Patent Application: US-5114608-A

Abstract:
log - likelihood ratios are approximated for encoded bits modulated with a 2 m - ary qam constellation . each symbol of the constellation is identified by a respective string of m bits . the log - likelihood ratio of each bit of the m bits is approximated with a product λ of a respective factor by a respective variable d that depends on a received signal and on communication channel characteristics . the approximating includes determining a value of at least one of the variables d using a parametric nonlinear function of an equalized replica z of a respective received signal .

Description:
the illustrated method is particularly suitable for implementation in a so de - mapper block for a qam system over flat fading channels . examples of such a system include convolutionally coded qam with orthogonal frequency division multiplexing ( ofdm ) in digital video broadcasting ( dvb ) and hiperlan / 2 or ieee 802 . 11a / n [ 15 ], [ 23 ], [ 24 ]; turbo convolutionally coded qam with ofdm in wimax [ 25 ] and homeplug av [ 16 ][ 26 ]. hereinafter , reference will be made to the homeplug av standard with turbo - coded qam with ofdm , but what is stated holds also for other kinds of standards with different coding and for systems which employ a single carrier modulation approach . the log - likelihood ratio of each bit of the m bits is approximated with the product λ of a respective factor by a respective variable d that depends on the received signal and on the channel characteristics . at least one variable d associated to a bit is a nonlinear function of an equalized replica z i [ k ] of the respective received signal y i [ k ]. as a result , the obtained values for the variable d approximate better the values obtainable with the max - log method than other known approximation methods . a sufficiently accurate approximation may be obtained by expressing the variable d of at least one bit as a parabolic function of the in phase component z l , i [ k ] ( or of the quadrature component z q , i [ k ]) of the equalized replica z i [ k ] of the respective received signal y i [ k ]. the variable d of only one bit may be a linear function of the in phase component z l , i [ k ]( and of the quadrature component z q , i [ k ]) of the respective equalized replica z i [ k ]. the variables d associated to the other bits may also be parametric parabolic functions of the respective z l , i [ k ] and z q , i [ k ]. in the explanation that follows , expressions for the computation of d l , i [ k ] and d q , i [ k ] for the 64 - qam , 256 - qam and 1024 - qam modulations are given , in which the nonlinear parametric function is a parabolic function , and in which certain values have been attributed to the parameters of the parametric function . later on it will be illustrated how the following formulas may be modified . those skilled in the art will appreciate that the illustrated method in which the nonlinear parametric function is a parabolic function ( hereafter referred as a parabolic method ) could be also employed with slight modifications when minor changes occur , due for instance to different gray patterns , normalization constants or other factors . in particular , it is possible to modify the signs of some of the equations from ( 37 ) to ( 60 ) and their order ( i . e ., the association among some equations and the bits ) depending on the particular gray pattern used . furthermore , the normalization constants may change if different constellation powers are employed . from fig3 to 5 the d l , i ,[ k ] values , relative to the in - phase bits , are depicted for the 1024 - qam modulation , with a comparison among the three methods . the parabolic method gives an approximation to the optimum max - log method which is closer than the tobi method . in fact , the curves obtained with the max - log method and the parabolic method are practically superimposed . a similar trend is observed also for the variable d q , i [ k ], relative to the quadrature bits , and for the 64 - qam and the 256 - qam modulations ( curves not shown ). it will be shown that performances of the above illustrated method are better in terms of bit error rate ( ber ) versus the received snr than those obtainable with the tobi method . for instance , in fig6 results are reported for the rate ½ homeplug av turbo code over a typical power line channel [ 27 ] after two and ten turbo iterations when an improved max - log map turbo decoder is used [ 28 ]. at a ber = 10 − 3 , the parabolic method gives a gain of 0 . 75 db after two turbo iterations . a further improvement of 0 . 2 db is obtained after ten turbo iterations . we note that the performance improvement , with respect to the tobi method , is obtained at the cost of a greater computational complexity . however , curves obtained with the parabolic method , for a much lower complexity , are almost superimposed to that obtained with the max - log method ( curves not shown in fig6 ). it is worth highlighting certain features of the embodiment described by equations ( 37 ) to ( 60 ): i ) the d l , i l ( k ) and the d q , i t ( k ) expressions for the in - phase and quadrature llr term are identical if the real part of the channel de - interleaved modulation symbol z l , i [ k ] is replaced by the imaginary part z q , i [ k ]. this feature was already present with the max - log and tobi methods ; ii ) the d l , i l ( k ) terms with l = 1 are the same in the three methods , since a close expression for the max - log method exists ; iii ) the parabolic terms d l , i l ( k ) with l & gt ; 1 can be simply implemented with a circuit like the one depicted in fig7 . the parameter c m depends on the modulation order m and is a normalization factor that can be computed in advance . in the case of the homeplug av system , it is c m =√{ square root over ( 42 )} for the 64 - qam modulation , c m =√{ square root over ( 170 )} for the 256 - qam modulation and c m =√{ square root over ( 682 )} for the 1024 - qam modulation . the second parameter b , for the particular embodiment that has been considered , is equal to ¼ ; iv ) the inputs to the circuit show a recursive behavior . for instance , choosing a 1024 - qam modulation and denoting by in ( l ) the circuit input which produces the d l , i l ( k ) term ( out ( l )), we obtain the following equations : the same set of equations ( and circuit ), starting with in ( 10 )= z q , i [ k ], yields the d q , i t ( k ) terms . the equations for the 64 - qam and the 256 - qam constellations present a similar recursive regular behavior . minor changes are required for communication systems using higher order qam modulations with different gray coded patterns and normalization factors . another aspect of the invention is directed to implementing the illustrated method in a soft - output de - mapper of a communication system for the 1024 - qam modulation ( equations ( 9 ) and ( 10 ) and equations from ( 51 ) and ( 60 )), or for the 256 - qam modulation ( equations ( 9 ) and ( 10 ) and equations from ( 43 ) to ( 50 )), or for the 64 - qam modulation ( equations ( 9 ) and ( 10 ) and equations from ( 37 ) to ( 42 )). yet another aspect of the invention is directed to a communication system which uses a soft - output de - mapper that implements the tobi method for lower - order constellations ( e . g ., bpsk , qpsk , 8 - qam , 16 - qam ), and the illustrated method for higher - order constellations ( 64 - qam , 256 - qam and 1024 - qam ). l . hanzo , w . webb and t . keller , “ single - and multi - carrier quadrature amplitude modulation : principles and applications for personal communications , wlans and broadcasting ,” chichester , uk : wiley , 2000 . berrou , a . glavieux and p . thitimashimajshima , “ near shannon limit error - correcting coding and decoding : turbo - codes i ,” ieee icc 1993 , pp . 1064 - 1070 , may 1993 . r . m . pyndiah , “ near - optimum decoding of product codes : block turbo codes ,” ieee trans . on comm ., vol . 46 , pp . 1003 - 1010 , august 1998 . s . benedetto and g . montorsi , “ serial concatenation of block and convolutional codes ,” ieee elect . lett ., vol . 32 , pp . 887 - 888 , may 1996 . g . caire , g . taricco and e . biglieri , “ bit - interleaved coded modulation ,” ieee trans . on inf . theory , vol . 44 , pp . 927 - 946 , may 1998 . g . ungerboeck , “ channel coding with multilevel / phase signals ,” ieee trans . on inf . theory , vol . it - 28 , pp . 55 - 67 , january 1982 . c . douillard , m . jézéquel and c . berrou , “ iterative correction of intersymbol interference : turbo - equalization ,” ett , vol . 6 , pp . 507 - 511 , september - october 1995 . g . bauch , h . khorram and j . hagenauer , “ iterative equalization and decoding in mobile communications systems ,” epmcc &# 39 ; 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