Patent Application: US-90197604-A

Abstract:
an improved transmission method for high - rate digital communication on unshielded twisted copper pairs for very - high speed digital subscriber loop modems . the new modulation scheme is a multi code multi carrier code division multiple access , hereafter named mc 2 cdma . the system takes advantage from both the cdma modulation and the multi - carrier transmission and , in addition , the channel throughput is increased adopting a multi - code approach . the novel scheme encompasses transmitter , channel and receiver . loading .

Description:
as shown in fig1 in a known vdsl modem after the steps of coding 1 and mapping 2 , the source data stream ( tx data ) enters an ifft processor 3 , which digitally performs multi - carrier modulation . then , a cyclic suffix ( cs ) and cyclic prefix ( cp ) are added in step 4 and pulse shaping 5 is performed digitally before digital to analog conversion 6 that stest up the tx signal . the received signal ( rx signal ) then , undergoes a reverse conversion in 16 and , after windowing in 15 and cs / cp removal in 14 , the fft processor 13 recovers the transmitted qam symbols ( quadrature amplitude modulation ). finally , demapping 12 and decoding 11 output the receiver data stream ( rx data ). in order to ease the following description of the mc 2 - cdma modulation method according to the invention , it is useful to introduce a frequency model of the transmission system . as known [ 8 ] under a frequency point of view , a multi - carrier system ( dmt , ofdm ) is equivalent to n c qam modulations performed in parallel where n c represents the number of system sub - carriers . this way , the ifft / fft processor and the timing processing blocks can be neglected , as well as the encoding / decoding are , which are beyond the aims of this invention . to describe the mc 2 - cdma system , the following parameters are introduced : n c number of system sub - carriers . g p processing gain factor . p = n c / g p number of transmission branches . c ( k ) =[ c 0 ( k ) c 1 ( k ) . . . c g p ( k ) − 1 ] t signature code k −, 0 ≦ k ≦ g p . x k , i ( u ) frequency sample of signal x , relating to user u , on branch k and the chip i . fig2 represents the information bit - stream coming from a certain binary source 20 . for the sake of simplicity , no coding and interleaving are considered here . a mapper 21 translates consecutive ( and variable in length ) blocks of bits b into the qam ( quadrature amplitude modulation ) symbol stream a , influenced by a bit - loading table 22 where the qam order of each branch is stored . finally , in s / p block 23 a parallelization is made into p = n c / g p transmission branches , each having symbol a k , with k in the range 0 ÷ p − 1 . each symbol a k then enters the mc 2 - cdma branch transmitter depicted in fig3 . here a further parallelization of each symbol stream a k into n u sub - stream symbols a k ( l ) , l = 0 , 1 , . . . , n u − 1 , is performed in block 30 , where n u is the number of signature codes used for transmission . qam symbols a k ( l ) are then used to build in chips 31 the multi - code multi - carrier cdma signal t k , i , which according to fig3 , can be derived as : t k , i = ∑ l = 0 n u - 1 ⁢ t k , i ( l ) = ∑ l = 0 n u - 1 ⁢ a k ( l ) · c i ( l ) eq . ⁢ 1 t k , i is the transmitted sample in the frequency domain ( before ifft 3 of fig1 ) related to branch k − and chip i . according to eq . 1 t k , i is derived as the sum of samples t k , i ( l ) , which are the terms related to the signature code 1 , t k , i ( l ) = a k ( l ) · c i ( l ) . as far as the signal spectrum is concerned , there are several ways to relate the transmitted samples t k , i to the vdsl sub - carriers , namely all the possible permutations on n c items , where n c is the number of system sub - carriers . this is because the frequency sample t k , i , k = 0 , 1 , . . . , p − 1 i = 0 , 1 , . . . , g p − 1 can be rearranged according to any strategy before they enter the ifft processor 3 of fig1 . as shown in fig4 , this result can be achieved by spreading samples on consecutive frequencies . in other words , the chips 31 belonging to the same branch are kept close in the frequency available band , which yields a two - fold result : on one hand the channel is almost flat on each branch , resulting in low signal distortion ; on the other hand the strong channel attenuation at high frequency turns out in bad system performance , that means that a few bits or no bits are loaded on high frequency branches . fig4 shows the transmitted spectrum for such a consecutive , not - interlaced transmission . as mentioned above , in opposition to a consecutive transmission , the branch chips can be transmitted after some interleaving , in an interlaced manner . a preferred interlaced transmission provides that the branch samples t k , i are equally spread in the frequency domain , as shown in fig5 . this way , each transmission branch has a similar set of complex channel coefficients , which results in similar performance , but as a drawback the channel transfer function is not flatter on each branch , which implies a certain increasing in the signal distortion . fig6 shows the frequency model for a typical vdsl transmission channel , described as a frequency selective stationary isi - free channel , with complex coefficients h k , i , k = 0 , . . . , p − 1 i = 0 , . . . , g p − 1 for the k - th branch at the i - th sub - carrier ( or chip ). this channel modeling applies whenever the number of used subcarriers n c is sufficiently large so that it can be considered invariant , both in phase and amplitude , on each sub - carrier [ 8 ]. the main noise sources of a vdsl communication are thermal noise ( represented with η k , i in fig6 ), alien interference , fext ( near end crosstalk ) and next ( far end crosstalk ) interferences [ 1 ] [ 2 ] [ 8 ]. the latter is neglected in the overall interference term i k , i of branch k and chip i ( added at the receiver on each subcarrier in our frequency modeling ), because an ideal modem synchronization and a proper duplexing method are assumed [ 1 ]. detectors for cdma systems can be grouped into two basic categories : single - user detectors ( sud ) and multi - user detectors ( mud ) [ 7 ], [ 9 ]. in the following example single - user detection schemes are used . the received signal , derived from fig6 , is expressed by : r k , i = h k , i · ∑ l = 0 n u - 1 ⁢ t k , i ( l ) + i k , i + η k , i eq . ⁢ 2 fig7 and 8 shows the frequency model of the mc 2 - cdma receiver . in particular , fig7 shows the frequency model of the receiver branch k . the received samples r k , i ( in the frequency domain , after fft ) on branch k undergo channel equalization , performed here in the frequency domain by means of a frequency equalizer ( feq ) filter 40 , which just multiplies them by the complex coefficients w k , i , chosen according to a certain equalization technique . then , the equalized samples enter n u despreaders 41 , each of whom just correlates the received samples with the related signature code c i ( l ) , ticking index l in the range 0 , 1 , . . . n u − 1 . finally , a first p / s converter 42 ( n u to 1 ) recovers the transmitted qam symbol stream z k on branch k . a second p / s converter 43 ( p to 1 ), shown in fig8 , recovers the transmitted qam symbol stream z which is eventually passed to the hard detector 44 ( de - mapper ). the latter , according to the bit - loading table 45 , outputs the eestimationte { overscore ( b )} of the transmitted bit stream b . developing from eq . 2 , the decision variable at the hard detector coming from the u th despreader can be split in three parts : s k ( u ) = ∑ i = 0 g p - 1 ⁢ ( c i ( u ) ) * · w k , i · h k , i · t k , i ( u ) = ∑ i = 0 g p - 1 ⁢ ( c i ( u ) ) * · w k , i · h k , i · a k ( u ) · c i ( u ) eq . ⁢ 4 term m k ( u ) in eq . 3 denotes the self - mui coming from the other signatures , arising when demodulating the u th signature code . that means : m k ( u ) = ∑ i = 0 g p - 1 ⁢ ( c i ( u ) ) * · w k , i · h k , i · [ ∑ l = 0 , l ≠ u n u - 1 ⁢ t k , i ( l ) ] = ∑ i = 0 g p - 1 ⁢ ( c i ( u ) ) * · w k , i · h k , i · [ ∑ l = 0 , l ≠ u n u - 1 ⁢ a k ( l ) · c i ( l ) ] eq . ⁢ 5 finally , the noise term n k in eq . 3 includes all the noise sources ( thermal noise and crosstalk interference ) after equalization and despreading : n k = ∑ i = 0 g p - 1 ⁢ c i · w k , i · ( η k , i + i k , i ) eq . ⁢ 6 in frequency equalization filter ( feq ) 40 of fig7 the following combining techniques may be implemented : orthogonal restoring combining ( orc ), maximum ratio combining ( mrc ), equal gain combining ( egc ) and minimum mean square error ( mmse ) [ 9 ]-[ 13 ]. they are summarized in tab . 1 , where the expression of the related branch equalization coefficients w k , i are given : feq type branch coefficients orc w k , i = 1 h k , i mrc w k , i = h k , i * ecg w k , i = h k , i *  h k , i  mmse w k , i = h k , i * n c ⁢  h k , i  2 + γ in the coefficients for mmse , the parameter γ = σ 2 / e , is the ratio between the overall received noise and the energy of the transmitted signal . note that mmse equalization does not imply any matrix product , but a simpler linear equalization . this approach properly applies to a full - load transmission , when n u = g p signature codes are used . otherwise , when this condition is not met , mmse equalization ends in a multiplication by a block - wise diagonal matrix , whose main blocks computation requires a matrix inversion , resulting in strong computational burden [ 10 ]. the main feature of a dmt transmission that distinguishes it from an usual multi carrier modulation such as ofdm , is the necessity of a bit - loading algorithm [ 8 ]. this means that the qam modulation order of ( or equivalently the number of bits to be loaded on ) each sub - carrier or branch has to be derived according to a certain strategy . on the contrary , using the same qam modulation order on each branch would severely affect the whole transmission because of the great attenuation on high frequency branches . the overall achievable channel rate c can be expressed as the sum of the branch rate c k which is due to n u codes , each of them bearing b k bits : c = 1 t ⁢ ∑ k = 0 p - 1 ⁢ n u · b k = ∑ k = 0 p - 1 ⁢ c k . eq . ⁢ 7 in eq . 7 t = 250 μs is the vdsl symbol time period , comprehensive of cyclic suffix ( cs ) and cyclic prefix ( cp ), and b k = ⌊ log 2 ⁡ ( m k ) ⌋ = ⌊ log 2 ⁡ ( 1 + snr k γ ) ⌋ , eq . ⁢ 8 being [ x ] the greater integer smallest than x , m k the qam order ( number of constellation points ) at the k - th branch , snr k the signal to noise ratio of the decision variable on the same branch , and finally γ the so - called snr gap ( or normalized snr ), defined as : γ = 1 3 ⁢ ( d min 2 ⁢ σ ) 2 . eq . ⁢ 9 the starting point to derive eq . 9 is the ( two - dimensional ) symbol error probability ( ser ) [ 8 ], closely up - bounded by p e ≤ 4 ⁢ q ⁡ ( d min 2 ⁢ σ ) , where q is the well - known q - function , d min is the minimum distance between qam received symbols at the channel output , d min 2 = d 2 | h k | 2 , and d is the distance between the symbols of the transmitted qam constellation . typically , a dsl application should assure a symbol error rate per dimension of 10 − 7 , which yields : ( d min 2 ⁢ σ ) db 2 = 14 , 5 ⁢ ⁢ db + γ m - γ c , eq . ⁢ 10 where γ m is the snr margin ( db ) and γ c is the code gain ( db ). equations 4 , 5 and 6 can be used to derive the signal to noise ratio ( snr ) at the receiver branch k , after preliminary rearrangements in terms of signal energy . thus , eq . 4 can be regarded as : s k ( u ) = ∑ i = 0 g p - 1 ⁢  c i ( u )  2 · w k , i · h k , i · a k ( u ) = d k ( u ) · a k ( u ) eq . ⁢ 11 d k ( u ) = ∑ i = 0 g p - 1 ⁢  c i ( u )  2 · w k , i · h k , i = ∑ i = 0 g p - 1 ⁢ w k , i · h k , i for antipodal binary codes (± 1 ). this way , the received energy per branch at the hard detector input turns out to be : e k ( u ) = e {| z k ( u ) | 2 }= d k ( u ) | 2 · e s ( u ) , eq . 12 where e s ( u ) is the transmitted symbol energy at every branch of the u - th reference code . ( e s ( u ) = e s / n u and e s =− 60 dbm / hz as standardized for a vdsl transmission [ 14 ]). m k ( u ) = ∑ l = 0 , l ≠ u n c - 1 ⁢ a k ( l ) · ∑ i = 0 g p - 1 ⁢ w k , i · h k , i · ( c i ( u ) ) * · c i ( l ) = ∑ l = 0 , l ≠ u n c - 1 ⁢ a k ( l ) · δ k ( l , u ) , ⁢ where eq . ⁢ 13 δ k ( l , u ) = ∑ i = 0 g p - 1 ⁢ w k , i · h k , i · ( c i ( u ) ) * · c i ( l ) eq . ⁢ 14 represents the cross - correlation term between the reference code u and the generic l - th interferer on branch k . this way , the mui interference affects the snr k at the hard detector input with the noise power e m ( u ) =  ∑ l = 0 , l ≠ u g - 1 ⁢ a k ( l ) · δ k ( l , u )  2 . it is important to point out that even dealing with orthogonal codes like the wh ones , depending from the respective feq type , the self - mui interference is not generally zero . the only case when it does happen relates to orc equalization , where w k , i · h k , i = 1 and δ k ( l , u ) = ∑ i = 0 g p - 1 ⁢ ( c i ( u ) ) * · c i ( l ) = g p · δ u , l is equal to g p just in the case of u = l . as far as the noise power is concerned , eq . 6 yields : σ n k 2 = e ⁢ {  n k  2 } = ∑ i = 0 g p - 1 ⁢  c i  2 ·  w k , i  2 · [ e ⁢ {  η k , i  2 } + e ⁢ {  i k , i  2 } ] = ∑ i = 0 g p - 1 ⁢  c i  2 ·  w k , i  2 · [ σ w , k 2 + σ i , k 2 ] = ∑ i = 0 g p - 1 ⁢  c i  2 ·  w k , i  2 · σ k 2 , eq . ⁢ 15 where σ w , k 2 = e { η k , i 2 } is the power spectral density of the input noise (− 140 dbm / hz for a typical vdsl application ) and σ l , k 2 is that of the interference noise on branch k . finally , we can rearrange eq . 15 in the form : f k = ∑ i = 0 g p - 1 ⁢  c i  2 ·  w k , i  2 . eq . ⁢ 17 in conclusion , merging eqs . 12 , 13 and 16 , we can easily derive the signal to noise ratio at the input of the hard detector on branch k for the u th reference code as : snr k ( u ) = e k ( u ) σ n k 2 + e m ( u ) =  d k  2 · e s ( u ) f k · σ k 2 + e m ( u ) eq . ⁢ 18 eq . 18 applies to the detection of the reference code c ( u ) , and used in eq . 8 gives the number of bits to be loaded on every vdsl symbol ( bit - loading ). note that it depends from the type of equalization performed on the receiver . this turns out in different channel capacity considering different feqs on the receiver side . this section shows the results carried out exploiting the mc 2 - cdma modulation scheme presented above , and the bit - loading algorithm strategy derived in section 5 . 1 . 5 . if not differently specified , all the presented results have been derived under the following assumptions : the channel type is ansi tp2 , with diameter of 0 . 5 mm ( or 24 awg ) and the system exploits n c = 4096 sub - carriers , whose spacing is set to 4312 . 5 hz ; a vdsl full duplex ( aggregated , upstream plus downstream ) frequency planning has been considered , featuring an occupation bandwidth from 138 khz ( lower bound ) to 12 mhz ( upper bound ), excluding some reserved ham bands as stated in [ 14 ]; the transmitted signal spectral power density level is − 60 dbm / hz , also according to [ 14 ]; the background thermal noise power spectral density is set to − 140 dbm / hz ; the qam constellation order has been limited to 14 bits per symbol , that seems reasonable taking into account vlsi implementation issues ; no snr margin nor code gain ( γ m = γ c = 0 db ) has been considered ; alien and fext interference comply with the etsi standard [ 14 ]. the latter exhibits a spectral density shaped as according to : p fext ( f , d )= p s ( f ) k f f 2 d | h ( f , d )| 2 ( n / 49 ) 0 . 6 , eq . 19 where p s ( f ) is power spectral density of the transmitted signal , k f = 3 . 27 · 10 − 18 is a constant parameter [ 14 ], d is the coupling length , h ( f , d ) is the channel transfer function of the considered wire , and n is the number of interferes . the first result is that in case of interlaced and true multi - code transmission ( n u & gt ; 1 ), no bit loading is possible and the overall resulting capacity is zero . this is because in an interlaced transmission , the branch transfer function yields heavy signal distortion , both in amplitude and phase . as a consequence , the signature codes orthogonality is corrupted , and a great residual power of self - mui is experienced after despreading . thus , we will consider hereafter a not - interlaced transmission . fig9 shows the bit - loading profile of a typical dmt transmission ( g p = n u = 1 ) in presence of alien and 15 fext interferers . the cable is ansi tp2 with length 1 . 1 km . note that no loading is performed below the start frequency of 138 khz , inside the reserved ham bands ( three bands are highlighted in fig6 ) and roughly beyond 9 mhz . the last result is due to the considered transmission conditions . applying eq . 7 to the profile sketched in figure , the relevant channel rate turns out to be 33 . 99 mbps , which means that 8498 bit are sent per dmt symbol . fig1 shows the simulated channel rate for the orc receiver and g p = 8 as a function of the number n u of signature codes . we can notice a nearly linear relationship between channel capacity and number of used codes , which suggest to use the maximum number of codes for transmission . in the following we will assume n u = g p in order to maximize the channel rate and this situation will be referred as full mc 2 - cdma . however , a deeper sight reveals a slight decreasing in the function slope . on the one hand orc equalization completely recovers the orthogonality among users codes destroyed by the channel , and no residual mui is experienced on the decision variable . on the other , the higher the number of used codes , the lower the transmission energy per code and consequently the snr k at the branch detector input , resulting in a lower number of bits allocated on each branch than expected with a linear low . the case n u = 1 relates to a standard mc - cdma transmission , where no multi - code is adopted . as foreseen in section 4 , the adoption of a mc - cdma modulation scheme yields worse performance than a standard dmt transmission ( 7 . 364 mbps when g p = 8 compared with 33 . 984 mbps ). the simulated channel rate is also plotted as a function of the code gain ( ranging in [ 1 - 64 ]) for different equalization techniques in fig1 . here , the case g p = 1 refers to the standard dmt transmission . we can see that orc as well as mmse outperforms the other combining techniques , and that they yield a channel rate independent of the processing gain itself . usually mmse assures better performance than orc [ 4 ]-[ 6 ], because it avoids the noise amplification on the weak sub - carriers , as happens with orc instead . on the other hand mmse does not maintain the signature codes orthogonality , which is the main issue in a multi - code environment , and the term e m ( u ) in eq . 18 is not zero as for orc . as a result , mmse and orc perform almost the same . however , from a system complexity point of view , the latter results in a simpler implementation , thus it is preferable to the former . finally , fig1 reports the simulated loading profile for a full mc 2 - cdma system , in presence of alien and 15 fext interferers as usual . the wire is 1 . 1 km - long , type ansi tp2 . here the total number of bits transmitted on a each branch ( given by the product of the qam modulation order and the number of used signature codes ), assuming n u = g p active codes per transmission , is plotted against the branch index . the branches have been numbered consecutively , and for instance the first branch lies from the frequency 138 khz up to 138 + 8 * 4 , 3125 = 172 , 5 khz . note that branch index 320 corresponds roughly to 320 · 8 · 4 , 3125 khz ≅ 12 mhz . for the sake of comparison , fig1 reports the bit - loading profile in the same condition as fig8 , relating to a mc - cdma modulation scheme with g p = 8 . the overall channel rate is 7 . 364 mbps . once the suitability of the mc 2 - cdma modulation in association with orc has been demonstrated ( see section 5 . 1 . 6 ) we further want to optimize it in terms of number of transmitted code per branch . that is , eq . 1 can be rearranged adopting a variable number of signature codes on each branch , i . e . n u = n u ( k ). this way the transmitted samples can be expressed as t k , i = ∑ l = 0 n u ⁡ ( k ) - 1 ⁢ t k , i ( l ) = ∑ l = 0 n u ⁡ ( k ) - 1 ⁢ a k ( l ) · c i ( l ) . eq . ⁢ 20 for each branch , the optimum value of n u ( k ) that maximizes the branch rate c k re - defined as the product of the number of bits b k by the number of used codes n u ( k ), has to be determined as a trade - off between the number of transmission codes ( acting linearly on c k ) and the number of bits sent on each signature codes ( decreasing for high value of n u ( k )). in other words , the number of bits ( per code ) loaded on each branch relates to the signal to noise ratio snr k through eq . 8 : the higher snr k , the higher b k . when orc is performed in the feq , no residual mui is experienced on the hard detector input , and eq . 18 can be simplified in : snr k ( u ) = e k ( u ) σ n k 2 =  d k  2 · e s ( u ) f k · σ k 2 eq . ⁢ 21 using n u ( k )≦ g p results in increased signal energy per transmitted code ( e s ( u ) = e s / n u ) with respect to full mc 2 - cdma , which can be translated in a higher number of bits sent on each branch . hence , n u ( k ) is just chosen as the argument maximizing the branch rate n u ( k )· b k : n u ( k )= arg max { n u ( k )· b k } eq . 22 this optimization was initially suggested by a simple observation : there is no possibility for medium - long wires to modulate roughly beyond the 200 - th branch ( depending on the system environment ) when a full mc 2 - cdma scheme is adopted . on the other hand , adopting n u & lt ; g p increases the bit loading upper bound , but at the same time the overall channel rate is lowered ( compare fig1 and fig1 ). the procedure described by eq . 22 can be implemented with a simple search algorithm . starting from n u ( k )= 1 , snr k ( u ) is first evaluated according to eq . 21 . then , exploiting eq . 8 , b k is derived . finally , the product c k 1 ≡ n u ( k )· b k | n u ( k )= 1 = b k of eq . 22 is calculated . next , the same steps are repeated with n u ( k )= 2 , and the product c k 2 ≡ n u ( k )· b k | n u ( k )= 2 = 2 · b k is calculated . this is done for any value of n u ( k ) up to n u ( k )= g p . finally , by simple comparison , the value n * of n u ( k ) that maximizes c k n u ( k ) is derived . the procedure described above is repeated for any branch k of the communication system . fig1 shows the simulated bit - loading profile carried out with the enhanced , optimized transmission scheme , compared with the not - optimized full mc 2 - cdma solution . the branch rate n u ( k )· b k has been plotted here versus the branch index ranging into [ 1 , p ]. as foreseen above , the optimized approach extends the loading bound at about branch 300 , resulting in a rate improvement of about 5 %. fig1 compares the channel rate of the enhanced mc 2 - cdma scheme as a function of the spreading gain against the ones obtained with different detection techniques . the value g p = 16 represents the best trade - off between hardware complexity and performance improvement , since no remarkable advantages are achieved with higher value of the processing gain . fig1 . a reports the channel rate for a standard dmt ( g p = 1 ), the full mc 2 - cdma modulation and the optimized one ( both with g p = 16 ) in presence of alien and 15 fext interferers . the optimized solution outperforms the others for any cable length , and the not - optimized mc 2 - cdma scheme performs almost the same as the standard dmt as expected , the longer the cable length , the lower the channel rate . fig1 . b provides the relative gain of both the enhanced algorithm and the full mc 2 - cdma w . r . t the usual dmt scheme , in the same condition of fig1 . a . an average gain of roughly 3 % w . r . t the standard dmt modulation for the enhanced algorithm has been demonstrated . moreover , the enhanced mc 2 - cdma modulation gains up to 5 % for medium - long wires w . r . t . dmt . eventually , the not - optimized mc 2 - cdma scheme is confirmed to perform almost the same as the classic dmt , and its average gain results almost zero . fig1 a and 17b compare the same modulation schemes as fig1 a and 16b , but in presence of 25 fext interferers . still , the enhanced mc 2 - cdma modulation overall gains roughly 3 % w . r . t standard dmt modulation and up to 5 % for medium - long wires ( longer than 1 km ). finally , fig1 a and 18b show the simulated channel rate in absence of alien and fext crosstalk ( ideal no noisy transmission ). as expected , the channel rate reaches higher value than before , but there is no clear gain between the two modulation techniques for short wires . even if there is an average relative gain of about 3 % for medium - long wires , the overall improvement is quite low , which means that the proposed optimized solution mainly suits in noisy environment with lots of cross - talkers . the upper bound of the channel rate for short wires is due to the considered qam order limitation ( set to 14 through these simulations ). for the sake of completeness , fig1 a and 19b report the channel rate and the relevant gain in presence of alien and 25 fext interferers , when an ansi tp1 wire ( 0 . 4 mm , 26 awg ) is used . again , an average gain of about 4 % for medium - long wires is demonstrated . the foregoing description of a specific embodiment will so fully reveal the invention according to the conceptual point of view , so that others , by applying current knowledge , will be able to modify and / or adapt for various applications such an embodiment without further research and without parting from the invention , and it is therefore to be understood that such adaptations and modifications will have to be considered as equivalent to the specific embodiment . the means and the materials to realise the different functions described herein could have a different nature without , for this reason , departing from the field of the invention . it is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation . f . sjöberg , the zipper duplex method in very high - 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