Abstract:
A kind of folding systolic array architecture for a CFRS decoding circuit that applies to a cell search in a wideband code division multiple access system. The invention involves using a systolic array for its decoding circuit and using a kind of folding technology to reduce the area of the systolic array. The systolic array for the decoding circuit comprises an input pattern generator, a processing element array designed in the form of a systolic array and a boundary processing element array. Given the skewed-form output results required by the systolic array and generated by the input pattern generator, the processing element array makes a set of correlating comparisons, and outputs the results of the correlating comparisons to the boundary processing elements, so as to acquire the decoding results required by the CFRS decoding. The results indicate the frame boundary and scrambling code groups of the cell search in a wideband code division multiple access system.

Description:
FIELD OF THE INVENTION  
         [0001]    The invention generally relates to a Comma-Free Reed-Solomon decoding circuit and method that applies to a cell search in a wideband code division multiple access (W-CDMA) system, and more particularly relates to a Comma-Free Reed-Solomon decoding circuit that employs a foldable systolic array as far as its circuit structure is concerned and the decoding circuit is folded.  
         BACKGROUND OF THE INVENTION  
         [0002]    As regards the third generation partnership project (hereinafter referred as the 3GPP) wideband code division multiple access (hereinafter referred as W-CDMA) system, the cell search process employed by a cellular phone has to execute a series of detections and testing procedures of synchronization codes in order to synchronize the cellular phone with its best base station. In general, the cell search algorithm of the 3GPP W-CDMA is divided into three ordered steps, namely 1) slot synchronization, 2) frame synchronization and code-group identification, and 3) scrambling-code determination. The first step involves using a primary synchronization code (hereinafter referred as PSC) to achieve slot synchronization. The second step involves using both the secondary synchronization codes (SSCs) and the Comma-Free Reed-Solomon (hereinafter referred as CFRS) codes to achieve frame synchronization and code-group identification. The third step involves using all the possible scrambling codes of the identified code group to execute a de-scrambling procedure for scrambling-code determination. Before achieving the synchronization, the cellular phone couldn&#39;t begin to decode various channel messages broadcasted by the base station or measure various channel effects.  
           [0003]    In this invention, we are concerned with that the second step of the synchronization procedure involves decoding the CFRS code so as to determine the frame boundary and code group. The CFRS code is a combination of Comma-Free code and Reed-Solomon code and thus it has the features of both Comma-Free code and Reed-Solomon code. The Comma-Free code has a feature that no new Comma-Free code could be created by combining any two Comma-Free codes. It is capable of both error detection and synchronization simultaneously. The synchronization capability of Comma-Free code is used by the W-CDMA to achieve frame synchronization. Generally, a Comma-Free code decoding circuit is composed of simple correlators. However, in the 3GPP W-CDMA, the Comma-Free code is transmitted intermittently as opposed to the continual transmission in other applications. Therefore, an ordinary Comma-Free code decoder is not applicable to the synchronization procedure of the 3GPP W-CDMA.  
           [0004]    The CFRS code is also a (15, 3) Reed-Solomon (hereinafter referred as RS) code with a powerful error correction feature that is essential to the 3GPP W-CDMA. As regards the design of a RS decoder, it has been discussed in detail in many articles, and the most widely used decoding method could be summed up in four steps: 1) syndrome calculation of the received codeword, 2) error locator polynomial and error evaluator computations, 3) error location identification, and 4) error value calculation. However, in the 3GPP W-CDMA, the set of CFRS codes is composed of 64 special RS codes and thus an ordinary RS decoder is unsuitable.  
           [0005]    The 3GPP W-CDMA uses 64 CFRS codes to represent 64 code groups. Each codeword consists of 15 symbols. Every code group includes eight scrambling codes. Every base station treats one of the eight scrambling codes of the code group to which it belongs as its scrambling code for differentiating itself from the other stations. To be connected through a certain base station, a cellular phone has to achieve scrambling code synchronization with the base station first. As described above, the synchronization process has to comprise the decoding procedure of CFRS code with a view to executing frame boundary detection and code-group determination.  
           [0006]    The symbols of CFRS code are chosen from the elements of Galois Field (GF) (16). Among the 16 secondary synchronization codes, the nth synchronization code is transmitted via a secondary synchronization channel represents that the nth element of GF (16) is regarded as the code symbol. Symbols are selected to form 64 CFRS codes to represent 64 code groups, each of which consists of 15 symbols. To transmit CFRS codes, a base station sends identical codes in each frame. However, prior to frame synchronization, the initial position for the receipt of CFRS codes is not necessarily occupied by the first code symbol, but can be one of the 15 code symbols. Since the same CFRS code is transmitted in each frame, it is possible to receive 15 code symbols continuously even before a frame boundary is determined. The consecutive received 15 code symbols result in a cyclic-shift version of a CFRS codeword. The aim of decoding is to identify the received codeword is which one of the 64 CFRS codes in order to determine the code group, and to detect the cyclic-shift time cyclic-shift so as to determine the frame boundary.  
           [0007]    According to the above description, there are 64 CFRS codes and 15 cyclic-shift versions of each codeword. Thus there can be a total of 960 (64×15) versions of cyclic-shift codeword. The determination of these 960 cyclic-shift hypotheses requires a lot of complicated calculations, and more importantly, timely accomplishment of these calculations in order to avoid delay in the synchronization procedure that may cause more serious problems. Hence, decoding speed has a direct impact on real-time synchronization. A “fast” CFRS decoder is an indispensable component for the cell search algorithm.  
           [0008]    The decoding methods discussed in the existing literature regarding the cell search algorithms merely involve direct comparison of these 960 versions, thus there is no other better decoding method, nor is there any effective architecture for hardware implementation. Therefore, it is a good idea to use the direct decoding method based on the 960 versions to develop decoding hardware architecture that works more effectively, as well as to put forward a decoding method that is more accurate.  
         SUMMARY OF THE INVENTION  
         [0009]    In view of the aforesaid technical problems, the invention provides a kind of speedy decoding circuit architecture that applies to the CFRS code of the 3GPP W-CDMA, not only to support various kinds of cell search algorithms, but also to meet the demand for frequent decoding in multi-candidate cell search algorithms.  
           [0010]    As regards the cell search procedure of the 3GPP W-CDMA, there are many options for the execution strategies. For example, serial execution of the three steps of the synchronization procedure, simultaneous execution of the synchronization procedure in a pipelined manner, or selecting several slot boundary candidates in step 1 and simultaneously executing steps 2 &amp; 3 by means of the various slot boundary candidates are all possible and feasible. Each algorithm requires different CFRS decoding speed. Serial cell search does not require fast decoding. Pipelined cell search requires a decoder with high decoding speed. The multi-candidate method requires a decoder with extremely high decoding speed because of the need for frequent decoding. The invention provides the means to solve the aforesaid problems, i.e. the decoding circuits that work at high or low decoding speeds. Whenever a high decoding speed is required, it could meet the need of the cell search algorithm. Whenever a low decoding speed is acceptable, it executes decoding with the minimal number of components so as to reduce power consumption.  
           [0011]    Another object of the invention is to provide a kind of architecture of folding systolic array (SA) for CFRS decoding circuit. This kind of architecture is able to perform speedy real-time execution of decoding procedure with a view to meeting the demand for various kinds of mathematical calculations of synchronization.  
           [0012]    In addition, the invention employs the folding technology of the SA architecture to reduce the area of its array without jeopardizing its speedy decoding feature. Furthermore, the incorporation of the folding concept into the design of a decoding circuit balances decoding speed with hardware cost, meeting various demands for cell search algorithms by means of the minimum hardware cost and power consumption.  
           [0013]    To gain further insight into the characteristics and the implementation of the invention, illustrations and detailed explanation of the preferred embodiment are provided below: 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]    [0014]FIG. 1 depicts the comparison of the efficiency of CFRS decoding in different decoding lengths;  
         [0015]    [0015]FIG. 2 shows a CFRS decoder based on SA architecture, wherein x, denotes the received code symbol and y j,i  denotes the result of a correlating comparison;  
         [0016]    [0016]FIG. 3 depicts the structure of IPG;  
         [0017]    [0017]FIG. 4 depicts the circuit of PE;  
         [0018]    FIGS.  5 A- 5 C show the table of 64 CFRS codes and the table of its segments after folding;  
         [0019]    [0019]FIG. 6 depicts the circuit of BPE;  
         [0020]    [0020]FIG. 7 shows a CFRS decoder based on the folding SA architecture; the number of times of folding is 2; the 64×15 array is reduced to a 16×15 one, but the decoding duration is still 94 cycles;  
         [0021]    [0021]FIG. 8 depicts the circuit of a refresh mechanism; 
     
    
       [0022]    Table 1 shows the array sizes and the decoding duration that result front the application of the folding technology; and  
         [0023]    Table 2 shows the comparison of the gate-count required by individual types of architecture.  
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0024]    As shown in FIG. 1, the 960 versions of CFRS codes can be decoded better with a complete set of 15 code symbols rather than with part of the code symbols. Hence, in the invention, after 15 code symbols have been received, a frame boundary is determined by making reference to a direct comparison of the 15 code symbols.  
         [0025]    In order to achieve the objects of the invention, the invention puts forward a kind of folding technology and builds a decoding circuit with SA architectural concepts. Explanation will be first given on the decoding circuit based on SA architecture, then, explanation will be given on the folding technology and the SA-based decoding circuit to which this technology applies. Finally, extension of folding technology will be discussed.  
         [0026]    As regards decoding strategy, the decoding method adopted by the invention can be denoted in the following way:  
               (     i   ,   j     )     =     A                 r                 g        {     max          {       X   i     ⊗     H   j       }       j   =     0   ∼   63         i   =     0   ∼   14           }               (   1   )                               
 
         [0027]    where i denotes the index for the 15 cyclic-shift versions, j denotes the index for the 64 CFRS codes, X i  denotes the result of i time(s) of rightward cyclic-shift of the received CFRS codes, while X 0  denotes the result of arbitrary cyclic-shift of the CFRS codes received in the beginning; and, X i ={x 1 ,x 2 ,x 3 , . . . ,x 15 }, x k ∈GF(16), 1≦k≦15. H j  denotes one of the 64 CFRS codes, and H j ={h 1 ,h 2 , h 3 , . . . ,h 15 }, h k ∈GF(16), 1≦k≦15. Finally, X         H j  refers to making a correlating comparison.  
         [0028]    I. SA-Based Decoding Circuit  
         [0029]    As shown in FIG. 2, the decoding circuit comprises several components, namely an Input Pattern Generator (IPG)  10 , a 64×15 Processing Element Array (PEA)  20 , and a 64×1 Boundary Processing Element Array (BPEA)  30 .  
         [0030]    The main function of the IPG  10  is to generate 15 cyclic-shift versions from the arbitrarily cyclic-shift CFRS codes received, X, wherein X i , 0≦i≦14, then input the cyclic-shift versions to the PEA  20  in a skewed form required by the SA architecture. The input comprises all the 15 cyclic-shift versions, and, as shown in FIG. 3, its circuit structure comprises a shift register  11 , a Johnson counter  13 , and a masking combinational circuit  12 . Its process is described below.  
         [0031]    First of all, a received code, X, is loaded to the shift register  11 . The shift register  11  then generates its 15 versions of cyclic-shift separately. The Johnson counter  13  generates the required skewed mask. With the masking combinational circuit  12 , the 15 cyclic-shift Versions cyclic-shift are turned into the required 15 cyclic-shift versions cyclic-shift in skewed form. The skewed 15 cyclic-shift versions of X are regarded as the input to the underlying WPEA  20  that is based on SA architecture.  
         [0032]    The PEA  20  is a kind of SA architecture composed of 64×15 PEs. The structure of each PE is shown in FIG. 4, and the primary function of the PE is to make a correlating comparison. IPG  10  generates all the 15 cyclic-shift versions cyclic-shift that are then compared with 64 sets of CFRS codes for correlations. There are three registers in each PE, namely the H register  202 , X register  201  and Y register  203 . The H register  202  is for storing the code symbols, h k , of CFRS code beforehand, or, in other words, the 64×15 CFRS code symbols table  40  shown in FIG. 5 is put in the H register  202  of every PE of the 64×15 PEA  20  correspondingly. Since there are 64 CFRS codes, and each codeword consists of 15 code symbols, it needs to be processed by a 64×15 PEA  20 . The X register  201  is for storing the code symbols, x k , sent by the overhead PE. Given the comparing combinational circuit  204  shown in FIG. 4, when the two code symbols stored in the X register  201  and the H register  202 , respectively, are identical, an accumulator  205  accumulates the result of the correlating comparison and stores the result in the Y register  203  first. It then sends the result to the PE on its right and sends the received code symbols x k  to the underlying PE.  
         [0033]    The 64×15 PEA  20  connects to a set of 64×1 BPEA  30  that lies on its right. Each row of the PEA  20  is in charge of making the correlating comparison with a CFRS codes. The last PE output of each row is the result of correlating comparison, y j,i . BPE compares this set of comparison results, y j,i  for i=0˜14. After comparing the 15 results of the same codeword, each BPE begins to compare the results of individual rows as shown in FIG. 6.  
         [0034]    The I comparator  301  is for comparing the results of the same row. A result that is greater is stored in the maximum value and cyclic-shift index register  306  first. After the maximum result of the same row has been generated, the J comparator  302  begins to compare the maximum value of the existing row with that of the overhead row. It selects the greater one, saves it and its code group index j and cyclic-shift index i in the maximum value and group &amp; cyclic-shift index register  308 , and sends them to the underlying BPE. The multiplexer  305  makes reference to the result of the I comparator  301 , and saves the greater result value, y j,i , and its cyclic-shift index i in the maximum value and cyclic-shift index register  306 . In the event that the new y j,i  value is greater than the y j,max  value, that is, when the multiplexer  305  chooses line  1 , then its cyclic-shift index i is provided by the cyclic-shift index  303 . The multiplexer  307  makes reference to the result of J comparator  302 , and saves the greater result value, y j,i , its cyclic-shift index i and code group index j, etc., in the maximum value and group &amp; cyclic-shift index register  308 . In the event that the result of the existing row, y j,max , is greater than the y j−1,max  value of the overhead row, then its group index is provided by the code group index  304 .  
         [0035]    The output of the BPE at the bottom (that is, the output result of the maximum value and group &amp; cyclic-shift index register  308 ) is the result of decoding. The comparison result of the greatest correlation is the desired decoding result. The code group index j of this result denotes that the received CFRS code, X, is the j th  code of all the possible 64 CFRS codes, while the cyclic-shift index i denotes that the received CFRS code, X, results from i times of cyclic-shift of the original code symbol. As described in the “Background of the Invention” section of this document, in the 3GPP W-CDMA, the code group index, j, denotes a code group, while the cyclic-shift index, i, denotes a frame boundary. This is the end of step 2 of the cell search.  
         [0036]    Please refer to FIG. 2 again. The whole decoding procedure is: load the CFRS codes received to IPG  10 ; the IPG  10  generates 15 cyclic-shift versions in order; input the 15 versions of skewed-style cyclic-shift to the 64×15 PEA  20 ; the PEA  20  makes a correlating comparison between the 15 types of cyclic-shift and 64 sets of codes saved beforehand; a comparison is made on each row with respect to one set of possible CFRS codes; as regards the comparison result of a row, the BPE of the row identifies the most probable cyclic-shift; search vertically, that is, from the top to the bottom, and find the greatest result of cyclic-shift of individual rows; the output of the BPE at the bottom is the decoding result.  
         [0037]    The decoding duration required by this decoding circuit is as follows: (Please refer to the aforesaid decoding process) 15 cycles after the IPG  10  has input the skewed-form cyclic-shift versions into the PEA  20 , the first correlating comparison result of the first row is generated; 14 cycles later, the last correlating comparison result of the first row is generated; one cycle later, the most possible cyclic-shift version of the first row is generated and, meanwhile, the last correlating comparison result of the second row has been generated, thus the BPE of the second row only generates the most probable cyclic-shift of the second row and begins to compare the results of individual rows vertically after one more cycle. It takes 63 cycles to generate the final result. Therefore, a total of 15+14+1+1+63=94 cycles is required to finish decoding. The length of each cycle varies according to the implementation method.  
         [0038]    From the point of view of a system, the chip rate is 3.84 MHz. In general, the minimum frequency designed by a circuit should be 3.84 MHz. In other words, the designed circuit only spends time for a maximum 94 chips on decoding. Thus, there is sufficient time to prepare for the following step of determining scrambling codes in an ordinary synchronization procedure. Even if decoding has to be executed ten or twenty times in multi-candidate cell search algorithms, this decoder is able to finish decoding before the end of the slot wherein the 15 th  secondary synchronization code is decoded. Thus it does not delay the execution of step 3 of the cell search procedure. The total time spent: 20 (number of times of decoding)*94 (the duration of decoding)+256 (receipt of the secondary synchronization code)=2136&lt;2560 (slot length).  
         [0039]    II. Folding Technology and the SA-Based Decoding Circuit to which this Technology Applies  
         [0040]    With the folding technology put forward by the invention, the SA of the PEA  20  of the decoding circuit based on SA architecture is folded so that its array size is reduced from 64×15 to 32×15 and thus its area is reduced. As regards the code symbols that have to be saved beforehand, the 64×15 CFRS code symbol table  40  (shown in FIG. 5A) is also folded and thus turned into 32×15, as shown in FIG. 5B, comprising an upper half segment  41  and a lower half segment  42 . Similarly, the 64×1 BPEA  30  is also folded and thus turned into 32×1. Despite the folding, a decoding speed of 94 cycles is maintained. The folding process impacts the decoding speed, depending on the number of times of folding. Explanation is herein provided for the folding technology in a case where, for example, folding is carried out twice successively. As shown in FIG. 7, after the PEA  20  has been folded twice, its original 64×15 systolic array is diminished and turned into a 16×15 systolic array. The CFRS code symbol table that has to be saved beforehand for the PEA  20  is, by the same token, turned into four segments, namely the first segment  43 , the second segment  44 , the third segment  45  and the fourth segment  46 , as shown in FIG. 5C.  
         [0041]    The maximum number of successive folds without jeopardizing decoding speed is two. FIG. 7 shows the architecture that results from the folding, wherein the IPG  10  and each PE remain identical to their appearance shown in FIGS. 3 and 4, respectively, thus they need not be modified. However, the BPE has to be slightly modified so that its architecture is capable of feedback, as shown in FIG. 6.  
         [0042]    After two times of successive folding, the size of the PEA 20  is reduced from 64×15 to 16×15, while the size of the BPEA 30  is also reduced from 64×1 to 16×1, thus the areas of both arrays decrease to one-fourth of their original sizes. The reduction in array area is achieved at the cost of the addition of a “refresh mechanism” for refreshing the code symbol, h k , stored beforehand in the H register of the PE. In other words, after two times of successive folding, the 64×15 CFRS code symbol table  40  originally stored in advance in the PEA  20  (shown in FIG. 5A) is divided into four segments  43 ,  44 ,  45  and  46 , as shown in FIG. 5C. The first time, only one segment is placed in the H register of the PEA 20  shown in FIG. 7. The second time, one segment is saved first, then, after the previous segment has been decoded, the code symbol of the next segment is refreshed by the refresh mechanism and saved in the PE.  
         [0043]    A refresh cluster is shown in FIG. 7, and code symbols are refreshed cluster by cluster. In other words, each time only one cluster is refreshed. The formation of clusters depends on the execution condition of SA. After each PE has made a correlating comparison with the last code symbol it receives, it should immediately make a correlating comparison for the code symbol of the next segment in the next cycle. Hence, it is necessary to refresh the code symbol saved beforehand in individual PEs, that is, to refresh the content value in the H register. Since the execution of SA is conducted in a hierarchical pipelined manner, PEs in individual rows must be refreshed, and the PEs are separated from each other by one position. All the PEs that have to be refreshed in the same cycle are collectively known as a refresh cluster. Clusters are refreshed in order, so that all the code symbols that are saved beforehand in 16 rows and are required to be refreshed can be refreshed simultaneously. There is a total of 15 refresh clusters, namely the first refresh cluster, the second refresh cluster, . . . the 15 th  refresh cluster. They are refreshed in order, or, in other words, every cluster is refreshed every 15 cycles.  
         [0044]    [0044]FIG. 8 shows the refresh mechanism that comprises 15 refresh counters  501 , a read circuit  502  of Read-Only Memory (ROM)  60 , a refresh register  503  and a cluster allocation circuit  504 . The 15 refresh counters  501  figure out the time taken to refresh individual refresh clusters. Once the refresh time runs out, the refresh counters  501  trigger the read circuit  502  of Read-Only Memory (ROM)  60 . The read circuit  502  then reads the code symbols of the next segment to be saved beforehand, and places the code symbols in the refresh register  503 . The cluster allocation circuit  504  sends the new code symbols to the corresponding H registers of the PEs (for saving CFRS code symbols beforehand). This is the way the refresh procedure is executed. The CFRS Read-Only Memory (ROM)  60  shown in FIG. 8 is the ROM that saves the 64×15 CFRS code symbol table  40 , as shown in FIG. 5A.  
         [0045]    In addition, as shown in FIG. 7, the code symbol received and sent downward by the 15 th  row of the PEA 20  has to be sent to the first row as feedback because, in the meantime, the second segment decoding has to be started in the first row. The direct feedback exempts IPG  10  from generating skewed input repeatedly whenever a new segment is to be decoded. As a result, power consumption is reduced.  
         [0046]    Please refer to FIG. 7. The decoding process of the folding architecture is as follows: IPG  10  generates the 15 types of cyclic-shift results of the received CFRS codes in order, and outputs these cyclic-shift results in a skewed form to the 16×15 PEA 20 . In the meantime, the refresh mechanism loads and refreshes the code symbols of the first segment  43  shown in FIG. 5C according to the sequence of the refresh clusters. The PEA 20  makes a correlating comparison between these 15 cyclic-shift versions and the refreshed segment code symbols. A correlating comparison is made on a possible CFRS codes for each row. As regards the correlating comparison result of a row, the BPE of the row finds the most probable result of cyclic-shift version, searches vertically, that is, from top to bottom, and finds the most probable result of cyclic-shift of individual rows. The output of the BPE at the bottom is the decoding result for the first segment. This result has to be sent to the first BPE as feedback, and compared with the result of the next segment.  
         [0047]    After the refresh procedure executed by the refresh mechanism on the first cluster and the lapse of the following 15 cycles, the correlating comparisons between the code symbols  43  of the first segment and the cyclic-shift of the received code symbols are completed. The code symbols  43  of the first segment have to be refreshed and turned into the code symbols  44  of the second segment, so that the third segment  45  and the fourth segment  46  can be refreshed by analogy. The process does not end unless and until the correlating comparisons of the fourth segment are completed. The output of the BPE at the bottom is the decoding result.  
         [0048]    The process of mathematical calculation for the decoding of folding architecture is similar to that of the architecture previously put forward, except that the components in charge of execution are different. The 16×15 PEA 20  and the 15×1 BPEA 30  shown in FIG. 7 are repeatedly used. The concept of refreshing the codes saved beforehand and the concept of the refresh mechanism are incorporated into the design. As a result, the area of a decoder is reduced, but the decoding speed of the decoder is not. The decoding time required by the decoder remains the same, that is, 94 cycles.  
         [0049]    III. Extension of Folding Technology  
         [0050]    The above description is of the consequence of two times of successive folding of a kind of folding architecture. The speedy decoding feature is retained, while the area of the decoder is reduced. It is feasible to apply the folding technology further, and fold a 16×15 PEA 20  in a symmetric manner, though its decoding duration increases with the number of times of symmetric folding. The size of the array decreases with the number of times of folding.  
         [0051]    Table 1 shows the size of the array and the decoding duration with respect to different number of times of folding. When folding is carried out once or twice, the decoding duration is 94 cycles, though the sizes of their arrays differ by one time. Therefore, folding an array twice is the best option as it achieves an optimal balance. In the event that the decoding speed is unimportant, folding an array six times will lead to the smallest array area, that is, 1×15 PEA  20  and 1×1 BPEA  30 , though the decoding duration becomes 975 cycles.  
         [0052]    Since the circuit designs of individual folding versions are very similar, it is feasible to put several versions in the same circuit. Take the aforesaid two versions as an example. Two times of symmetric folding may be performed in the 16×15 PEA  20  and the 16×1 BPEA  30 . As a result, decoding can be completed in 94 cycles, meeting the demand for speedy decoding in the cell search. When the cell search does not require a high decoding speed, it is feasible to use architecture that is folded 6 times, that is, the 1×15 PEA  20  and the 1×1 BPEA  30 , and the decoding may be completed in 975 cycles. The advantage of folding architecture 6 times is that its power consumption is reduced.  
         [0053]    Given the aforesaid folding method, a circuit may work at different decoding speeds when the folding number varies, so that the flexibility in the design of cell search algorithms is greatly enhanced at the cost of a slight increase in the complexity of hardware.  
         [0054]    IV Practical Testing  
         [0055]    The decoding function and the decoding duration of the aforesaid 64×15, folding 16×15, and folding 1×15 architectures have been verified with Hardware Description Language, Verilog. The aforesaid architectures are also syntheiszed by synthesis tools, such as Synopsys™, into gate-level circuits, so that the decoding function and the decoding duration of the aforesaid architecture are verified once more. Table 2 shows the gate-count of the components of different architectures. The decoding duration of both the 64×15 SA architecture and the 16×15 architecture that is folded twice is 94 cycles. The gate-count of their PEAs differ by four times because of the folding technology put forward herein. However, the gate-count of BPEA  30  merely differs from its counterpart by approximately three times because the BPE needs a greater gate-count after folding. With a refresh circuit, the total gate-count of a decoder of the folding architecture is reduced to a half of that of the 64×15 SA architecture.  
         [0056]    Since the 1×15 architecture works together with the 16×15 architecture, the refresh circuit of the former is as complicated as that of the latter. In practice, it is feasible to adopt a simple ROM single-code-symbol read circuit that is also equipped with independent BPEs, as opposed to the aforesaid two types of architecture.  
       EFFECT OF THE INVENTION  
       [0057]    The CFRS decoding circuit put forward by the invention is based on SA architecture. The decoding duration of the 64×15 array is 94 cycles. The 64×15 array may be reduced to a 16×15 array by means of the folding technology put forward by the invention. Its speedy decoding feature is retained—it still takes 94 cycles, though an additional refresh circuit is required. The folding technology may be extended. On the premise of meeting the demand for decoding in the cell search algorithms, an array is folded several times, reducing the number of components required for execution and thus minimizing power consumption. Another option of folding technology extension is to have several types of folded decoding architecture in the same circuit. For example, given an additional special BPE, when a 1×15 architecture is added to a 16×15 architecture, a CFRS decoder works in a multi-mode manner and thus is able to support various decoding speeds, meeting the various needs of different types of cell search algorithms.  
         [0058]    While the invention has been described by way of example and in terms of a preferred embodiment, it is to be understood that the invention is not limited thereto. It should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. Therefore the scope of protection for the invention should conform to the claims attached below.