Here are some coding theory scripts I’ve written in python for ease of learning and to handle homework tasks from the Hankerson textbook.
KBITS
KBITS FUNCTION for generating all binary numbers of length n and k 1 bits.
import itertools
def kbits(n, k):
result = []
for bits in itertools.combinations(range(n), k):
s = ['0'] * n
for bit in bits:
s[bit] = '1'
result.append(''.join(s))
return resultLikelihood
LIKE FUNCTION for finding out probability that if v is sent, w is received.
input: word sent, word received, probability of error
output: probability that the word w is received
def like(v,w,p):
exp = len(v)
if v == w is True:
print('same same haha youre lame')
else:
summ = sum(x!=y for x,y in zip(v,w))
probs = p**(exp - summ) * (1-p)**(summ)
return round(probs, 10)Most Likely Word Send
BEST FUNCTION for finding out best w for given V”
input format: word received, all elements of C as individual string arguments
output: best possible value of v
def best(w,*args):
sume = sum(len(str(x)) for x in args)
listie = list()
for x in args:
summ = sum(a!=b for a,b in zip(w,x))
listie.append(summ)
dictie = dict(zip(args,listie))
for i in dictie:
if dictie[i] == min(dictie[i] for i in dictie):
closest = i
return dictieError Pattern
EP FUNCTION for finding out error pattern
input format: word received, all elements of C as individual string arguments
output: all error patterns of w
def ep(w,*args):
listie = list()
for x in args:
thing = int(w,2) ^ int(x,2)
news = '{0:0{1}b}'.format(thing,len(w))
listie.append(news)
dictie = dict(zip(args,listie))
return listieIncomplete Maximum Likelihood Decoder
IMLD FUNCTION for finding out the best fit v for a given w through xor’ing through all the possible words in C
input format: word received, all elements of C as individual string arguments
output: error patterns of w, closest v value, dictionary of word in C : weight of error pattern for reference
def imld(w, *args):
eplist = list()
listie = list()
for x in args:
thing = int(w,2) ^ int(x,2)
news = '{0:0{1}b}'.format(thing,len(w))
eplist.append(news)
summ = sum(a!=b for a,b in zip(w,x))
listie.append(summ)
dictie = dict(zip(args,listie))
for i in dictie:
if dictie[i] == min(dictie[i] for i in dictie):
closest = i
return ' '.join(eplist), closest, dictieReliability of MLD
REL FUNCTION for finding out probability theta p as sum of probability of v = w
input format: word sent, probability of error, set L(v)
output: theta p
ENTER P AS NUMBER NOT STRING!”””
def rel(v,p,*args):
exp = len(v)
theta = 0
listie = list()
for w in args:
if v == w is True:
print('same same haha youre lame')
else:
summ = sum(x!=y for x,y in zip(v,w))
probs = p**(exp-summ) * (1-p)**(summ)
listie.append(probs)
theta += probs
return thetaCorrectable Error Patterns
ERR FUNCTION for finding out all error patterns that will be corrected
input format:setC containing, all error patterns,
output: list of correctable things
def err(a,b,*args):
patterns = list()
argu = list(args)
for x in args:
thing = int(a,2) ^ int(x,2)
tidy = '{0:0{1}b}'.format(thing,len(a))
distancea = sum(x!=y for x,y in zip(a,tidy))
distanceb = sum(x!=y for x,y in zip(b,tidy))
if distancea < distanceb:
patterns.append(tidy)
return patterns
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