Abstract:
A method and apparatus are disclosed for reducing the computational complexity of the RSSE technique. The apparatus and associated method does not assume that the signal energy of a pulse that has gone through a channel is always concentrated primarily in the initial taps, as is true for a minimum phase channel. The present invention, however, recognizes that the signal energy is often concentrated in just a few channel coefficients, with the remaining channel coefficients being close to zero. A receiver apparatus and associated method is disclosed for reducing the number of channel coefficients to be processed with a high complexity cancellation algorithm from L to V+K which contain the majority of the signal energy, while processing the L−(K+V) non-selected coefficients with a lower complexity algorithm. By only processing the intersymbol interference caused by a reduced number of channel coefficients (i.e., L−(K+V)) using the tap-selectable TS-RSSE technique, while processing the intersymbol interference caused by the remaining channel coefficients with the tap-selectable decision feedback prefilter TS-DFP technique, a good bit error rate (BER) versus signal-to-noise ratio (SNR) performance is insured for a well-chosen value of V, where V represents the number of channel coefficients processed with the TS-RSSE technique (i.e., high complexity algorithm). No presumption is made apriori concerning which V taps will be processed by the TS-RSSE algorithm, but rather, an a posteriori determination is made in response to a changing channel impulse response.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates generally to equalization and decoding in communication systems, and in particular, to sequence estimation techniques with reduced complexity. 
     2. Discussion of the Prior Art 
     A limiting factor in the performance of digital communication systems which are designed to transmit digital data over a time-dispersive channel is intersymbol interference (ISI). FIG. 1 shows the block diagram for a conventional receiver  100  in a channel environment associated with, for example, the Gigabit Ethernet 1000 Base-T standard. As shown in FIG. 1, the receiver  100  includes an analog-to-digital (A/D) converter  110  for converting the received analog signal to a digital signal. The digitized data is then processed by a feed forward equalizer (FFE)  120 ; an echo canceller  130  and a crosstalk canceller  140 . Generally, the feed forward equalizer (FFE)  120  makes the channel impulse causal, and additionally whitens the noise. In addition, the echo canceller  130  removes echo from the received signal and the crosstalk canceller  140  removes the crosstalk, as is well known in the art. The equalizer/decoder  150  performs data detection, for example, using maximum likelihood sequence estimation (MLSE), to produce output symbols or bits. 
     It is well known that MSLE is the optimum method for the recovery of a data sequence in the presence of ISI and additive white Gaussian noise (AWGN). For a more detailed discussion of a maximum likelihood sequence estimation (MLSE), see G. D. Forney Jr., “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 363-378, May 1972, incorporated by reference herein. 
     The Viterbi Algorithm is a computationally efficient implementation of MLSE, however, it requires an excessive amount of computing power for most practical channels found in broadband communication systems. For a more detailed discussion of the Viterbi algorithm, see G. D. Forney, Jr. “The Viterbi Algorithm,” Proc. IEEE, vol. 61, pp. 268-278, March 1973. Several sub-optimal modifications to the Viterbi algorithm have been introduced to reduce the computational complexity of the Viterbi algorithm. One such technique is reduced state sequence estimation (RSSE). Referring to FIG. 1, block  150 , the equalizer/decoder may be implemented as an RSSE circuit. Two special cases of RSSE are Decision-feedback sequence estimation (DFSE), and parallel decision feedback decoding (PDFD). DFSE employs a trellis that takes into account only the first K of the L channel coefficients {f i }, 1≦i≦L, where L is the channel memory. PDFD is a special case of DFSE when K=0, where the reduced trellis becomes the TCM code trellis and decision feedback equalization is performed for each code state based on its survivor history. For a discussion of reduced state sequence estimation (RSSE) techniques and for the special cases (i.e., DFSE and PDFD), see, for example, P. R. Chevillat and E. Eleftheriou, “Decoding of Trellis-Encoded Signals in the Presence of Intersymbol Interference and Noise”, IEEE Trans. Commun., vol. 37, 669-76, (July 1989) and M. V. Eyuboglu and S. U. H. Qureshi, “Reduced-State Sequence Estimation For Coded Modulation On Intersymbol Interference Channels”, IEEE JSAC, vol. 7, 989-95 (August 1989), each incorporated by reference herein. RSSE is well suited for implementation in dedicated hardware due to its high parallelism, unlike other reduced complexity sequence estimation techniques such as the M-algorithm. For a discussion of M-algorithms (MA), see, for example, N. Seshadri and J. B. Anderson, “Decoding of Severely Filtered Modulation codes Using the (M,L) Algorithm”, IEEE JSAC, vol. 7, 1006-1016 (August 1989), incorporated by reference herein. Although RSSE has been proposed as a means to reduce the computational complexity of MLSE, the hardware cost of RSSE can still be very high. 
     FIG. 2 is an implementation of an RSSE equalizer/decoder which attempts to reduce the intersymbol interference associated with all channel coefficients, {f i }, 1≦i≦L, of the channel impulse response with memory L. The R decision feedback cells  209  of FIG. 2 compute R ISI estimates in the decision feedback unit (DFU)  208  based on the survivor symbols from the corresponding survivor path cells  207  of FIG. 2 in the survivor memory unit (SMU)  206 . These estimates are fed into the branch metric unit (BMU)  202  in which each branch metric cell  203  of FIG. 2 computes the b metrics for the transitions emanating from the corresponding state. In the add/compare select unit (ACSU)  204  each add/compare select cell selects the best survivor path among all paths entering the state. 
     While RSSE reduces the complexity of MLSE, its hardware costs can still be very high in practical applications. To reduce the hardware costs of RSSE, it has been proposed to account only for the ISI introduced by the first U taps of the channel impulse response, {f i }, 1≦i≦U with an RSSE structure  302 , as shown in FIG. 3, and cancel the remaining ISI with a simple equalizer structure  304 . Referring again to block  150  of FIG. 1, it was previously stated that block  150  could be implemented as structure  200  of FIG.  2 . Structure  300  of FIG. 3 represents another possible structure to implement block  150  to reduce the complexity of MLSE. 
     FIG. 4 is an illustration of the RSSE structure  302  of FIG.  3 . In the decision feedback unit (DFU)  408  each decision feedback cell  409  takes care of the ISI introduced by the first U channel coefficients, {f}, 1≦i≦U, where the number U is predetermined. The ISI from only the first U channel coefficients are considered in the RSSE apparatus  302  of FIG. 3 based on an assumption that the channel impulse response which is seen by the equalizer/decoder (See block  150  of FIG. 1) is concentrated in the first U taps, as shown by the graph of signal energy v. coefficient index, i, in FIG. 5 a . Further, Block  304  of FIG. 3 reduces the intersymbol interference from other than the first U taps, {f i }, U+1≦i≦L. This assumption is often valid for a minimum phase channel, however, in general the channel impulse response may be concentrated in taps other than the first U taps (e.g. Gigabit Ethernet over copper), or components in the tail of the channel impulse response may be significant. Furthermore, the distribution of the channel impulse response may change over time. As such, the channel energy will be concentrated in different taps as a function of time. FIG. 5 b  illustrates a channel impulse response graph with significant channel coefficients in the tail. In these cases the reduced complexity RSSE equalizer/decoder  300  of FIG. 3, would exhibit significantly inferior performance. Thus, there is a need for a low computationally complex RSSE equalizer/decoder that exhibits acceptable performance in a wide variety of channel impulse responses and which is adaptively reconfigurable in response to changing channel environments and does not change the number of states as disclosed in the prior art. 
     SUMMARY OF THE INVENTION 
     The present invention provides an apparatus and method for reducing the computational complexity of the RSSE technique by reducing the intersymbol interference caused by significant channel coefficients with a tap selectable TS-RSSE (i.e., high complexity equalization and decoding algorithm). The more significant channel coefficients are adaptively selected in response to changes in the channel impulse response. Further, the intersymbol interference caused by the less significant channel coefficients is processed by a tap selectable decision feedback prefilter TS-DFP (i.e., a low complexity equalization algorithm). Referring again to FIG. 1, which is an illustration of the channel environment associated with, for example, the Gigabit Ethernet 1000 Base-T standard, the equalizer/decoder of the present invention could be used to implement the block  150 . Utilizing the equalizer/decoder of the present invention to implement block  150  is advantageous because of its reduced complexity and also because of its improved adaptivity to a changing channel impulse response as compared to the prior art. 
     The present invention is based on the observation that for a communication channel having a channel memory L and comprising L+1 channel coefficients, {f i }, 0≦i≦L, only a subset of the L channel coefficients associated with the memory, {f i }, 1≦i≦L, will contribute most significantly to the intersymbol interference caused by the channel. Prior art approaches have assumed the most significant coefficients associated with the channel memory to be concentrated in the initial taps of the channel impulse response {f i }, 1≦i≦U. However, this assumption does not hold true in some applications like Gigabit ethernet over copper or broadband wireless communication systems. In these cases, it cannot be foreseen which of the L channel coefficients contribute most significantly to the intersymbol interference. The present invention determines these most significant coefficients adaptively, and then processes the intersymbol interference caused by them using a tap-selectable RSSE, i.e., TS-RSSE. The present invention also adaptively processes the intersymbol interference caused by the less significant coefficients with a tap selectable DFP technique (TS-DFP). With each change of the channel impulse response, a new determination is made concerning which of the L channel coefficients associated with the memory, i.e., {f i }, 1≦i≦L, are to be adaptively selected for processing in accordance with either the TS-DFP technique or the TS-RSSE technique. It should be noted, that unlike prior art implementations the present invention does not reduce the number of states of the trellis considered by the tap selectable RSSE technique (TS-RSSE). 
     Accordingly, the invention provides a receiver apparatus and associated method for reducing the number of channel coefficients whose intersymbol interference is to be processed with the high complexity TS-RSSE cancellation algorithm. In a preferred embodiment, channel coefficients are adaptively selected as contributing most significantly to the intersymbol interference, and are processed by the TS-RSSE technique. The non-selected channel coefficients are processed with a TS-DFP technique. 
     The determination as to which channel coefficients contribute most significantly to the intersymbol interference is implemented in a number of alternate embodiments. In a first embodiment, channel coefficients are adaptively selected for processing by the TS-RSSE technique based on whether the coefficient&#39;s squared or absolute value is above a predetermined threshold. Those coefficients exceeding the threshold will be processed by the TS-RSSE technique, and those coefficients below the threshold will be processed by the TS-DFP technique. 
     In a second embodiment, channel coefficients are adaptively selected for processing by the TS-RSSE technique by establishing a threshold and summing the squared or absolute value of the channel coefficients in decreasing squared or absolute value order until the threshold is met. The intersymbol interference associated with the channel coefficients which collectively sum to the threshold value are processed by the TS-RSSE technique. While the intersymbol interference associated with those coefficients not included in the summation are processed by the TS-DFP technique. 
     In a third embodiment, channel coefficients are adaptively selected for processing by the TS-RSSE technique by selecting only those channel coefficients whose absolute or squared value is highest. A prescribed number of coefficients may be selected for inclusion in the set. 
     The receiver of the present invention is referred to as a tap-selectable RSSE equalizer/decoder (TS-RSSE) with a tap-selectable decision prefilter (TS-DFP). The channel impulse response is modeled in the receiver by L+1 taps, {f i }, 0≦i≦L, (i.e., the memory is L). The first K taps associated with the channel memory, {f i }, 1≦i≦K, are referred to as non-selectable taps and are processed with a high complexity TS-RSSE cancellation algorithm. The remaining taps associated with the channel memory, {f i }, K+1≦i≦L, are referred to as selectable taps and are analyzed to adaptively select V taps to achieve a reasonably low bit error rate BER. The tap selection process is adaptive in the sense that the V taps identified in any selection period change with a changing channel environment. The intersymbol interference caused by the adaptively selected V taps are processed with the high complexity TS-RSSE cancellation algorithm. The intersymbol interference caused by the non-selected L−(K+V) taps are processed with a lower complexity TS-DFP cancellation algorithm. 
     The adaptive TS-RSSE equalizer/decoder of the present invention advantageously reduces the complexity of a conventional RSSE equalizer/decoder (See FIG. 2) by only processing the intersymbol interference caused by a reduced number of channel coefficients with a high complexity TS-RSSE equalizer/decoder and processing the intersymbol interference caused by the remaining channel coefficients with a lower complexity TS-DFP circuit. The present invention is advantageous over the prior art RSSE equalizer/decoder in that the prior art RSSE equalizer/decoder processes the intersymbol interference due to all channel coefficients of the channel impulse response. By contrast, the present invention is of lower complexity by virtue of only processing the intersymbol interference caused by a reduced number of channel coefficients with a TS-RSSE circuit. The present invention, however, does not further change the number of states which are processed in the RSSE circuit, which facilitates the implementation in dedicated hardware and preserves the bit error rate performance of a conventional RSSE circuit. Further, the receiver of the present invention provides superior performance over a prior art reduced complexity RSSE equalizer/decoder, as illustrated in FIG. 3, in that the prior art receiver assumes that the more significant channel coefficients are located in the beginning of the channel impulse. Advantageously, the hardware increase in constructing a TS-RSSE equalizer/decoder of the present invention over a reduced complexity RSSE equalizer/decoder of the prior art, as shown in FIGS. 3 and 4 is moderate. No presumption is made apriori concerning which channel coefficients are more significant to process their associated intersymbol interference by the TS-RSSE circuit, but rather, an a posteriori determination is made in response to a changing channel impulse response. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The features of the disclosed tap selectable equalizer/decoder and method will become more readily apparent and may be better understood by referring to the following detailed description of an illustrative embodiment of the present invention, taken in conjunction with the accompanying drawings, where: 
     FIG. 1 is a schematic block diagram of a prior art receiver; 
     FIG. 2 is a schematic block diagram of an RSSE equalizer/decoder according to the prior art; 
     FIG. 3 is a schematic block diagram of a reduced complexity RSSE equalizer/decoder according to the prior art; 
     FIG. 4 is a schematic block diagram of an RSSE structure of FIG. 3; 
     FIG. 5 a  is graph illustrating the channel impulse response of a minimum phase channel; 
     FIG. 5 b  is a graph illustrating the channel impulse response with significant energy in the tail; 
     FIG. 6 is a schematic block diagram of a tap selectable RSSE equalizer/decoder (TS-RSSE) with a tap selectable decision feedback prefilter (TS-DFP); 
     FIG. 7 illustrates the discrete states of a trellis code associated with Gigabit Ethernet 1000Base-T; 
     FIG. 8 is a diagram of a discrete time channel model using a discrete time FIR filter; 
     FIGS. 9 a - 9   c  are schematic block diagrams which illustrate three embodiments for selecting channel coefficients by the tap selector; 
     FIG. 10 illustrates one embodiment of a tap-selectable decision feedback pre-filter (TS-DFP) in accordance with the present invention; 
     FIG. 11 illustrates a second embodiment of a tap-selectable decision feedback pre-filter (TS-DFP) in accordance with the present invention; 
     FIG. 12 illustrates a third embodiment of a tap-selectable decision feedback pre-filter (TS-DFP) in accordance with the present invention; 
     FIG. 13 illustrates a fourth embodiment of a tap-selectable decision feedback pre-filter (TS-DFP) in accordance with the present invention; 
     FIG. 14 is a block diagram of a tap-selectable RSSE equalizer/decoder (TS-RSSE) in accordance with the present invention; 
     FIG. 15 is an illustration of one of the SPC cells corresponding to state  1  of FIG. 7 of the SMU of FIG. 14; 
     FIG. 16 is an illustration of a TS-DFC cell of FIG. 14; 
     FIG. 17 is an illustration of a U-DFC cell of FIG. 16; 
     FIG. 18 is an embodiment of a V-DFC cell of FIG. 16 in accordance with the present invention; 
     FIG. 19 is a second embodiment of a V-DFC cell of FIG. 16 in accordance with the present invention; 
     FIG. 20 is a second embodiment of a schematic block diagram of a tap selectable RSSE equalizer/decoder (TS-RSSE) with a tap selectable decision feedback prefilter (TS-DFP); 
     FIG. 21 is an embodiment of the tap-selectable TS-RSSE equalizer/decoder of FIG. 20; 
     FIG. 22 is one embodiment of a tap-selectable DFP (TS-DFP) of FIG. 20; 
     FIG. 22 is another embodiment of a tap-selectable DFP (TS-DFP) of FIG. 20; 
     FIG. 24 is a schematic block diagram of a tap selectable RSSE equalizer/decoder (TS-RSSE) with a tap selectable decision feedback prefilter (TS-DFP) illustrating three embodiments of a method of power control; and 
     FIG. 25 is a schematic block diagram of a TS-DFP structure of the present invention illustrating one embodiment of obtaining a channel quality metric from the TS-DFP. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 6 illustrates an equalizer/decoder  600  in accordance with the present invention that reduces the computational complexity of reduced state sequence estimation (RSSE) algorithm for a given number of states. The receiver of the present invention is designed for a communication system based on the channel model using a discrete time FIR filter, having a channel memory of L, where the channel impulse response is assumed to have a length of (L+1) symbol periods denoted by {f i } iε[0, . . , L] where f i  is the coefficient for channel tap i, and the zeroeth tap of the channel impulse response, f 0 , is assumed to be one without loss of generality. The zeroeth tap is not in the memory and just multiplies the signal. The discrete time channel model presumes a trellis coded modulation (TCM) system which is corrupted by intersymbol interference and additive white gaussian noise (AWGN). 
     FIG. 7 illustrates the discrete states of a trellis code associated with Gigabit Ethernet 1000Base-T. It should be noted that present invention is equally applicable to non-trellis coded modulation systems. 
     FIG. 8 illustrates the discrete time model of a communication system, generally designated as numeral  800 . Information symbols X n  consisting of m bits are fed into the TCM encoder  802 . The rate m′/(m′+1) encoder operates on m′ input bits and produces m′+1 encoded bits, which are used to select one of the 2 m′+1  subsets (each of size 2 m−m′ ) from the employed signal constellation of size 2 m+1  by the symbol mapper  804 , while the uncoded bits are used to select one symbol a n  within the chosen subset. The selected symbol is sent over the equivalent discrete-time channel modeled as a discrete time FIR filter  806 . The channel output z n  at time instant n is given by                z   n     =         q   n     +     w   n       =         ∑     i   =   0     L                       f   i     ·     a     n   -   i           +     w   n                 (   1   )                                
     where q n  is the signal corrupted by ISI, {f i }, iε[0, . . . , L] are the tap coefficients of the equivalent discrete-time channel impulse response (CIR) (f 0 =1 is assumed without loss of generality), L is the length of the channel memory, and {w n } represents white Gaussian noise with zero mean and variance σ 2 . 
     According to a feature of the present invention, the intersymbol interference caused by the L tap coefficients associated with the channel memory, {f i }, 1≦i≦L, are processed in either the TS-DFP  604  or the TS-RSSE  608  under the control of the tap selector  606 . The TS-DFP  604  is discussed further below in conjunction with FIG. 10-13, and the TS-RSSE  508  is discussed further below in conjunction with FIGS. 14-19. 
     In accordance with a preferred embodiment of the invention, the first K tap coefficients associated with the channel memory, {f i }, 1≦i≦K, belong to the set referred to herein as non-selectable tap coefficients N={f 1 , . . . , f K }, |N|=K=the number of elements in set N. The intersymbol interference caused by the channel coefficients associated with these tap coefficients is processed in the tap selectable reduced state sequence estimator TS-RSSE  608 . Typically, the first K tap coefficients associated with the channel memory, {f i }, 1≦i≦K, are also used to contribute to the TS-RSSE trellis structure, however, some number of taps other than K may be used for the construction of the trellis structure. That is, the number of taps selected for the TS-RSSE trellis structure may range from 0 to L and is independent of the number of non-selectable tap coefficients, denoted by K, selected for processing in the TS-RSSE  608 . 
     The remaining K+1 through L tap coefficients, i.e., {f i } iε[K+1, . . . , L], are collectively referred to herein as selectable taps, S={f K+1 , . . . , f L }, |S|=L−K, and are further divided into two subsets, a set referred to as more significant selectable tap coefficients and a set referred to as less significant selectable tap coefficients. The set of more significant selectable tap coefficients is defined as set A, where A={f i     j   |f i     j   εS{circumflex over ( )}(1≦j≦V)}, |A|=V=the number of elements in set A. Set A describes a set of tap coefficients having a set size equal to V, selected from among those coefficients in the set S (i.e., f K+1  through f L ). Coefficient f i     j    is characterized such that it is contained in set S (the set of selectable taps) and (1≦j≦V). The set of less significant selectable taps is defined as set B, where B=S\A=set S without set A, and |B|=L−K−V=the number of elements in set B. The tap selector  606  analyzes the set of selectable tap coefficients (i.e., set S) to select V tap coefficients as being more significant (i.e., set A), based on a predetermined criteria to be discussed below. The L−(K+V) taps not selected by the tap selector  606  are considered the less significant selectable tap coefficients (set B). 
     Table 1 below summarizes the processing the ISI caused by each of the L channel coefficients, f 1  through f L , which are associated with the channel memory of the discrete time filter modeling the communication channel illustrated in FIG.  8 . It should be noted that K may assume a zero value, in which case all tap coefficients are referred to as tap selectable. 
     
       
         
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Coefficient Classification 
                 Processing Means 
               
               
                   
               
             
             
               
                 NON-SELECTABLE TAP 
                 Tap-selectable 
               
               
                 COEFFICIENTS 
                 Reduced state sequence 
               
               
                 Coefficients 1 through K 
                 estimation 
               
               
                 Set N = {f 1 ,...,f k },|N| = K 
                 (i.e., TS-RSSE 608) 
               
               
                 MORE SIGNIFICANT SELECTABLE 
                 Tap-selectable 
               
               
                 TAP COEFFICIENTS 
                 Reduced state sequence 
               
               
                 V coefficients 
                 estimation 
               
               
                 (representing those coefficients selected by 
                 (i.e., TS-RSSE 608) 
               
               
                 the tap selector from those coefficients with 
               
               
                 index k + 1 through L) 
               
               
                 set A = {fi j |fi j  ∈S{circumflex over ( )}(1 ≦ j ≦ V)}, |A| = V 
               
               
                 LESS SIGNIFICANT SELECTABLE TAP 
                 Tap-selectable 
               
               
                 COEFFICIENTS 
                 Decision feedback prefilter 
               
               
                 L-(K + V) Coefficients 
                 (i.e., TS-DFP 604) 
               
               
                 (representing those coefficients not selected 
               
               
                 by the tap selector from those coefficients 
               
               
                 with index k + 1 through L) 
               
               
                 set B = S\A, |B| = L − K − V 
               
               
                   
               
               
                 Note: Set S defines the set of selectable coefficients, equal to the union of sets B and A.  
               
             
          
         
       
     
     Referring to FIG. 6, upon selecting the V more significant coefficients from set S, the tap selector  606  outputs L−K control signals {s i }, K+1≦i≦L. Those control signals which correspond to the V more significant selectable coefficients (set A), identified by the tap selector  606 , will be assigned an identifying control signal value. Similarly, those control signals which correspond to the (L−(K+V) less significant selectable channel tap coefficients (set B) will be assigned an identifying control signal value. 
     In one embodiment, the control signals corresponding to the V more significant selectable channel tap coefficients (set A) are assigned a value of 1, while the control signals corresponding to the L−(V+K) non-significant selectable channel tap coefficients (set B) are assigned a control signal value of 0, defined as 
     
       
           f   i   εA→s   i =1 
       
     
     
       
           f   i   εB→s   i =0  (2) 
       
     
     According to one aspect of the present invention, the channel coefficients may be analyzed by the tap selector  606  periodically or according to different specified criteria. For example, in a packet based system, often employed in wireless applications, the tap selector  606  might analyze the L−K selectable channel coefficients (set S) at the beginning of each received packet. 
     Referring to FIG. 6, the tap selector  606  analyzes the selectable L−K channel tap coefficients {f i }, K+1≦i≦L, (i.e., set S) to select V tap coefficients according to a predetermined criteria. In one embodiment, V tap coefficients are selected as those having the largest relative squared or absolute value from among the selectable L−K channel tap coefficients (set S) as defined by: 
       f   i   εA{circumflex over ( )}f   j   εB→|f   i   |&gt;|f   j |  (3) 
     FIG. 9 a  illustrates a hardware embodiment of the present invention corresponding to equation (3) for finding the V more significant tap coefficients (set A). The sorter  92  prioritizes the channel coefficients in descending absolute or squared value at its output to facilitate selection of the V most significant coefficients. 
     A variation of selecting a predetermined number of tap coefficients, V, as described above would be to sum the absolute values of f i     j   εA in decreasing absolute value order until a predetermined threshold E is met, once the threshold is met, the number of tap coefficients included in the sum determines the value V. The threshold criteria is expressed as:                  ∑     j   =   1     V                          f     i   j              &gt;   E           (   4   )                                
     A further variation of the embodiment expressed by equation (3) would be to sum the absolute values of f i εN and those f i     j   εA such that the following condition is met:                      ∑     l   =   1     K                          f   l            +       ∑     j   =   1     V                          f     i   j                    ∑     i   =   1     L                          f   i              &gt;   E           (   5   )                                
     The f i     j   εA are evaluated in decreasing absolute value order for possible inclusion ins set A. The number of coefficients, f i     j   εA, selected determines the value of V. The threshold criteria expressed by equation (5) states that the ratio of the sum of the non-selectable tap coefficients (set N), added to the sum of the more significant tap selectable coefficients (set A), which form the numerator, divided by the sum of all tap coefficients, must exceed a threshold ratio, E. The threshold ratio E could, for example, be set some fraction close to 1 (e.g., 0.95). 
     In an alternate embodiment, the V coefficients are determined by setting a general coefficient threshold T. Those channel coefficients exceeding the general coefficient threshold, T, are included as one of the V tap coefficients, defined by 
     
       
           f   i   εS{circumflex over ( )}|f   i   |&gt;T→f   i   εA   (6) 
       
     
     FIG. 9 b  illustrates a hardware implementation of equation (6). FIG. 9 b  illustrates that each coefficient is tested against the threshold T. 
     A further variation of equation (6) would be to choose the coefficient threshold T such that when the absolute values of those coefficients which exceed the coefficient threshold, f i     j   εA are summed such that the following condition is met                  ∑     j   =   1     V                          f     i   j              &gt;   E           (   7   )                                
     A further variation of equation (5) would be to choose T such that when the absolute values of f i εN and those Fij, f i     j   εA, which exceed T, are summed up, the following condition is met:                      ∑     l   =   1     K                          f   l            +       ∑     j   =   1     V                          f     i   j                    ∑     i   =   1     L                          f   i              &gt;   E           (   8   )                                
     In a further alternate embodiment, to determine the V more significant coefficients, the threshold method of the previously described embodiment is modified such that each coefficient has associated therewith a unique coefficient threshold {T i }, iε[K+1, . . . , L] for each selectable tap f i εA: 
     
       
           f   i   εS{circumflex over ( )}|f   i   |&gt;T   i→f   i   εA   (9) 
       
     
     FIG. 9 c  illustrates a hardware implementation of equation (9). FIG. 9 c  illustrates that each coefficient is tested against its unique coefficient threshold, T K+1  through T L . 
     A variation of equation (9) would be to choose the respective coefficient thresholds {T i } such that when the absolute values of f i     j   εA, which exceed their associated thresholds are summed up, the following condition is met:                  ∑     j   =   1     V                          f     i   j              &gt;   E           (   10   )                                
     A further variation of equation (9) would be to choose the respective coefficient thresholds {T i } such that when the absolute values of f i     j   εA, exceeding their associated threshold are summed up, the following condition is met:                      ∑     l   =   1     K                          f   l            +       ∑     j   =   1     V                          f     i   j                    ∑     i   =   1     L                          f   i              &gt;   E           (   11   )                                
     It should be noted that squared values may be substituted for absolute values as used throughout equations (3) through (11). 
     FIG. 10 illustrates one embodiment of a tap-selectable decision feedback pre-filter (TS-DFP)  604  of FIG. 6, generally designated as reference numeral  1000 , for processing the ISI due to the less significant selectable channel tap coefficients (set B). The embodiment of FIG. 10 is referred to as a flexible TS-DFP. It is referred to as a flexible TS-DFP because it reduces the ISI due to the L−(K+V) less significant selectable tap coefficients (set B), where the parameter V, which denotes the number of more significant selectable coefficients can assume any value in the range 0 to L−K. Referring now to FIG. 6, the TS-DFP  604  receives a copy of the L channel coefficients  610 , {f i }, 1≦i≦L, from the channel estimator  602 . The TS-DFP  604  further receives as input L−K tap selector control signal outputs {s i }, K+1≦i≦L,  612  from the tap selector  606 . 
     The flexible TS-DFP  1000  of FIG. 10 cancels the intersymbol interference from the less significant selectable channel tap coefficients (set B) such that the input to the TS-RSSE  608  is                y   n     =       z   n     -       ∑     i   =     K   +   1       L                         s   _     i                     f   i                       a   ⋓       n   -   i                     (   12   )                                
     where {overscore (s)} i  is the negation of s i  (see Eq. 2) and {haeck over (a)} n  is a tentative decision for data symbols an-i. The tentative decision {haeck over (a)} n  is obtained by slicing d n  by slicer  1008 , which may be embodied as a hard decision or soft decision slicer, defined as                d   n     =       z   n     -       ∑     i   =   1     L                       f   i                         a   ⋓       n   -   i       .                   (   13   )                                
     The flexible TS-DFP  1000  of the embodiment illustrated in FIG. 10 differs from a conventional decision feedback equalizer (DFE) in that its filter taps  1006  are selectable via multiplexors  1002  and  1004  so that only the ISI terms from the less significant selectable coefficients (set B) are selected for cancellation from the channel output z n    508  to form the TS-DFP output y n . 
     FIG. 10 shows two sets of multiplexers  1002  and  1004 , where each multiplexer pair (e.g.,  1002   a  and  1004   a ) corresponds to one of the respective tap-selectable tap coefficients f i , iε[K+1, . . . , L]. Effectively, only one multiplexer of each respective pair  1002   a    1004   a  outputs a non-zero value at any one time in accordance with the associated tap control signal s i , defined by equation 2. For example, a positive tap control signal (See eq. 2) would cause each multiplexer of the respective pairs to output the upper input value. For each multiplexer pair of FIG. 10, a zero will be output from one multiplexer and a tap-selectable tap coefficient value will be output from the other multiplexer. Those multiplexers in the bottom row of the pair which output non-zero values in the TS-DFP  1000 , correspond to the (L−(K+V)) less significant selectable coefficients (set B), as determined by the tap selector signal analysis which analyzes coefficients {f i }, iε[K+1, . . . , L]. It is therefore shown, by way of Equations (12) and (13), that the combination of multiplexors and associated tap control signals enable the adaptive selection of those coefficients determined to be less significant for processing their ISI by TS-DFP  1000  to form the output y n . 
     FIG. 11 illustrates another embodiment of a tap-selectable decision feedback pre-filter (TS-DFP)  604  of FIG. 6, generally designated as reference numeral  1100 , for processing the ISI due to the less significant selectable channel coefficients (set B). The embodiment illustrated in FIG. 11 is referred to as a modified flexible tap-selectable decision feedback pre-filter (DFP). The embodiment of FIG. 11 is a modified version of FIG. 10 which similarly computes equations (12) and (13). 
     FIG. 12 illustrates another embodiment of a tap-selectable decision feedback pre-filter (TS-DFP)  604  of FIG. 6, generally designated as reference numeral  1200 , for processing the ISI due to the L−(K+V) less significant selectable channel coefficients (set B). The embodiment illustrated in FIG. 12 is referred to as a minimum area tap-selectable decision feedback pre-filter (DFP). The embodiment of FIG. 12 is a modified version of FIG. 10 which similarly computes equations (12) and (13). 
     As distinguished from the embodiment illustrated in FIGS. 10 and 11 which utilize multiplexers  1002  and  1004  to select channel coefficients, the present embodiment, as illustrated in FIG. 12 utilizes selectors  1202 ,  1204 ,  1206 , and  1208  instead of multiplexers. Selector  1204  selects V channel tap coefficients, set (A), at its respective output from L−K input channel tap coefficients (set S). Selector  1202  selects V symbols which correspond to the more significant selectable channel coefficients (set A) at its respective output from L−K symbols which correspond to the selectable channel coefficients (set S). Selector  1208  selects the L−(K+V) less significant selectable coefficients (set B) at its respective output from the L−K selectable channel coefficients (set S). Selector  1206  selects L−(K+V) symbols (set B), which correspond to the less significant selectable channel coefficients at its respective output from the L−K symbols which correspond to the selectable channel coefficient (set S). 
     FIG. 13 illustrates another embodiment of a tap-selectable decision feedback pre-filter (TS-DFP)  604  of FIG. 6, generally designated as reference numeral  1300 , for processing the ISI due to the (L−(K+V) less significant channel coefficients (set B). The embodiment illustrated in FIG. 13 is referred to as a modified minimum area tap-selectable decision feedback pre-filter (DFP). The embodiment of FIG. 13 is a variation of the embodiment of FIG. 12 which similarly computes equations (12) and (13). 
     FIG. 14 illustrates an embodiment of the tap selectable reduced state sequence estimator (TS-RSSE)  608  of FIG. 6 designated generally by reference numeral  1400 . TS-RSSE  1400  utilizes a reduced state sequence estimation (RSSE) technique to process the ISI due to both the first K tap coefficients (i.e., set N, the non-selectable taps) of the channel impulse response and the V more significant selectable tap coefficients (set A) adaptively selected at each selection interval by the tap selector  606 . 
     The TS-RSSE  1400  of FIG. 14 includes a branch metric unit (BMU)  1402  for calculating the metrics for the transitions from the R states, where R is the number of reduced states. Each branch metric cell (BMC) calculates the b=2 m′  metrics for the b transitions leaving a particular state. The branch metric for reduced state τ n  under input a n  is given by 
     
       
         λ n ( z   n   ,a   n ,τ n )=( z   n   −a   n   −x   n (τ n )) 2   (14) 
       
     
     In the above equation, x n (τ n ) is the ISI estimate for state τ n  and calculated as                    x   n                     (     τ   n     )       =         u   n                     (     τ   n     )       +       v   n                     (     τ   n     )                
          where                   u   n                     (     τ   n     )                   is                 calculated                 as             (   15   )                     u   n                     (     τ   n     )       =       ∑     j   =   1     K                       f   i                       a   ^       n   -   i                       (     τ   n     )                
          and                   v   n                     (     τ   n     )                   can                 be                 either                 calculated                 as             (   16   )                     v   n                     (     τ   n     )       =       ∑     j   =   1       j   =   V                         f     i   j                         a   ^       n   -   ij                       (     τ   n     )                
          or   ,     equivalently                 as               (   17   )                   v   n                     (     τ   n     )       =       ∑     i   =     K   +   1       L                       s   i                     f   i                       a   ^       n   -   i                         (     τ   n     )     .                 (   18   )                                
     In the above equations, â n−i (τ n ) is the survivor symbol corresponding to the data symbol a n-i , from the survivor path into state τ n . An ISI estimate x n (τ n ) is calculated for each of the R states by taking the survivor symbols of the corresponding survivor path as tentative decisions. The calculation of x n (τ n ) according to (15) for a particular state is performed in the TS-DFC  1409 , which is shown in FIG.  16 . 
     The surviving paths into each state are determined in the add-compare-select cells. (ACSC) of the add-compare-select unit (ACSU)  1404 . Among all b paths entering state r n+1  from predecessor states {τ n }, the most likely path is chosen according to following path metric calculation referred to as add-compare-select:                  Γ     n   +   1                       (     τ     n   +   1       )       =       min       {     τ   n     }     →     τ     n   +   1                           (         Γ   n                     (     τ   n     )       +       λ   n                     (       z   n     ,     a   n     ,     τ   n       )         )               (   19   )                                
     The R paths with the surviving symbols are stored in the corresponding survivor path cells (SPCs) of the survivor memory unit (SMU)  1406 . R soft output values are computed by the decision feedback cells (DFCs)  1409  in the decision feedback unit (DFU)  1408  based on the survivors in the SMU  1406 . 
     FIG. 15 is an illustration of one of the SPC cells  1412  of the SMU  1406  of FIG. 14, SPC  1 , corresponding to state  1  of the trellis shown in FIG. 7. A register exchange architecture is assumed where for each state and trellis stage a multiplexer selects a symbol which corresponds to the survivor path. For a more detailed explanation of a register exchange architecture for a survivor memory unit see R. Cypher and C. B. Shung, “Generalized trace-back techniques for survivor memory management in the Viterbi algorithm,” Journal of VLSI Signal Processing, vol. 5, pp. 85-94, 1993. FIG. 15 illustrates multiplexer  1502  which selects at each stage the current symbol corresponding to the survivor path into state  1 . FIG. 15 also illustrates multiplexers  1504  which select at each stage a previous symbol corresponding to the survivor path into state  1 . The candidate symbols are selected from survivor symbols stored in SPC cells  1 ,  3 ,  5 , and  7 . The survivor sequence stored in SPC cell  1  is sent to the TS-DFC cell  1  to calculate an ISI estimate according to equations (15), (16), and (17) or (18). 
     FIG. 16 illustrates a general block diagram of a TS-DFC cell  1409  of FIG. 14 in accordance with the present invention. As shown in FIG. 16, the TS-DFC cell  1409  of FIG. 14 is made up of a U-DFC cell  1604  and a V-DFC unit  1602 . An ISI estimate is calculated by the U-DFC  804  for the first K taps, {f i }, 1≦i≦K, (set N) as illustrated by equation (16). The V-DFC cell of FIG. 16 calculates an ISI estimate for the V channel tap coefficients, set A, as illustrated by equation (17) or (18), which have been selected by the tap selector  606  from among the selectable channel coefficients (set S). The results of equations (16) and (17) or (18) are summed in the summer  1606  of the TS-DFC  1606  to produce an ISI estimate for each of the R states at each discrete time interval. 
     FIG. 17 illustrates one embodiment of a U-DFC cell of FIG.  16 . The embodiment illustrated in FIG. 17 performs equation (16). The U-DFC cell calculates an ISI estimate for the first K non-selectable channel coefficients, f 1  through f K , (set N). 
     FIG. 18 illustrates an embodiment of the V-DFC cell  1602  of FIG. 16, generally designated by the reference numeral  1800 , referred to as a flexible architecture implementation. In the present embodiment, the parameter V can be adaptively set to take any value from 0 to L−K in accordance to changes of the channel characteristics. Here the V-DFC cell  1800  is implemented for all of the selectable channel taps (set S), {f i }, iε[K+1, . . . , L]. For each tap a multiplexer  1802  outputs a channel coefficient or a zero value depending on the control signal values {s i }. The DFC  1800  calculates the ISI for the V more significant selectable channel coefficients (set A) using Equation (18). 
     FIG. 19 illustrates an embodiment of a V-DFC cell  1602  of FIG. 16, referred to herein as a reduced area implementation  1900 . The embodiment illustrated in FIG. 19 performs equation (17). It is a reduced area embodiment in that it accounts for only a fixed number, V, of significant selectable channel taps (set A) for a particular channel environment. That is, the value V is predetermined to be an integer less than or equal to L−K. It is noted that while the total number of significant selectable channel taps, V, are fixed, the indices {i j }, jε[1, . . . , V], however, are not fixed and can be adaptively set during data detection depending on the analysis performed in the selector  606 . 
     FIG. 20 illustrates an alternate embodiment of a tap selectable TS-RSSE equalizer/decoder (TS-RSSE) with a tap selectable decision feedback prefilter (TS-DFP)  2004  in accordance with the present invention. FIG. 21 illustrates a detailed block diagram of a TS-RSSE in accordance with the present embodiment. As shown in FIG. 20, a feedback loop is shown directed from the TS-RSSE  2008  to the TS-DFP  2004 . The feedback loop feeds back the best survivor path from the TS-RSSE  2008  to cancel the intersymbol interference caused by the less significant selectable channel tap coefficients (set B). By contrast, in the embodiment of FIG. 6, the intersymbol interference due to the less significant selectable channel coefficients is cancelled by using tentative decisions obtained in the TS-DFP structure. 
     FIG. 21 illustrates an embodiment of the TS-RSSE  2008  of FIG.  20 . As shown in FIG. 21, the survivor symbols associated with each SPC cell (i.e. SPC  1  through R)  2207  of the SMU  2106  is output to the DFU  2110  and to MUXU  2108 . The ACSU  2104  determines the state of the best path metric and feeds the state number to the MUXU  2108  to select the survivor sequence corresponding to the state with the best path metric (e.g., SPC cell output  1  or  2  or . . . R) to be fed back as tentative data symbols to the TS-DFP  2004  of FIG.  20 . 
     FIG. 22 illustrates one embodiment of a tap-selectable decision feedback pre-filter (TS-DFP)  2004  of FIG. 20, generally designated as reference numeral  2200 , for processing the ISI due to the less significant selectable channel tap coefficients (set B). The embodiment illustrated in FIG. 22 is referred to as a flexible tap-selectable decision feedback pre-filter (DFP). The embodiment of FIG. 22 computes equation (20):                y   n     =       z   n     -       ∑     i   =     K   +   1       L                         s   _     i                     f   i                       a   ^       n   -   i                       (     τ   n   ′     )                   (   20   )                                
     In this equation, â n-i (τ′ n ) is the survivor symbol into the state τ′ n  with the best path metric among all R states and it corresponds to data symbol a n−i . 
     FIG. 23 illustrates another embodiment of a tap-selectable decision feedback pre-filter (TS-DFP)  2004  of FIG. 20, generally designated as reference numeral  2300 , for processing the ISI due to the less significant selectable channel coefficients (set B). The embodiment illustrated in FIG. 23 is referred to as a minimum area tap-selectable decision feedback pre-filter (DFP). The embodiment of FIG. 23 computes equation (20). 
     Power Consumption 
     According to another aspect of the present invention, reduced power consumption may be realized over prior art reduced complexity sequence estimators in accordance with three embodiments to be disclosed below. In each embodiment, a channel quality metric, Q, is measured. The channel quality metric is obtained from either the TS-RSSE, the channel estimator, or the TS-DFP. The channel quality metric selected can be, for example, the bit error rate BER, the signal to noise ratio (SNR), the mean squared error, or the path metric if the state with the best path metric. The present invention also contemplates the use of other channel quality metrics not explicitly disclosed above. FIG. 24 illustrates each of the three respective embodiments for determining the number of coefficients to be processed in the tap selectable reduced state sequence estimator TS-RSSE  608  to achieve reduced power consumption. Specifically, FIG. 24 illustrates the variable V for use in a first embodiment, the variable T for use in the second embodiment, and the variable E for use in the third embodiment. In the three embodiments of FIG. 24, Q is obtained from the TS-DFP as an example. 
     In operation, the channel quality metric chosen, Q, is measured and compared against a quality threshold (not shown) to make a channel quality determination(i.e., high or low). The following table illustrates how the variables V, T, and E, representing the respective embodiments, are adjusted in accordance with the comparison of the channel quality metric Q with the quality threshold, as indicated by column  1 . 
     
       
         
               
               
               
             
           
               
                 TABLE II 
               
               
                   
               
               
                   
                 Resulting 
                   
               
               
                   
                 Channel 
                 Resulting 
               
               
                 Comparison of Q with quality 
                 Quality 
                 Action for each 
               
               
                 threshold 
                 Determination 
                 embodiment 
               
               
                   
               
             
             
               
                 SNR &gt; quality threshold 
                 High quality 
                 Decrease V, or 
               
               
                 BER &lt; quality threshold 
                 channel 
                 Increase threshold, 
               
               
                 Mean sq.error &lt; quality threshold 
                   
                 T, or 
               
               
                 Path metric &lt; quality threshold 
                   
                 Decrease threshold 
               
               
                   
                   
                 E 
               
               
                 SNR &lt; quality threshold 
                 Low quality 
                 Increase V, or 
               
               
                 BER &gt; quality threshold 
                 channel 
                 Decrease threshold, 
               
               
                 Mean sq.error &gt; quality threshold 
                   
                 T, or 
               
               
                 Path metric &gt; quality threshold 
                   
                 Increase threshold, 
               
               
                   
                   
                 E 
               
               
                   
               
             
          
         
       
     
     Referring to row  1  of Table II, satisfying any of the comparisons of column  1  of row  1  results in a high quality channel, as indicated in column  2 . For the embodiment which describes adjusting the number of coefficients, V, to be processed in the tap selectable reduced state sequence estimator TS-RSSE  608  to achieve reduced power consumption, a high quality channel determination would result in a decrease in the value of V (i.e., less coefficients are selected). This is further illustrated in the apparatus illustrated in FIG. 9 a.    
     In the second embodiment, which utilizes a coefficient threshold T, if the channel quality is determined to be high, the threshold T is increased (See FIG. 9 b ) thereby causing a decreased number of channel coefficients to be processed in the tap selectable reduced state sequence estimator TS-RSSE  608 , and more coefficients are processed in the less power consumptive tap-selectable decision feedback prefilter TS-DFP  504 . In the third embodiment, the threshold, E, is decreased causing a decreased number of channel coefficients to be processed in the tap selectable reduced state sequence estimator TS-RSSE  608 , and more coefficients are processed in the less power consumptive tap-selectable decision feedback prefilter TS-DFP  504  (See equations 4 and 5). 
     The second row of Table II describes the case for a low quality channel which gives essentially an opposite result from that described above for a high quality channel. 
     FIG. 25 is an embodiment of the TS-DFP circuit illustrated in FIG.  24 . FIG. 25 illustrates that the channel quality metric can be derived from the TS-DFP circuit structure by computing the mean-squared error. In this case, the channel quality metric, Q, is obtained as the square of the difference between d n  and a n , where d n  is given by equation (13). a n  represents the value of d n  at the output of the slicer  2702 . The noisier the channel, the larger the difference between d n  and a n . The difference measure is averaged over time for use as the quality metric. The squared difference is fed back to the power control unit  2506  of FIG. 24 to adjust the V, E, or T threshold accordingly. 
     By adjusting V, E, or T, corresponding to the respective embodiments, it is shown that a power saving may be realized in that fewer coefficients are processed in the more power consumptive TS-RSSE  608  when it is determined that the channel quality is acceptable. It is therefore recognized that by adaptively shifting a portion of the processing load from the TS-RSSE  608  to the TS-DFP  504 , when appropriate, a power savings is realized. 
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and have been described in detail. It should be understood, however, that it is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the invention as defined by the appended claims.