
'''
g_enc = []
for i, _ in self.symbols:
ba = octet_array(self.L*8)
ba.setall(0)
d, a, b, d1, a1, b1 = param_gen.tuples(self, i)
ba[b*8] = True
for j in xrange(1,d):
b = (b + a) % self.W
ba[b*8] = True
while b1 >= self.P:
b1 = (b1+a1) % self.P1
ba[(self.W + b1)*8] = True
for j in xrange(1, d1):
b1 = (b1 + a1) % self.P1
while b1 >= self.P:
b1 = (b1+a1) % self.P1
ba[(self.W+b1)*8] = True
g_enc.append(ba)
return g_enc
def gen_hdpc_IH(self):
'''
HDPC is MT*GAMMA.
MT is Hx(K'+S) matrix made up of 1's for random values generated based on our columns
or alpha^^i for column K'+S-1 for all rows
GAMMA is (K'+S)x(K'+S) matrix of alpha^^i-j for i>=j or 0
Append I_H to the end
'''
MT = []
#Fill up MT with 0's
for i in xrange(self.H):
ba = octet_array()
for j in xrange(self.KP + self.S):
ba += octet_array('00000000')
MT.append(ba)
#If is is rand_1 or rand_2 set values to 1
for i in xrange(self.H):
for j in xrange(self.KP + self.S):
start = j*8
rand_1 = param_gen.random(j+1,6,self.H)
rand_2 = (rand_1 + param_gen.random(j+1,7,self.H-1) + 1) % self.H
if i == rand_1 or i == rand_2:
MT[i][start] = True
#For column K'+S-1 set all row values to alpha^^row_index
j = self.KP + self.S - 1
start = j*8
end = (j+1)*8
for i in xrange(self.H):
alpha_exp = octet_array.from_val(constants.OCT_EXP[i])
MT[i][start:end] = alpha_exp
#GAMMA[i,j] = alpha ^^ (i-j) for i >= j, 0 otherwise
GAMMA = []
for i in xrange(self.KP + self.S):
ba = octet_array()
for j in xrange(self.KP + self.S):
if i >= j:
ba += octet_array.from_val(constants.OCT_EXP[i-j])
else:
ba += octet_array('00000000')
GAMMA.append(ba)
hdpc = matrix.octet_mat_multiply_bit(MT, GAMMA)
#Throw I_H on the end
for i in xrange(self.H):
for j in xrange(self.H):
if i == j:
hdpc[i] += octet_array('10000000')
else:
hdpc[i] += octet_array('00000000')
return hdpc
def gen_ldpc(self):
'''
LDPC is three parts really
LDPC,1 and 2 have 1's in places correspoding to indices of C
that are added based on LDPC relations
'''
ldpc = []
for i in xrange(self.S):
ba = octet_array(self.L*8)
ba.setall(0)
ldpc.append(ba)
#Create LDPC,1
for i in xrange(self.B):
a = int(1 + math.floor(i / self.S))
b = i % self.S
ldpc[b][i*8] = True
b = (b+a) % self.S
ldpc[b][i*8] = True
b = (b+a) % self.S
ldpc[b][i*8] = True
#Throw I_S in the middle of LDPC
for i in xrange(self.S):
row = i
col = i + self.B
ldpc[row][col*8] = True
#Create LDPC,2
for i in xrange(self.S):
a = i % self.P
b = (i+1) % self.P
ldpc[i][(self.W + a)*8] = True
ldpc[i][(self.W + b)*8] = True
return ldpc