Time Division Multiplexing for Green Broadcasting

Transcription

1 Time Division Multiplexing for Green Broadcasting Pulkit Grover UC Berkeley with Anant Sahai There are handouts for this talk. Please take one!

2 Short-distance green communication C = W 2 log (1 + SNR) *, *.1:-,,+12;<-..8.1=60>*/,*8.4!# $!# #!#!$!#!%!#!' 60 GHz (1 GHz bandwidth) 1 Gbps 3 GHz (20 MHz bandwidth) 20 Mbps! "!# $# %# &#!'# ($# '%# )*+,-./ GHz path-loss exponent = 3 receiver noise-figure = 5 db T = 300 K 3 GHz path-loss exponent = 3 receiver noise-figure = 20 db T = 300 K 2 /14

3 Short-distance green communication C = W 2 log (1 + SNR) *, *.1:-,,+12;<-..8.1=60>*/,*8.4!# $!# #!#!$!#!%!#!' Power of high throughput LDPC decoders of [Zhang et al] 60 GHz (1 GHz bandwidth) 1 Gbps 3 GHz (20 MHz bandwidth) 20 Mbps! "!# $# %# &#!'# ($# '%# )*+,-./ GHz path-loss exponent = 3 receiver noise-figure = 5 db T = 300 K 3 GHz path-loss exponent = 3 receiver noise-figure = 20 db T = 300 K Decoding power is substantial 2 /14

4 The black-box model for decoding energy Tx Rx [Massaad, Medard, Zheng 04] 3 /14

5 The black-box model for decoding energy Tx Rx [Massaad, Medard, Zheng 04] Tx Rx Tx [Massaad, Zheng, Medard 08] 3 /14

6 The black-box model for decoding energy Tx Rx [Massaad, Medard, Zheng 04] Tx Tx Rx Rx Tx Relay [Massaad, Zheng, Medard 08] [e.g. Prabhakaran, Kumar 09] 3 /14

7 A proxy for decoding energy : Complexity 4 /14

8 A proxy for decoding energy : Complexity Block codes Block length m log 1 P e E r (R) [Gallager]... [Wiechman, Sason][Polyanskiy et al] 4 /14

9 A proxy for decoding energy : Complexity Block codes Block length Convolutional codes Constraint length m log 1 P e E r (R) L c log 1 P e E conv (R) [Gallager]... [Wiechman, Sason][Polyanskiy et al] [Viterbi] 4 /14

10 A proxy for decoding energy : Complexity Block codes Block length Convolutional codes Constraint length m log 1 P e E r (R) L c log 1 P e E conv (R) [Gallager]... [Wiechman, Sason][Polyanskiy et al] [Viterbi]!$ log 10 (P e )!%!'!&!!#!!$!!%!!' energy per operation E = 1 pj, f = 3 GHz distance = 17 m, path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3!!&!$#!$$ Shannon waterfall (BPSK = BSC)!$%! "!# $# %# &# ()*+,-./012030*45260*!7.829)32-)42:;,-0< 4 /14

11 A proxy for decoding energy : Complexity Block codes Block length Convolutional codes Constraint length m log 1 P e E r (R) L c log 1 P e E conv (R) [Gallager]... [Wiechman, Sason][Polyanskiy et al] [Viterbi] log 10 (P e )!$!%!'!&!!#!!$!!%!!' Rate 1/3 convolutional code energy per operation E = 1 pj, f = 3 GHz distance = 17 m, path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3!!&!$#!$$ Shannon waterfall (BPSK = BSC)!$%! "!# $# %# &# ()*+,-./012030*45260*!7.829)32-)42:;,-0< 4 /14

12 A proxy for decoding energy : Complexity Block codes Block length Convolutional codes Constraint length m log 1 P e E r (R) L c log 1 P e E conv (R) [Gallager]... [Wiechman, Sason][Polyanskiy et al] [Viterbi] log 10 (P e )!$!%!'!&!!#!!$!!%!!' (4,6) regular LDPC code Gallager B decoding Rate 1/3 convolutional code energy per operation E = 1 pj, f = 3 GHz distance = 17 m, path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3!!&!$#!$$ Shannon waterfall (BPSK = BSC)!$%! "!# $# %# &# ()*+,-./012030*45260*!7.829)32-)42:;,-0< 4 /14

13 Lower bounds for message-passing decoding Message-passing decoding 5 /14

14 Lower bounds for message-passing decoding Graphical complexity Message-passing decoding Number of iterations 5 /14

15 Lower bounds for message-passing decoding Graphical complexity [Gallager 63] [Burshtein et al 02] [Sason, Urbanke 03][Sason 09] Message-passing decoding Number of iterations 5 /14

16 Lower bounds for message-passing decoding Graphical complexity [Gallager 63] [Burshtein et al 02] [Sason, Urbanke 03][Sason 09] Message-passing decoding Number of iterations [Khandekar, McEliece 01] [Sason 08] 5 /14

17 Number of iterations for any code 6 /14

18 Number of iterations for any code Bit nodes Channel output nodes Helper nodes 6 /14

19 Number of iterations for any code Bit nodes Channel output nodes Helper nodes a B i a - 1 a /14

20 Number of iterations for any code Bit nodes Channel output nodes Helper nodes a B i a - 1 a - 1 # iterations 1 log(α 1) log ( log 1 P e (C(P T ) R) 2 ) 6 /14

21 Number of iterations for any code Bit nodes Channel output nodes Helper nodes a B i a - 1 a - 1 # iterations 1 log(α 1) log ( log 1 P e (C(P T ) R) 2 ) Regular LDPCs : # iterationsl = Θ ( log (log 1Pe )) 6 /14

22 Regular LDPC s are order optimal! energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 7 /14

23 Regular LDPC s are order optimal!!%!&!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 7 /14

24 Regular LDPC s are order optimal!!%!& 5"?&(%,"4'@% "'%!"!#$%&'&()*%+&(!,-!!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 7 /14

25 Regular LDPC s are order optimal!!%!& 5"?&(%,"4'@% "'%!"!#$%&'&()*%+&(!,-!!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% A+!-B#$%%!(#'CB-!%+"?&(."(%$"?&(%,"4'@ energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> 7 /14

26 Regular LDPC s are order optimal!!%!& 5"?&(%,"4'@% "'%!"!#$%&'&()*%+&(!,-!!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% A+!-B#$%%!(#'CB-!%+"?&(."(%$"?&(%,"4'@ D:(&C:"$@%+"?&(."(%/0123%(&)4$#(% %"+!-B#$%!(#'CB-!%+"?&( energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> 7 /14

27 Green broadcasting 8 /14

28 Decoding energy in broadcast channel Joint schemes : e.g. Superposition or Dirty-Paper Coding Decoder Encoder Decoder 9 /14

29 Decoding energy in broadcast channel Time-division multiplexing Decoder Encoder Decoder 10/14

30 Outer bounds on error exponents for Gaussian broadcast 11/14

31 Outer bounds on error exponents for Gaussian broadcast E P/! 0 2 = 10 h 1 2 = h2 2 =1, R 1 = R 2 = 0.5 nats/ channel use Best previously known bound [Weng et al, 08] E 1 11/14

32 Outer bounds on error exponents for Gaussian broadcast E P/! 0 = 10 2 h = 2 h2 =1, 1 R = R = 0.5 nats/ channel use 1 2 Best previously known bound [Weng et al, 08] 0.2 Our Bound E 1 11/14

33 TDM better than superposition/dpc at short distances! Energy gain for TDM (db) Energy gain with TDM over joint schemes (db)!'(!')!'#!'&!!!'&!!'#!!')!"+,"-./0!"*"&'#!!'(!""" #$" $! %$ &!! &#$ &$! &%$ Distance distance of the the closer closer receiver receiver ζ = r2 2 r 2 1 energy per operation E = 1 pj, path-loss exponent = 2, T = 300 K, Rate = 1/3, (Noise + fading) figure = 30 db 12/14

34 TDM better than superposition/dpc at short distances! Energy gain for TDM (db) Energy gain with TDM over joint schemes (db)!'(!')!'#!"*"&'#!'&!"+,"-./0!!"*"#'#$!!'&!!'#!!')!!'(!""" #$" $! %$ &!! &#$ &$! &%$ Distance distance of the the closer closer receiver receiver ζ = r2 2 r 2 1 energy per operation E = 1 pj, path-loss exponent = 2, T = 300 K, Rate = 1/3, (Noise + fading) figure = 30 db 12/14

35 TDM better than superposition/dpc at short distances! Energy gain for TDM (db) Energy gain with TDM over joint schemes (db)!'(!')!"*"&'#!'#!'&!"+,"-./0!!!'&!!'#!"*"(!!')!"*"#'#$!!'(!""" #$" $! %$ &!! &#$ &$! &%$ Distance distance of the the closer closer receiver receiver ζ = r2 2 r 2 1 energy per operation E = 1 pj, path-loss exponent = 2, T = 300 K, Rate = 1/3, (Noise + fading) figure = 30 db 12/14

36 The crucial distance ratio r 1 r 2 R 2 R 1 13/14

37 The crucial distance ratio r 1 r 2 R 2 R 1 13/14

38 The crucial distance ratio r 1 r 2 R 2 R 1 13/14

39 Summary 14/14

40 Summary Broadcast channels : TDM can outperform superposition/dpc at short distances 14/14

41 Summary Broadcast channels : TDM can outperform superposition/dpc at short distances - does not mean that TDM is optimal 14/14

42 Summary Broadcast channels : TDM can outperform superposition/dpc at short distances - does not mean that TDM is optimal - we are comparing lower bounds. The hope is that sparse-graph codes approach these bounds. 14/14

43 Summary Broadcast channels : TDM can outperform superposition/dpc at short distances - does not mean that TDM is optimal - we are comparing lower bounds. The hope is that sparse-graph codes approach these bounds. Error exponents with neighborhood size and bit-error probability aid in understanding the relevant tradeoffs 14/14

44 Summary Broadcast channels : TDM can outperform superposition/dpc at short distances - does not mean that TDM is optimal - we are comparing lower bounds. The hope is that sparse-graph codes approach these bounds. Error exponents with neighborhood size and bit-error probability aid in understanding the relevant tradeoffs - Tighter bounds can be derived for specific code classes. 14/14

45 Summary Broadcast channels : TDM can outperform superposition/dpc at short distances - does not mean that TDM is optimal - we are comparing lower bounds. The hope is that sparse-graph codes approach these bounds. Error exponents with neighborhood size and bit-error probability aid in understanding the relevant tradeoffs - Tighter bounds can be derived for specific code classes. Shannon theory needs augmentation at short distances because of decoding power 14/14

46 15/14

47 Backup slides begin 16/14

48 Uncoded vs coded transmission [Howard et al, 2006] 17/14

49 !%!& 5"A&(%,"4'C% "'%!"!#$%&'&()*%+&(!,-!!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% D+!-?#$%%!(#'@?-!%+"A&(."(%$"A&(%,"4'C B:(&@:"$C%+"A&(."(%/0123%(&)4$#(%5678 5"A&(%,"4'C%!:#!%-)'"(&@%)#+.("?%E#+#E-!* 9:#''"'%;#!&(.#$$ /<79=%%>%%%< %"+!-?#$%!(#'@?-!%+"A&(!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> 18/14

50 Regular LDPC s are order optimal!!%!&!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 19/14

51 Regular LDPC s are order optimal!!%!&!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% 5678%"+!-?#$%!(#'@?-!%+"A&( energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> 19/14

52 Regular LDPC s are order optimal!!%!&!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% B:(&@:"$C%+"A&(."(%/0123%(&)4$#(% %"+!-?#$%!(#'@?-!%+"A&( energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> 19/14

53 Regular LDPC s are order optimal!!%!& 5"A&(%,"4'C% "'%!"!#$%&'&()*%+&(!,-!!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! ;? 2 4>!'!$(!)% D+!-?#$%%!(#'@?-!%+"A&(."(%$"A&(%,"4'C B:(&@:"$C%+"A&(."(%/0123%(&)4$#(% %"+!-?#$%!(#'@?-!%+"A&( energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 9:#''"'%;#!&(.#$$ /<79=%%>%%%<983!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> 19/14

54 Regular LDPC s are order optimal!!%!& 5"A&(%,"4'C% "'%!"!#$%&'&()*%+&(!,-!!"!#$%&'&()*%+&(!,-!%."( /0123%(&)4$#(%5678 /+6 $! $! ;? 2 4>!'!$(!)% D+!-?#$%%!(#'@?-!%+"A&(."(%$"A&(%,"4'C B:(&@:"$C%+"A&(."(%/0123%(&)4$#(%5678 5"A&(%,"4'C%!:#!%-)'"(&@%)#+.("?%E#+#E-!* 9:#''"'%;#!&(.#$$ /<79=%%>%%%< %"+!-?#$%!(#'@?-!%+"A&(!(&!"# $ % & ' $( *+,-./ ,67482,!90:4;+54/+64<=./2> energy per operation E = 1 pj, distance = 17 m, f = 3 GHz path-loss exponent = 3, maximum node connectivity= 4 T = 300 K Rate = 1/3 19/14

55 Green communication at long distances P 1 P 2 P 3 20/14

56 Green communication at long distances P 1 P 2 P 3 P R 1 Decoder Encoder R 2 Decoder 20/14

57 Green communication at long distances P 1 P 2 P 3 P Encoder P R 1 Decoder R 2 R 2 Decoder R 1 20/14

58 Lower bounds on complexity 21/14

59 Lower bounds on complexity Block codes m log 1 P e E r (R) 21/14

60 Lower bounds on complexity Block codes m log 1 P e E r (R) Conv. codes L c log 1 P e E conv (R) 21/14

61 Lower bounds on complexity Block codes m log 1 P e E r (R) Conv. codes L c log 1 P e E conv (R) Sparse-graph codes 21/14

62 Lower bounds on complexity Block codes m log 1 P e E r (R) Graphical complexity Conv. codes L c log 1 P e E conv (R) Sparse-graph codes Number of iterations 21/14

63 Lower bounds on complexity Block codes m log 1 P e E r (R) [Gallager 63] [Burshtein et al 02] [Sason, Urbanke 03][Sason 09] Graphical complexity Conv. codes L c log 1 P e E conv (R) Sparse-graph codes Number of iterations 21/14

64 Lower bounds on complexity Block codes m log 1 P e E r (R) [Gallager 63] [Burshtein et al 02] [Sason, Urbanke 03][Sason 09] Graphical complexity Conv. codes L c log 1 P e E conv (R) Sparse-graph codes Number of iterations [Khandekar, McEliece 01] [Sason 08] 21/14