4.8.yingyao.ps

是multiuser detection 这本书的习题解答, 很有用的书.

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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin @letter
%%EndSetup
%%Page: 1 1
bop 812 307 a Fj(Solution)21 b(to)d(4.8)866 357 y Fi(Yingw)o(ei)13
b(Y)m(ao)262 457 y(4.8)e(Since)i(w)o(e)g(can)g(precompute)g(the)h(v)n(alues)e
(of)g Fh(b)1060 442 y Fg(T)1085 457 y Fh(Hb)p Fi(,)h(w)o(e)g(only)f(need)h
(to)g(compute)f(the)262 506 y(v)n(alues)i(of)h Fh(b)462 491
y Fg(T)487 506 y Fh(Ay)g Fi(=)609 475 y Ff(P)653 486 y Fg(K)653
519 y(k=1)721 506 y Fi(A)752 512 y Fg(k)772 506 y Fi(b)795
512 y Fg(k)815 506 y Fi(y)837 512 y Fg(k)871 506 y Fi(for)g(all)f(2)1016
491 y Fe(K)1063 506 y Fi(p)q(ossible)h Fh(b)p Fi(.)22 b(W)m(e)15
b(need)h Fd(K)i Fi(op)q(erations)262 556 y(to)c(compute)g Fd(A)513
562 y Fe(k)534 556 y Fd(y)554 562 y Fe(k)574 556 y Fd(;)45
b(k)14 b Fi(=)f(1)p Fd(;)7 b Fc(\001)g(\001)g(\001)e Fd(;)i(K)s
Fi(.)20 b(Due)14 b(to)h(the)g(fact)g(that)g(w)o(e)f(are)h(using)g(an)o(tip)q
(o)q(dal)262 606 y(mo)q(dulation,)9 b(only)j(addition)f(and)i(subtraction)g
(are)g(needed)h(in)e(the)h(rest)h(of)e(the)h(compu-)262 656
y(tation.)k(This)d(can)g(b)q(e)g(done)g(using)g(the)h(tree)g(structure)h(sho)
o(wn)e(here.)971 804 y Fb(\000)930 846 y(\000)888 887 y(\000)847
929 y(\000)805 970 y(\000)796 980 y(\000)1013 804 y(@)1054
846 y(@)1096 887 y(@)1137 929 y(@)1179 970 y(@)1198 989 y(@)777
1031 y(\012)750 1072 y(\012)722 1114 y(\012)694 1155 y(\012)667
1197 y(\012)654 1216 y(\012)805 1050 y(A)826 1091 y(A)847 1133
y(A)867 1174 y(A)888 1216 y(A)890 1220 y(A)1214 1031 y(\024)1189
1072 y(\024)1165 1114 y(\024)1140 1155 y(\024)1115 1197 y(\024)1104
1214 y(\024)640 1257 y(\002)626 1299 y(\002)613 1340 y(\002)599
1382 y(\002)585 1423 y(\002)579 1442 y(\002)654 1257 y(C)664
1299 y(C)675 1340 y(C)685 1382 y(C)696 1423 y(C)700 1442 y(C)908
1257 y(\003)898 1299 y(\003)887 1340 y(\003)877 1382 y(\003)866
1423 y(\003)862 1442 y(\003)918 1276 y(B)932 1318 y(B)946 1359
y(B)960 1401 y(B)974 1442 y(B)974 1444 y(B)1100 1257 y(\005)1093
1299 y(\005)1086 1340 y(\005)1079 1382 y(\005)1073 1423 y(\005)1069
1442 y(\005)1107 1276 y(C)1118 1318 y(C)1128 1359 y(C)1138
1401 y(C)1149 1442 y(C)1149 1444 y(C)1371 1276 y(C)1382 1318
y(C)1392 1359 y(C)1403 1401 y(C)1413 1442 y(C)1413 1444 y(C)1363
1277 y(\003)1352 1318 y(\003)1342 1360 y(\003)1331 1401 y(\003)1321
1443 y(\003)1321 1444 y(\003)1239 1031 y(A)1260 1072 y(A)1281
1114 y(A)1302 1155 y(A)1322 1197 y(A)1343 1238 y(AA)767 876
y Fa(-1)376 b(1)673 1102 y(-1)168 b(1)202 b(-1)k(1)579 1310
y(-1)92 b(1)108 b(-1)92 b(1)165 b(1)240 b(1)-420 b(-1)224 b(-1)262
1545 y Fi(This)18 b(tree)h(has)g Fd(K)i Fi(la)o(y)o(ers,)e(where)h
Fd(K)h Fi(is)d(the)h(n)o(um)o(b)q(er)f(of)g(users.)32 b(Eac)o(h)19
b(no)q(de)g(in)f(this)262 1595 y(tree\(except)k(the)e(lea)o(v)o(es\))g(has)g
(t)o(w)o(o)f(c)o(hildren.)36 b(The)20 b(left)f(c)o(hild)g(is)h(connected)h
(to)f(the)262 1645 y(paren)o(t)e(b)o(y)g(an)g(arc)h(asso)q(ciated)g(with)f
Fc(\000)p Fi(1)g(and)g(the)h(righ)o(t)f(c)o(hild)g(is)g(connected)i(to)e(the)
262 1695 y(paren)o(t)c(b)o(y)f(an)g(arc)h(asso)q(ciated)h(with)e(1.)k(W)m(e)d
(assign)f(a)g(v)n(alue)g(to)h(eac)o(h)g(no)q(de)g(in)f(this)g(tree)262
1745 y(in)f(the)h(follo)o(wing)d(w)o(a)o(y:)16 b(the)e(ro)q(ot)e(will)f(b)q
(e)i(assigned)g(the)g(v)n(alue)f(0,)g(for)h(a)f(no)q(de)h(at)f(the)h
Fd(ith)262 1795 y Fi(la)o(y)o(er,)f(the)h(v)n(alue)f(assigned)i(to)e(it)h(is)
f Fd(x)867 1801 y Fe(p)894 1795 y Fi(+)7 b Fd(c)g Fc(\002)h
Fd(A)1029 1801 y Fe(i)1043 1795 y Fd(y)1063 1801 y Fe(i)1077
1795 y Fi(,)k(where)i Fd(x)1244 1801 y Fe(p)1276 1795 y Fi(is)f(the)g(v)n
(alue)g(assigned)g(to)262 1844 y(its)f(paren)o(t)h(and)f Fd(c)g
Fi(=)g Fc(\000)p Fi(1)g(if)g(this)h(no)q(de)g(is)f(the)h(left)f(c)o(hild)g
(of)g(its)h(paren)o(t,)g(otherwise)g Fd(c)f Fi(=)f(1.)262 1894
y(W)m(e)g(can)h(see)h(that)f(this)f(tree)i(has)f(2)810 1879
y Fe(K)854 1894 y Fi(lea)o(v)o(es)g(and)f(the)i(v)n(alues)e(asso)q(ciated)i
(to)e(these)i(lea)o(v)o(es)262 1944 y(are)f(exactly)f Fh(b)496
1929 y Fg(T)522 1944 y Fh(Ay)h Fi(=)639 1913 y Ff(P)683 1923
y Fg(K)683 1956 y(k=1)751 1944 y Fi(A)782 1950 y Fg(k)802 1944
y Fi(b)825 1950 y Fg(k)844 1944 y Fi(y)866 1950 y Fg(k)897
1944 y Fi(for)g(all)e(p)q(ossible)i Fh(b)p Fi(.)k(Starting)c(from)e(the)i(ro)
q(ot,)f(w)o(e)262 1994 y(need)16 b(one)g(addition/subtraction)e(for)h
(computing)f(the)i(v)n(alue)f(assigned)g(to)h(eac)o(h)g(no)q(de.)262
2044 y(So)d(the)i(n)o(um)o(b)q(er)e(of)g(op)q(erations)h(needed)i(is)704
2135 y(2)9 b(+)h(2)797 2118 y Fg(2)825 2135 y Fi(+)f Fc(\001)e(\001)g(\001)h
Fi(+)h(2)986 2118 y Fe(K)1030 2135 y Fi(=)i(2\(2)1131 2118
y Fe(K)1172 2135 y Fc(\000)f Fi(1\))262 2226 y(Hence)16 b(the)f(generation)g
(of)f(all)f(the)i(v)n(alues)f(of)g(\012\()p Fh(b)p Fi(\))h(needs)h
Fd(O)q Fi(\(2)1300 2211 y Fe(K)1331 2226 y Fi(\))f(op)q(erations)g(and)f(w)o
(e)262 2276 y(can)g(maxim)o(ize)d(\012\()p Fh(b)p Fi(\))j(with)f(time)g
(complexit)o(y)f(p)q(er)j(bit)e(equal)h(to)g Fd(O)q Fi(\(2)1394
2261 y Fe(K)1425 2276 y Fd(=K)s Fi(\).)967 2574 y(1)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF