network coding

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1、(a)(b)b1Sbb1Sb22TUTUb1b2b1WWb1bb2b1b1b21b2XXb2b1b1YZYZSSb2b3b1b2TUTUb3b1b2WWb2b3b3b1bb21§b2b3Xb1§b2Xb1§b2YZYZ(c)(d)b1b2b1b2SUSÅSUSÅb1b2b1§b2b2b1b1§b2b1§b2TVTÅTVTÅTimeunit1:b1UVSTSÅTÅTimeunit2:b2UVSTSÅTÅTimeunit3:b1§b2UVSTSÅTÅSTUWXYZfOS=⊬∆1·¸fOSÅ=⊬∆0·¸∆¸∆¸«0¹«1¹⊬10·SKS=∆∆¸¸«01¹KT=(11)

2、⊬1·⊬0·KU=(11)∆∆¸¸∆∆¸¸«0¹«1¹TU⊬1·KW=∆∆¸¸«1¹⊬1·⊬0·∆∆¸¸W∆∆¸¸«0¹«1¹⊬1·⊬0·∆∆¸¸⊬1·∆∆¸¸«0¹∆∆¸¸«1¹«1¹⊬1·⊬1·∆∆¸¸∆∆¸¸«1¹X«1¹YKX=(11)ZfOS=⊬∆1·¸fOSÅ=⊬∆0·¸∆¸∆¸«0¹«1¹⊬nq·SKS=∆∆pr¸¸«¹KT=(st)KU=(uv)⊬n·⊬q·∆∆¸¸∆∆¸¸T«p¹«r¹U⊬w·KW=∆∆¸¸«x¹⊬ns·⊬qu·∆∆¸¸W∆∆¸¸«ps¹«ru¹⊬nt·⊬qv·∆∆pt¸¸⊬nsw+qux·∆∆¸¸«¹∆∆¸¸«rv¹⊬∆nsw

3、y+quxy·¸«psw+rux¹∆¸«pswy+ruxy¹XYKX=(yz)⊬nswz+quxz·Z∆∆¸¸«pswz+ruxz¹(a)(b)⊬1·⊬0·⊬1·⊬∆1·¸∆∆¸¸S∆∆¸¸∆∆¸¸S∆0¸«0¹«1¹«0¹«¹⊬0·⊬0·T∆∆0¸¸UT∆∆1¸¸U«¹«¹⊬1·⊬0·⊬1·⊬∆1·¸∆∆¸¸W∆∆1¸¸∆∆0¸¸W∆0¸«0¹«¹«¹«¹⊬0·⊬1·⊬1·⊬∆1·¸S∆¸∆∆¸¸S∆∆0¸¸∆0¸∆«0¸¹«0¹«¹«¹⊬0·⊬∆0·¸T∆∆1¸¸UT∆«1¸¹U«¹⊬0·⊬1·⊬0·∆∆¸¸⊬∆0·¸∆∆¸¸W∆∆¸¸«0¹W∆0¸«0¹«

4、0¹«¹(c)(d)⊬1·⊬0·∆∆¸¸∆∆¸¸«0¹«1¹S⊬1·⊬1·∆∆¸¸∆∆¸¸«1¹⊬1·«1¹∆¸∆¸«0¹XYs⊬y1·⊬y4·∆∆¸¸∆∆¸¸«z1¹«z4¹⊬y2·⊬y3·∆∆¸¸∆∆¸¸«z2¹«z3¹UU2U13U4T1T2T3T4T5T6⊬1·⊬0·∆¸∆¸∆¸∆¸«0¹«1¹S⊬1·⊬0·∆∆¸¸∆∆¸¸«0¹«1¹⊬0·⊬1·∆¸∆¸∆¸∆¸«1¹«0¹XY⊬1·⊬0·∆∆¸¸∆∆¸¸«0¹«1¹⊬101·SKS=∆∆¸¸«011¹cde⊬13·g∆¸KX=∆32¸XY∆«11¸¹h⊬1·⊬0·∆∆¸¸∆∆1¸¸«0¹«¹⊬10·S

5、KS=∆∆¸¸«01¹⊬1·⊬0·∆∆0¸¸∆∆¸¸«¹⊬1·«1¹KU=∆∆1¸¸«¹⊬1·⊬1·KT=∆∆¸¸TUT’KT’=∆∆0¸¸«0¹1⊬0·«¹⊬·∆∆¸¸∆∆1¸¸«0¹«¹⊬1·∆∆¸¸«1¹⊬1·⊬1·∆∆1¸¸∆∆¸¸«¹«1¹VKV=(11)⊬1·⊬0·∆∆¸¸∆∆1¸¸ab«0¹«¹⊬10·SKS=∆∆¸¸S«01¹⊬1·⊬0·ab∆∆¸¸∆∆¸¸«0¹«1¹⊬1·fXY=∆∆¸¸+fWXp=a+r⊬1·«0¹⊬1·KX=∆∆¸¸XYKY=∆∆¸¸XY«1¹«1¹⊬0·r=qq=b+pfWX=fYWfWZ=∆∆¸¸+fXY«1¹WWKW

6、=(1)(a)(b)t=0t=1t=2t=3t=4t=5XXXXX4X5X60123aa3a0+a0a0a12a+ba+b400aa120310a0aa2a3a4a51b0bb2b3b4b51SS4S5S6S0S1S230b0b1b2b3b4YYY2YY4Y5Y6013000b0a0+b1a1+b200b0a0+b1a1+b2a2+b0+b3W0W1WW3W4W5W6⊬1·⊬0·∆∆¸¸∆∆¸¸«0¹«1¹⊬10·SKS=∆∆¸¸«01¹⊬z·∆¸⊬0·∆0¸∆∆¸¸«¹z23«¹⊬z/(1-z)·∆¸∆43¸⊬1·«z/(1-z)¹⊬1·KX=∆∆1¸¸XYK

7、Y=∆∆¸¸«¹«1¹43⊬z3/(1-z3)·⊬z/(1-z)·∆¸∆¸∆z3/(1-z3)¸∆z2/(1-z3)¸«¹«¹WKW=(1)⊬1·⊬0·∆∆¸¸∆∆¸¸«0¹«1¹⊬10·⊬z·SKS=∆∆¸¸∆¸«01¹∆¸«0¹⊬0·∆∆¸¸«z¹⊬2·z∆¸3∆z4¸⊬1-z·«¹⊬1-z3·KX(z)=∆∆¸¸XYKY(z)=∆¸«1¹∆«1¸¹4⊬z3·⊬z·∆¸∆¸∆z3¸∆z2¸«¹W«¹KW(z)=(1)t=0t=1t=2t=3t=4t=5XXXXXXX0a0a1a2a3a400a0a1a2+b0a3+b1SSSSSSS0b0b1b2b3b4YY

8、YYYYY000b0a0