def TwoHops_CF_ICFsch3(Ps, P3, P4, g13, g14, g23, g24):
'''
First, take the intersection of rate regions of 1st and 2nd hop
Then, the the convex hull.
Note:
Conceptually, we should do
1). for bigR1, take the intersection of CF_bigR1 and ICF_bigR2
2). for bigR2, take the intersection of CF_bigR2 and ICF_bigR2
3). take the union of the above two intersections
4). take the convex hull.
Actually, we did
a) take the union of ICF_bigR1 and ICF_bigR2
b) take the intersection of a) and CF_whole
c) take the convex hull of b)
'''
alternative = True
if alternative:
# use alternative_rate_region.py
return rr.intersection( [rr.union( [alternative_compute.ICF_sch3_bigR1(P3, P4),
alternative_compute.ICF_sch3_bigR2(P3, P4)]),
CF_scheme_integerCoeff(Ps, g13, g14, g23, g24)] ).convexHull()
else:
# use rate_region.py
return rr.intersection( [rr.union( [ICF_sch3_bigR1(P3, P4),
ICF_sch3_bigR2(P3, P4)]),
CF_scheme_integerCoeff(Ps, g13, g14, g23, g24) ] ).convexHull()
def TwoHops_CF_ICFsch3_fromRegions(cf_scheme_integerCoeff,
*icf_sch3
):
'''
compute the achievable rate region for the (whole) two-hop network from the
given rate regions for the 1st and 2nd hops
'''
if len(icf_sch3) == 1:
return rr.intersection( [rr.union( [icf_sch3[0],
icf_sch3[0].symmetricRegion_yEqualToX() ]),
cf_scheme_integerCoeff] ).convexHull()
elif len(icf_sch3) == 2:
return rr.intersection( [rr.union( [icf_sch3[0],
icf_sch3[1]]),
cf_scheme_integerCoeff] ).convexHull()
def TwoHops_CF_ICFsch2_fromRegions(icf_sch2_bigR1,
icf_sch2_bigR2,
cf_scheme_integerCoeff):
'''
compute the achievable rate region for the (whole) two-hop network from the
given rate regions for the 1st and 2nd hops
'''
return rr.intersection( [rr.union( [icf_sch2_bigR1,
icf_sch2_bigR2]),
cf_scheme_integerCoeff ] ).convexHull()
def display(oneSimulation,pathString ,saveOnly=True):
'''
Produce a graph that compare three ICF schemes
'''
self = oneSimulation
# get the union rate region for plotting
icf_sch1 = rr.union( [self.icf_sch1_bigR1, self.icf_sch1_bigR2] )
icf_sch2 = rr.union( [self.icf_sch2_bigR1, self.icf_sch2_bigR2] )
icf_sch3 = rr.union( [self.icf_sch3_bigR1, self.icf_sch3_bigR2] )
pylab.rc('axes', linewidth=2) # make the axes boundary lines bold
fig, ax = plt.subplots()
rr.plot( icf_sch1, 'g', axes=ax, label='Scheme 1')
rr.plot( icf_sch2, 'b', axes=ax, label='Scheme 2')
rr.plot( icf_sch3, 'r', axes=ax, label='Scheme 3')
# plot the line: R2 = R1
tmp = np.asarray(self.icf_sch1_bigR1._geometry.boundary)
tmp2 = [[0, tmp[1, 0]], [0, tmp[1, 1] ] ]
ax.plot( [0, tmp[1, 0]], [0, tmp[1, 1] ] , 'k--', lw=2)
ax.set_title(r'$ P_3={}, \, P_4={}, \, N=1$'.format(self.P3, self.P4) , fontdict=self.font)
ax.set_xlabel('$R_1$', fontdict=self.font)
ax.set_ylabel('$R_2$', fontdict=self.font)
ax.set_xlim(xmin=0, xmax=3.5)
ax.set_ylim(ymin=0, ymax=3.5)
ax.legend(loc='upper right')
savefig.save(path='{}/compare_three_ICF_Schemes/P3P4_{}_{}'.format(pathString, self.P3, self.P4 ), ext='pdf', close=saveOnly, verbose=True)
if (0):
# add annotations for 3 regions
plt.text(0.7, 2.3, 'capacity region by coherent coding with cardinality-bounding', color='red')
plt.text(1, 1.8, 'non-coherent coding with cardinality-bounding', color='blue')
plt.text(1.3, 1.4, 'capacity region by coherent coding with cardinality-bounding', color='green')
bbox_props = dict(boxstyle="round,pad=0.1", fc="white", ec="g", lw=1)
plt.text(1, 0.5, r'$1$', color='black', bbox=bbox_props)
bbox_props = dict(boxstyle="round,pad=0.1", fc="white", ec="b", lw=1)
plt.text(1.7, 0.4, r'$2$', color='black', bbox=bbox_props)
bbox_props = dict(boxstyle="round,pad=0.1", fc="white", ec="r", lw=1)
plt.text(2.2, 0.3, r'$3$', color='black', bbox=bbox_props)
