Abstract:
An apparatus and method for encoding/decoding a transport format combination indicator (TFCI) in a CDMA mobile communication system. In the TFCI encoding apparatus, a one-bit generator generates a sequence having the same symbols. A basis orthogonal sequence generator generates a plurality of basis orthogonal sequences. A basis mask sequence generator generates a plurality of basis mask sequences. An operation unit receives TFCI bits that are divided into a first information part representing biorthogonal sequence conversion, a second information part representing orthogonal sequence conversion, and a third information part representing mask sequence conversion and combines an orthogonal sequence selected from the basis orthogonal sequence based on the second information, a biorthogonal sequence obtained by combining the selected orthogonal sequence with the same symbols selected based on the first information part, and a mask sequence selected based on the biorthogonal sequence and the third information part, thereby generating a TFCI sequence.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to an information transmitting apparatus and method in an IMT 2000 system, and in particular, to an apparatus and method for transmitting a transport format combination indicator (TFCI). 
     2. Description of the Related Art 
     A CDMA mobile communication system (hereinafter, referred to as an IMT 2000 system) generally transmits frames that provide a voice service, an image service, a character service on a physical channel such as a dedicated physical data channel (DPDCH) at a fixed or variable data rate. In the case where the data frames which include that sort of services are transmitted at a fixed data rate, there is no need to inform a receiver of the spreading rate of each data frame. On the other hand, if the data frames are transmitted at a variable data rate, which implies that each data frame has a different data rate, a transmitter should inform the receiver of the spreading rate of each data frame determined by its data rate. A data rate is proportional to a data transmission rate and the data transmission rate is inversely proportional to a spreading rate in a general IMT 2000 system. 
     For transmission of data frames at a variable data rate, a TFCI field of a DPCCH informs a receiver of the data rate of the current service frame. The TFCI field includes a TFCI indicating a lot of information including the data rate of a service frame. The TFCI is information that helps a voice or data service to reliably be provided. 
       FIGS. 1A  to  1 D illustrate examples of applications of a TFCI.  FIG. 1A  illustrates application of the TFCI to an uplink DPDCH and an uplink dedicated physical control channel (DPCCH).  FIG. 1B  illustrates application of the TFCI to a random access channel (RACH).  FIG. 1C  illustrates application of the TFCI to a downlink DPDCH and a downlink DPCCH.  FIG. 1D  illustrates application of the TFCI to a secondary common control physical channel (SCCPCH). 
     Referring to  FIGS. 1A  to  1 D, one frame is comprised of  16  slots and each slot has a TFCI field. Thus, one frame includes 16 TFCI fields. A TFCI field includes N TFCI  bits and a TFCI generally has 32 bits in a frame. To transmit the 32-bit TFCI in one frame, 2 TFCI bits can be assigned to each of the 16 slots (T slot =0.625 ms). 
       FIG. 2  is a block diagram of a base station transmitter in a general IMT 2000 system. 
     Referring to  FIG. 2 , multipliers  211 ,  231 , and  232  multiply input signals by gain coefficients G 1 , G 3 , and G 5 . Multipliers  221 ,  241 , and  242  multiply TFCI codewords (TFCI code symbols) received from corresponding TFCI encoders by gain coefficients G 2 , G 4 , and G 6 . The gain coefficients G 1  to G 6  may have different values according to service types or handover situations. The input signals include pilots and power control signals (TPCs) of a DPCCH and a DPDCH data. A multiplexer  212  inserts 32 bit TFCI code symbols(TFCI codeword) received from the multiplier  221  into the TFCI fields as shown in FIG  1 C. A multiplexer  242  inserts 32-bit TFCI code symbols received from the multiplier  241  into the TFCI fields. A multiplexer  252  inserts 32-bit TFCI code symbols received from the multiplier  242  into the TFCI fields. Insertion of TFCI code symbols into TFCI fields is shown in  FIGS. 1A  to  1 D. The 32 code symbols are obtained by encoding TFCI bits(information bits) that define the data rate of a data signal on a corresponding data channel. 1 st , 2 nd , and 3 rd  serial to parallel converters (S/Ps)  213 ,  233 , and  234  separate the outputs of the multiplexers  212 ,  242 , and  252  into I channels and Q channels. Multipliers  214 ,  222 , and  235  to  238  multiply the outputs of the S/Ps  213 ,  233 , and  234  by channelization codes C ch1 , C ch2 , and C ch3 . The channelization codes are orthogonal codes. A first summer  215  sums the outputs of the multipliers  214 ,  235 , and  237  and generates an I channel signal and a second summer  223  sums the outputs of the multipliers  222 ,  236 , and  238  and generates a Q channel signal. A phase shifter  224  shifts the phase of the Q channel signal received from the second summer  223  by 90°. A summer  216  adds the outputs of the first summer  215  and the phase shifter  224  and generates a complex signal I+jQ. A multiplier  217  scrambles the complex signal with a complex PN sequence C scramb  assigned to the base station. A signal processor(S/P)  218  separates the scrambled signal into an I channel and a Q channel. Low-pass filters (LPFs)  219  and  225  limits the bandwidths of the I channel and Q channel signals received from the S/P  218  by low-pass-filtering. Multipliers  220  and  226  multiply the outputs of the LPFs  219  and  225  by carriers cos(2πf c t) and sin(2πf c t), respectively, thereby transforming the outputs of the LPFs  219  and  225  to an RF (Radio Frequency) band. A summer  227  sums the RFI channel and Q channel signals. 
       FIG. 3  is a block diagram of a mobile station transmitter in the general IMT 2000 system. 
     Referring to  FIG. 3 , multipliers  311 ,  321 , and  323  multiply corresponding signals by channelization codes C ch1 , C ch2 , and C ch3 . Signals  1 ,  2 ,  3  are first, second and third DPDCH signal. An input signal  4  includes pilots and TPCs of a DPCCH.TFCI information bits are encoded into 32 bit TFCI code symbols by a TFCI encoder  309 . A multiplier  310  inserts a 32 bit TFCI code symbols into the signal  4  as shown in  FIG. 1A. A  multiplier  325  multiplies a DPCCH signal which include TFCI code symbol received from the multiplier  310  by a channelization code C ch4 . The channelization codes C ch1  to C ch4  are orthogonal codes. The 32 TFCI code symbols are obtained by encoding TFCI information bits that define the data rate of the DPDCH signals. Multipliers  312 ,  322 ,  324 , and  326  multiply the outputs of the multipliers  311 ,  321 ,  323 , and  325  by gain coefficients G 1  to G 4 , respectably. The gain coefficients G 1  to G 4  may have different values. A first summer  313  generates an I channel signal by adding the outputs of the multipliers  312  and  322 . A second summer  327  generates a Q channel signal by adding the outputs of the multipliers  324  and  326 . A phase shifter  328  shifts the phase of the Q channel signal received from the second summer  327  by 90°. A summer  314  adds the outputs of the first summer  313  and the phase shifter  328  and generates a complex signal I+jQ. A multiplier  315  scrambles the complex signal with a PN sequence C scramb  assigned to a base station. An S/P  329  divides the scrambled signal into an I channel and a Q channel. LPFs  316  and  330  low-pass-filter the I channel and Q channel signals received from the SIP  329  and generate signals with limited bandwidths. Multipliers  317  and  331  multiply the outputs of the LPFs  316  and  330  by carriers cos(2πf c t) and sin(2πf c t), respectively, thereby transforming the outputs of the LPFs  316  and  330  to an RF band. A summer  318  sums the RF I channel and Q channel signals. 
     TFCIs are categorized into a basic TFCI and an extended TFCI. The basic TFCI represents 1 to 64 different information including the data rates of corresponding data channels using 6 TFCI information bits, whereas the extended TFCI represents 1 to 128, 1 to 256, 1 to 512, or 1 to 1024 different information using 7, 8, 9 or 10 TFCI information bits. The extended TFCI has been suggested to satisfy the requirement of the IMT 2000 system for more various services. TFCI bits are essential for a receiver to receive data frames received from a transmitter. That is the reason why unreliable transmission of the TFCI information bits due to transmission errors lead to wrong interpretation of the frames in the receiver. Therefore, the transmitter encodes the TFCI bits with an error correcting code prior to transmission so that the receiver can correct possibly generated errors in the TFCI. 
       FIG. 4A  conceptionally illustrates a basic TFCI bits encoding structure in a conventional IMT 2000 system and  FIG. 4B  is an exemplary encoding table applied to a biorthogonal encoder shown in FIG.  4 A. As stated above, the basic TFCI has 6 TFCI bits (hereinafter, referred to as basic TFCI bits) that indicate 1 to 64 different information. 
     Referring to  FIGS. 4A and 4B , a biorthogonal encoder  402  receives basic TFCI bits and outputs 32 coded symbols(TFCI codeword or TFCI code symbol). The basic TFCI is basically expressed in 6 bits. Therefore, in the case where a basic TFCI bits of less than 6 bits are applied to the biorthogonal encoder  402 , 0s are added to the left end, i.e., MSB (Most Significant Bit) of the basic TFCI bits to increase the number of the basic TFCI bits to 6. The biorthogonal encoder  402  has a predetermined encoding table as shown in  FIG. 4B  to output 32 coded symbols for the input of the 6 basic TFCI bits. As shown in  FIG. 4B , the encoding table lists 32(32-symbol) orthogonal codewords c 32.1  to c 32.32  and 32 biorthogonal codewords {overscore (C 32.1 )} to {overscore (c 32.32 )} that are the complements of the codewords c 32.1  to c 32.32 . If the LSB (Least Significant Bit) of the basic TFCI is 1, the biorthogonal encoder  402  selects out of the 32 biorthogonal codewords. If the LSB is 0, the biorthogonal encoder  402  selects out of the 32 orthogonal codewords. One of the selected orthogonal codewords or biorthogonal codewords is then selected based on the other TFCI bits. 
     A TFCI codeword should have powerful error correction capability as stated before. The error correction capability of binary linear codes depends on the minimum distance (dmin) between the binary linear codes. A minimum distance for optimal binary linear codes is described in “An Updated Table of Minimum-Distance Bounds for Binary Linear Codes”, A. E. Brouwer and Tom Verhoeff, IEEE Transactions on Information Theory, vol. 39, No. 2, March 1993 (hereinafter, referred to as reference 1). 
     Reference 1 gives 16 as a minimum distance for binary linear codes by which 32 bits are output for the input of 6 bits. TFCI codewords output from the biorthogonal encoder  402  has a minimum distance of 16, which implies that the TFCI codewords are optimal codes. 
       FIG. 5A  conceptionally illustrates an extended TFCI bits encoding structure in the conventional IMT 2000 system,  FIG. 5B  is an exemplary algorithm of distributing TFCI bits in a controller shown in  FIG. 5A , and  FIG. 5C  illustrates an exemplary encoding table applied to biorthogonal encoders shown in FIG.  5 A. An extended TFCI is also defined by the number of TFCI bits. That is, the extended TFCI includes 7, 8, 9 or 10 TFCI bits (hereinafter, referred to as extended TFCI bits) that represent 1 to 128, 1 to 256, 1 to 512, or 1 to 1024 different information, as stated before. 
     Referring to  FIGS. 5A ,  5 B, and  5 C, a controller  500  divides TFCI bits into two halves. For example, for the input of 10 extended TFCI bits, the controller  500  outputs the first half of the extended TFCI as first TFCI bits (word 1) and the last half as second TFCI bits (word 2). The extended TFCI are basically expressed in 10 bits. Therefore, in the case where an extended TFCI bits of less than 10 bits are input, the controller  500  adds 0s to the MSB of the extended TFCI bits to represent the extended TFCI in 10 bits. Then, the controller  500  divides the 10 extended TFCI bits into word 1 and word 2. Word 1 and word 2 are fed to biorthogonal encoders  502  and  504 , respectively. A method of separating the extended TFCI bits a 1  to a 10  into word 1 and word 2 is illustrated in FIG.  5 B. 
     The biorthogonal encoder  502  generates a first TFCI codeword having 16 symbols by encoding word 1 received from the controller  500 . The biorthogonal encoder  504  generates a second TFCI codeword having 16 symbols by encoding word 2 received from the controller  500 . 
     The biorthogonal encoders  502  and  504  have predetermined encoding tables to output the 16-symbol TFCI codewords for the two 5-bit TFCI inputs (word 1 and word 2). An exemplary encoding table is illustrated in FIG.  5 C. As shown in  FIG. 5C , the encoding table lists  16  orthogonal codewords of length 16 bits c 16.1  to c 16.16  and biorthogonal codewords {overscore (c 16.1 )}, to {overscore (c 16.16 )} that are the complements of the 16 orthogonal codewords. If the LSB of 5 TFCI bits is 1, a biorthogonal encoder ( 502  or  504 ) selects the 16 biorthogonal codewords. If the LSB is 0, the biorthogonal encoder selects the 16 orthogonal codewords. Then, the biorthogonal encoder selects one of the selected orthogonal codewords or biorthogonal codewords based on the other TFCI bits and outputs the selected codeword as the first or second TFCI codeword. 
     A multiplexer  510  multiplexes the first and second TFCI codewords to a final 32-symbol TFCI codeword. 
     Upon receipt of the 32-symbol TFCI codeword, a receiver decodes the TFCI codeword separately in halves (word 1 and word 2) and obtains 10 TFCI bits by combining the two decoded 5-bit TFCI halves. In this situation, a possible error even in one of the decoded 5-bit TFCI output during decoding leads to an error over the 10 TFCI bits. 
     An extended TFCI codeword also should have a powerful error correction capability. To do so, the extended TFCI codeword should have the minimum distance as suggested in reference 1. 
     In consideration of the number 10 of extended TFCI bits and the number 32 of the symbols of a TFCI codeword, reference 1 gives 12 as a minimum distance for an optimal code. Yet, a TFCI codeword output from the structure shown in  FIG. 5A  has a minimum distance of 8 because an error in at least one of word 1 and word 2 during decoding results in an error in the whole 10 TFCI bits. That is, although extended TFCI bits are encoded separately in halves, a minimum distance between final TFCI codewords is equal to a minimum distance 8 between codeword outputs of the biorthogonal encoders  502  and  504 . 
     Therefore, a TFCI codeword transmitted from the encoding structure shown in  FIG. 5A  is not optimal, which may increase an error probability of TFCI bits in the same radio channel environment. With the increase of the TFCI bit error probability, the receiver misjudges the data rate of received data frames and decodes the data frames with an increased error rate, thereby decreasing the efficiency of the IMT 2000 system. 
     According to the conventional technology, separate hardware structures are required to support the basic TFCI and the extended TFCI. As a result, constraints are imposed on implementation of an IMT 2000 system in terms of cost and system size. 
     SUMMARY OF THE INVENTION 
     It is, therefore, an object of the present invention to provide an apparatus and method for encoding an extended TFCI in an IMT 2000 system. 
     It is also an object of the present invention to provide an apparatus and method for encoding a basic TFCI and an extended TFCI compatibly in an IMT 2000 system. 
     It is another object of the present invention to provide an apparatus and method for coding an extended TFCI in an IMT 2000 system. 
     It is still another object of the present invention to provide an apparatus and method for decoding a basic TFCI and an extended TFCI compatibly in an IMT 2000 system. 
     It is yet another object of the present invention to provide an apparatus and method for generating an optimal code by encoding an extended TFCI in an IMT 2000 system. 
     It is a further object of the present invention to provide a method of generating mask sequences for use in encoding/decoding an extended TFCI in an IMT 2000 system. 
     To achieve the above objects, there is provided a TFCI encoding/decoding apparatus and method in a CDMA mobile communication system. In the TFCI encoding apparatus, a one-bit generator generates a sequence having the same symbols. A basis orthogonal sequence generator generates a plurality of basis orthogonal sequences. A basis mask sequence generator generates a plurality of basis mask sequences. An operation unit receives TFCI bits that are divided into a 1 st  information part representing biorthogonal sequence conversion, a 2 nd  information part representing orthogonal sequence conversion, and a 3 rd  information part representing mask sequence conversion and combines an orthogonal sequence selected from the basis orthogonal sequence based on the 2 nd  information, a biorthogonal sequence obtained by combining the selected orthogonal sequence with the same symbols selected based on the 1 st  information part, and a mask sequence selected based on the biorthogonal code sequence and the 3 rd  information part, thereby generating a TFCI sequence. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which: 
         FIGS. 1A  to  1 D illustrate exemplary applications of a TFCI to channel frames in a genera IMT 2000 system; 
         FIG. 2  is a block diagram of a base station transmitter in the general IMT 2000 system; 
         FIG. 3  is a block diagram of a mobile station transmitter in the general IMT 2000 system; 
         FIG. 4A  conceptionally illustrates a basic TFCI encoding structure in a conventional IMT 2000 system; 
         FIG. 4B  is an example of an encoding table used in a biorthogonal encoder shown in  FIG. 4A ; 
         FIG. 5A  conceptionally illustrates an extended TFCI encoding structure in the conventional IMT 2000 system; 
         FIG. 5B  is an example of an algorithm of distributing TFCI bits in a controller shown in  FIG. 5A ; 
         FIG. 5C  is an example of an encoding table used in biorthogonal encoders shown in  FIG. 5A ; 
         FIG. 6  conceptionally illustrates a TFCI encoding structure in an IMT 2000 system according to the present invention; 
         FIG. 7  is a flowchart illustrating an embodiment of a mask sequence generating procedure for TFCI encoding in the IMT 2000 system according to the present invention; 
         FIG. 8  is a block diagram of an embodiment of a TFCI encoding apparatus in the IMT 2000 system according to the present invention; 
         FIG. 9  is a block diagram of an embodiment of a TFCI decoding apparatus in the IMT 2000 system according to the present invention; 
         FIG. 10  is a flowchart illustrating a control operation of a correlation comparator shown in  FIG. 9 ; 
         FIG. 11  is a flowchart illustrating an embodiment of a TFCI encoding procedure in the IMT 2000 system according to the present invention; 
         FIG. 12  is a flowchart illustrating another embodiment of the TFCI encoding procedure in the IMT 2000 system according to the present invention; 
         FIG. 13  illustrates an embodiment of the structures of orthogonal sequences and mask sequences determined by a TFCI according to the present invention; 
         FIG. 14  is a block diagram of another embodiment of the TFCI encoding apparatus in the IMT 2000 system according to the present invention; 
         FIG. 15  is a block diagram of another embodiment of the TFCI decoding apparatus in the IMT 2000 system according to the present invention; 
         FIG. 16  is a flowchart illustrating another embodiment of the TFCI encoding procedure in the IMT 2000 system according to the present invention; and 
         FIG. 17  is a block diagram of a third embodiment of the TFCI decoding apparatus in the IMT 2000 system according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will be described herein below with reference to the accompanying drawings. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail. 
     The present invention is directed to a TFCI encoding concept of outputting final code symbols (a TFCI codeword) by adding first code symbols (a first TFCI codeword) resulting from first TFCI bits and second code symbols (a second TFCI codeword) resulting from second TFCI bits in an IMT 2000 system. The TFCI encoding concept is shown in FIG.  6 . Here, a biorthogonal sequence and a mask sequence are given as the first TFCI codeword and the second TFCI codeword, respectively. 
     Referring to  FIG. 6 , TFCI bits are separated into the first TFCI bits and the second TFCI bits. A mask sequence generator  602  generates a predetermined mask sequence by encoding the second TFCI bits and a biorthogonal sequence generator  604  generates a predetermined biorthogonal sequence by encoding the first TFCI bits. An adder  610  adds the mask sequence and the biorthogonal sequence and outputs final code symbols (a TFCI codeword). The mask sequence generator  602  may have an encoding table that lists mask sequences for all possible second TFCI bits. The biorthogonal sequence generator  604  may also have an encoding table that lists biorthogonal sequences for all possible first TFCI bits. 
     As described above, mask sequences and a mask sequence generating method should be defined to implement the present invention. Walsh codes are given as orthogonal sequences by way of example in embodiments of the present invention. 
     1. Mask Sequence Generating Method 
     The present invention pertains to encoding and decoding of TFCI bits and use of an extended Reed Muller code in an IMT 2000 system. For this purpose, predetermined sequences are used and the sequences should have a minimum distance that ensures excellent error correction performance. 
     A significant parameter that determines the performance or capability of a linear error correcting code is a minimum distance between codewords of the error correcting code. The Hamming weight of a codeword is the number of its symbols other than 0. If a codeword is given as “0111”, its Hamming weight is 3. The smallest Hamming weight of a codeword except all “0” codeword is called a minimum weight and the minimum distance of each binary linear code is equal to the minimum weight. A linear error correcting code has a better error correcting performance as its minimum distance is increased. For details, see “The Theory of Error-Correcting Codes”, F. J. Macwilliams and N. J. A. Sloane, North-Holland (hereinafter, referred to as reference 2). 
     An extended Reed Muller code can be derived from a set of sequences each being the sum of the elements of an m-sequence and a predetermined sequence. To use the sequence set as a linear error correcting code, the sequence set should have a large minimum distance. Such sequence sets include a Kasami sequence set, a Gold sequence set, and a Kerdock sequence set. If the total length of a sequence in such a sequence set is L=2 2m , a minimum distance=(2 2m −2 m )/2. For L=2 2m+1 , the minimum distance (2 2m+1 −2 2m )/2. That is, if L=32, the minimum distance=12. 
     A description will be made of a method of generating a linear error correcting code with excellent performance, i.e., an extended error correcting code (Walsh codes and mask sequences). 
     According to a coding theory, there is a column transposition function for making Walsh codes from m-sequences in a group which has been formed by cyclically shifting an originating m-sequence by one to ‘n’ times, where the ‘n’ is a length of the m-sequence. In other words, each of the m-sequences is formed by cyclically shifting the originating m-sequence by a particular number of times. The column transposition function is a converting function which converts the sequences in the m-sequence group to Walsh codes. We assume there is a sequence such as a Gold sequence or a Kasami sequence which is formed by adding the originating m-sequence with another originating m-sequence. Another group of m-sequences is similarly formed by cyclically shifting the other originating m-sequence one to ‘n’ times, where ‘n’ is the length of the predetermined sequence. Afterwards, a reverse column transposition function is applied to the second group of m-sequences formed from the other originating m-sequence. The application of the reverse column transposition function to the second group of m-sequences creates another set of sequences which shall be defined as mask sequences. 
     In an embodiment of the present invention, a mask sequence generating method is described in connection with generation of a (2 n , n+k) code (extended Reed Muller code) (here, k=1, . . . , n+1) using a Gold sequence set. The (2 n , n+k) code represents output of a 2 n -symbol TFCI codeword for the input of (n+k) TFCI bits (input information bits). It is well known that a Gold sequence can be expressed as the sum of two different m-sequences. To generate the (2 n , n+k) code, therefore, Gold sequences of length (2 n −1) should be produced. Here, a Gold sequence is the sum of two m-sequences m 1 (t) and m 2 (t) that are generated from generator polynomials f 1 ( x ) and f 2 ( x ). Given the generator polynomials f 1 ( x ) and f 2 ( x ), the m-sequences m 1 (t) and m 2 (t) are computed using a Trace function. 
                     m   1     ⁢           ⁢     (   t   )       =       Tr   ⁢           ⁢     (     A   ⁢           ⁢     α   t       )     ⁢           ⁢   t     =   0       ,   1   ,   …   ⁢           ,     30   ⁢           ⁢   and       ⁢           ⁢     
     ⁢         Tr   ⁢           ⁢     (   a   )       =       ∑     k   =   0       n   -   1       ⁢           ⁢     α     2   k           ,     a   ∈     GF   ⁢           ⁢     (     2   n     )                   (     Eq   .           ⁢   1     )             
 
where A is determined by the initial value of an m-sequence, α is the root of the polynomial, and n is the order of the polynomial.
 
       FIG. 7  is a flowchart illustrating a mask sequence generating procedure for use in generating a (2 n , n+k) code from a Gold sequence set. 
     Referring to  FIG. 7 , m-sequences m 1 (t) and m 2 (t) are generated in Eq. 1 using the generator polynomials f 1 ( x ) and f 2 ( x ), respectively in step  710 . In step  712 , a sequence transposition function σ(t) is calculated to make Walsh codes from a sequence set having m-sequences formed by cyclically shifting m 2 (t) 0 to n−2 times where all ‘0’ column is inserted in front of the m-sequences made from m 2 (t), as shown below: 
               σ   :           ⁢       {     0   ,   1   ,   2   ,   …   ⁢           ,       2   n     -   2       }     →     {     1   ,   2   ,   3   ,   …   ⁢           ,       2   n     -   1       }         ⁢     
     ⁢         σ   ⁢           ⁢     (   t   )       =         ∑     t   =   0       n   -   1       ⁢           ⁢       m   2     ⁢           ⁢     (     t   +   i     )     ⁢           ⁢     2     n   -   1   -   i       ⁢           ⁢   t       =   0       ,   1   ,   2   ,   …             (     Eq   .           ⁢   2     )             
 
     A set of 31 sequences produced by cyclically shifting the m-sequence m 1 (t) 0 to 30 times are column-transposed with the use of σ −1 (t)+2 derived from the reverse function of σ(t) in step  730 . Then, 0s are added to the start of each of the resulting column-transposed sequences to make the length of the sequence 2 n . Thus, a set d i (t) of (2 n −1) sequences of length 2 n (i=0, . . . , 2 n −2, t=1, . . . , 2 n ) are generated. 
                       {       d   i     ⁡     (   t   )            ⁢   t     =   1     ,   …   ⁢           ,     2   n     ,     i   =   0     ,   …   ⁢           ,       2   n     -   2       }     ⁢     
     ⁢         d   i     ⁡     (   t   )       =     (           0   ,           if   ,     t   =   1                     m   1     ⁡     (         σ     -   1       ⁡     (     t   +   i     )       +   2     )       ,           if   ,     t   =   2     ,   3   ,   …   ⁢           ,     2   n             )               (     Eq   .           ⁢   3     )             
 
     A plurality of d i (t) are mask functions that can be used as 31 masks. 
     d i (t) is characterized in that two different masks among the above masks are added to one of (2 n −1) masks except for the two masks. To further generalize it, each of the (2 n −1) masks can be expressed as the sum of at least two of particular n masks. The n masks are called basis mask sequences. When the (2 n , n+k) code is to be generated, the total number of necessary codewords is 2 n+k  for n+k input information bits (TFCI bits). The number of 2 n  orthogonal sequences (Walsh sequences) and their complements, i.e. biorthogonal sequences, is 2 n ×2=2 n+1 . 2 k−1 −1(=(2 n+k /2 n+1 )−1) masks that are not 0s are needed for generation of the (2 n , n+k) code. Here, the 2 k−1 −1 masks can be expressed by the use of k−1 basis mask sequences, as stated before. 
     Now, a description will be given of a method of selecting the k−1 basis mask sequences. The m-sequence m 1 (t) is cyclically shifted 0 to 2 n−1  times to generate a set of sequences in step  730  of FIG.  7 . Here, an m-sequence obtained by cyclically shifting the m-sequence m 1 (t) i times is expressed as Tr(α i ·α t ) according to Eq. 1. That is, a set of sequences are generated by cyclically shifting the m-sequence m i (t) 0 to 30 times with respect to an initial sequence A={1, α, . . . , α 2n−2 }. Here, linearly independent k−1 basis elements are found from the Galois elements 1, α, . . . , α 2     n     −2  and mask sequences corresponding to the output sequences of a Trace function with the k−1 basis elements as an initial sequence become basis mask sequences. A linear independence condition is expressed as 
                     ⟺     c   1       ⁢     α   1       +       c   2     ⁢     α   2       +   …   +       c     k   -   1       ⁢     α     k   -   1           ≠   0     ,     ∀     c   1       ,     c   2     ,   …   ⁢           ,     c     k   -   1               (     Eq   .           ⁢   4     )             
 
     To describe the above generalized mask function generation method in detail, how to generate a (32, 10) code using a Gold sequence set will be described referring to FIG.  7 . It is well known that a Gold sequence is expressed as the sum of different predetermined m-sequences. Therefore, a Gold sequence of length 31 should be generated first in order to generate the intended (32, 10) code. The Gold sequence is the sum of two m-sequences generated respectively from polynomials x 5 +x 2 +1 and x 5 +x 4 +x+1. Given a corresponding generator polynomial, each of the m-sequences m 1 (t) and m 2 (t) is computed using a Trace function by 
                     m   1     ⁢           ⁢     (   t   )       =       Tr   ⁢           ⁢     (     A   ⁢           ⁢     α   t       )     ⁢           ⁢   t     =   0       ,   1   ,   …   ⁢           ,     30   ⁢           ⁢   and       ⁢          ⁢         Tr   ⁢           ⁢     (   a   )       =       ∑     n   =   0     4     ⁢           ⁢     α     2   n           ,     a   ∈     GF   ⁢           ⁢     (     2   5     )                   (     Eq   .           ⁢   5     )             
 
where A is determined by the initial value of the m-sequence, a is the root of the polynomial, and n is the order of the polynomial, here 5.
 
       FIG. 7  illustrates the mask function generating procedure to generate the (32, 10) code. 
     Referring to  FIG. 7 , m-sequences m 1 (t) and m 2 (t) are generated in Eq. 1 using the generator polynomials f 1 ( x ) and f 2 ( x ), respectively in step  710 . In step  712 , the column transposition function σ(t) is calculated to make a Walsh code of the m-sequence m 2 (t) by 
               σ   :           ⁢       {     0   ,   1   ,   2   ,   …   ⁢           ,   30     }     →     {     1   ,   2   ,   3   ,   …   ⁢           ,   31     }         ⁢     
     ⁢       σ   ⁢           ⁢     (   t   )       =       ∑     t   =   0     4     ⁢           ⁢       m   2     ⁢           ⁢     (     t   -   i     )     ⁢           ⁢     2     4   -   i                     (     Eq   .           ⁢   6     )             
 
     Then, a set of 31 sequences produced by cyclically shifting the m-sequence m 1 (t) 0 to 30 times are column-transposed with the use of σ −1 (t)+2 derived from the reverse function of σ(t) in step  730 . Then, 0s are added to the start of each of the resulting sequence-transposed sequences to make the length of the sequence 31. Thus, 31 d i (t) of length 32 are generated. Here, if i=0, . . . , 31, t=1, . . . , 32. The sequences set generated in step  730  can be expressed as 
                       {       d   i     ⁡     (   t   )            ⁢   t     =   1     ,   …   ⁢           ,   32   ,     i   =   0     ,   …   ⁢           ,   30     }     ⁢     
     ⁢         d   i     ⁡     (   t   )       =     (           0   ,           if   ,     t   =   1                     m   1     ⁡     (         σ     -   1       ⁡     (     t   +   i     )       +   2     )       ,           if   ,     t   =   2     ,   3   ,   …   ⁢           ,   32           )               (     Eq   .           ⁢   7     )             
 
     A plurality of d i (t) obtained from Eq. 7 can be used as 31 mask sequences. 
     d i (t) is characterized in that two different masks among the above masks are added to one of the 31 masks except for the two masks. In other words, each of the 31 masks can be expressed as a sum of 5 particular masks. These 5 masks are basis mask sequences. 
     When the (32, 10) code is to be generated, the total number of necessary codewords is 2 n =1024 for all possible 10 input information bits (TFCI bits). The number of biorthogonal sequences of length 32 is 32×2=64. 15 masks are needed to generate the (32, 10) code. The 15 masks can be expressed as combinations of 4 basis mask sequences. 
     Now, a description will be given of a method of selecting the 4 basis mask sequences. An m-sequence obtained by cyclically shifting the m-sequence m 1 (t) i times is expressed as Tr(α i ·α t ) according to Eq. 1. That is, a set of sequences are generated by cyclically shifting the m-sequence m 1 (t) 0 to 30 times with respect to an initial sequence A={1, α, . . . , α 2n−2 }. Here, 4 linearly independent basis elements are found from the Galois elements 1, α, . . . , α 2n−2  and mask sequences corresponding to the output sequences of a Trace function with the 4 basis elements as an initial sequence becoming basis mask sequences. A linear independence condition is expressed as 
             α   ,   β   ,   γ   ,       δ   ⁢     :     ⁢           ⁢   linearly   ⁢           ⁢     independent   ⁢     
     ⟺     c   1       ⁢     α   1       +       c   2     ⁢   β     +       c   3     ⁢   γ       ,         +     c   4       ⁢   δ     ≠   0     ,     ∀     c   1       ,     c   2     ,     c   3     ,     c   4             (     Eq   .           ⁢   8     )             
 
     In fact, 1, α, α 2 , α 3  in the Galois GF(2 5 ) are polynomial sub-bases that are well known as four linearly independent elements. By replacing the variable A in Eq. 1 with the polynomial bases, four basis mask sequences M 1 , M 2 , M 4 , and M 8  are achieved.
         M 1 =00101000011000111111000001110111   M 2 =00000001110011010110110111000111   M 4 =00001010111110010001101100100101   M 8 =000110000110011010111101010001       

     There will herein below be given a description of an apparatus and method for encoding/decoding a TFCI using basis mask sequences as obtained in the above manner in an IMT 2000 system according to embodiments of the present invention. 
     2. First Embodiment of Encoding/Decoding Apparatus and Method 
       FIGS. 8 and 9  are block diagrams of TFCI encoding and decoding apparatuses in an IMT 2000 system according to an embodiment of the present invention. 
     Referring to  FIG. 8 , 10 TFCI bits a 0  to a 9  are applied to corresponding multipliers  840  to  849 . A one-bit generator  800  continuously generates a predetermined code bit. That is, since the present invention deals with biorthogonal sequences, necessary bits are generated to make a biorthogonal sequence out of an orthogonal sequence. For example, the one-bit generator  800  generates bits having 1s to inverse an orthogonal sequence (i.e., a Walsh code) generated from a basis Walsh code generator  810  and thus generate a biorthogonal sequence. The basis Walsh code generator  810  generates basis Walsh codes of a predetermined length. The basis Walsh codes refer to Walsh codes from which all intended Walsh codes can be produced through arbitrary addition. For example, when Walsh codes of length 32 are used, the basis Walsh codes are 1 st , 2 nd , 4 th , 8 th , and 16 th  Walsh codes W 1 , W 2 , W 4 , W 8 , and W 16 , wherein:
         W 1 : 01010101010101010101010101010101   W 2 : 00110011001100110011001100110011   W 4 : 00001111000011110000111100001111   W 8 : 00000000111111110000000011111111   W 16 : 00000000000000001111111111111111.       

     A basis mask sequence generator  820  generates a basis mask sequence of a predetermined length. A basis mask sequence generating method has already been described before and its details will not be described. If a mask sequence of length 32 is used, basis mask sequences are 1 st , 2 nd , 4 th , and 8 th  mask sequences M 1 , M 2 , M 4 , M 8 , wherein:
         M 1 : 00101000011000111111000001110111   M 2 : 00000001110011010110110111000111   M 4 : 00001010111110010001101100101011   M 8 : 00011100001101110010111101010001.       

     The multiplier  840  multiplies 1s output from the one-bit generator  800  by the input information bit a 0  on a symbol basis. 
     The multiplier  841  multiplies the basis Walsh code W 1  received from the basis Walsh code generator  810  by the input information bit a 1 . The multiplier  842  multiplies the basis Walsh code W 2  received from the basis Walsh code generator  810  by the input information bit a 2 . The multiplier  843  multiplies the basis Walsh code W 4  received from the basis Walsh code generator  810  by the input information bit a 3 . The multiplier  844  multiplies the basis Walsh code W 8  received from the basis Walsh code generator  810  by the input information bit a 4 . The multiplier  845  multiplies the basis Walsh code W 16  received from the basis Walsh code generator  810  by the input information bit a 5 . The multipliers  841  to  845  multiply the received basis Walsh codes W 1 , W 2 , W 4 , W 8 , and W 16  by their corresponding input information bits symbol by symbol. 
     Meanwhile, the multiplier  846  multiplies the basis mask sequence M 1  by the input information bit a 6 . The multiplier  847  multiplies the basis mask sequence M 2  by the input information bit a 7 . The multiplier  848  multiplies the basis mask sequence M 4  by the input information bit a 8 . The multiplier  849  multiplies the basis mask sequence M 8  by the input information bit a 9 . The multipliers  846  to  849  multiply the received basis mask sequences M 1 , M 2 , M 4 , and M 8  by their corresponding input information bits symbol by symbol. 
     An adder  860  adds the encoded input information bits received from the multipliers  840  to  849  and outputs final code symbols of length 32 bits (a TFCI codeword). The length of the final code symbols (TFCI codeword) is determined by the lengths of the basis Walsh codes generated from the basis Walsh code generator  810  and the basis mask sequences generated from the basis mask sequence generator  820 . 
     For example, if the input information bits a 0  to a 9  are “0111011000”, the multiplier  840  multiplies 0 as a 0  by 1s received from the one-bit generator  800  and generates 32 code symbols being all “0s”. The multiplier. 841 multiplies 1 as a 1  by W 1  received from the basis Walsh code generator  810  and generates code symbols “01010101010101010101010101010101”. The multiplier  842  multiplies 1 as a 2  by W 2  received from the basis Walsh code generator  810  and generates code symbols “00110011001100110011001100110011”. The multiplier  843  multiplies 1 as a 3  by W 4  received from the basis Walsh code generator  810  and generates code symbols “00001111000011110000111100001111”. The multiplier  844  multiplies 0 as a 4  by W 8  received from the basis Walsh code generator  810  and generates 32 code symbols being all “0s”. The multiplier  845  multiplies 1 as a 5  by W 16  received from the basis Walsh code generator  810  and generates “00000000000000001111111111111111”. The multiplier  846  multiplies 1 as a 6  by M 1  received from the basis mask sequence generator  820  and generates “00101000011000111111000001110111”. The multiplier  847  multiplies 0 as a 7  by M 2  received from the basis mask sequence generator  820  and generates 32 code symbols being all 0s. The multiplier  848  multiplies 0 as a 8  by M 4  received from the basis mask sequence generator  820  and generates 32 code symbols being all 0s. The multiplier  849  multiplies 0 as a 9  by M 8  received from the basis mask sequence generator  820  and generates 32 code symbols being all 0s. The adder  860  adds the code symbols received from the multipliers  840  to  849  and outputs final code symbols “01000001000010100110011011100001”. The final code symbols can be achieved by adding the basis Walsh codes W 1 , W 2 , W 4  and W 16  corresponding to the information bits Is to the basis mask sequence M 1  symbol by symbol. In other words, the basis Walsh codes W 1 , W 2 , W 4  and W 16  are summed to W 23  and the Walsh code W 23  and the basis mask sequence M 1  are added to form the TFCI codeword (final code symbols) (=W 23 +M 1 ) which is outputted from the adder  860 . 
       FIG. 11  is a flowchart illustrating an embodiment of a TFCI encoding procedure in an IMT 2000 system according to the present invention. 
     Referring to  FIG. 11 , 10 input information bits (i.e., TFCI bits) are received and variables sum and j are set to an initial value 0 in step  1100 . The variable sum indicates final code symbols, and j indicates the count number of final code symbols output after symbol-basis addition. In step  1110 , it is determined whether j is 32 in view of the length 32 symbols of Walsh codes and mask sequences used for encoding the input information bits. Step  1110  is performed in order to check whether the input information bits are all encoded with the Walsh codes and the mask sequences symbol by symbol. 
     If j is not 32 in step  1110 , which implies that the input information bits are not encoded completely with respect to all symbols of the Walsh codes, the mask sequences, j th  symbols W 1 ( j ), W 2 ( j ), W 4 ( j ), W 8 ( j ), and W 16 ( j ) of the basis Walsh codes W 1 , W 2 , W 4 , W 8 , and W 16  and j th  symbols M 1 ( j ), M 2 ( j ), M 4 ( j ), and M 8 ( j ) of the basis mask sequences M 1 , M 2 , M 4 , and M 8  are received in step  1120 . Then, the received symbols are multiplied by the input information bits on a symbol basis and the symbol products are summed in step  1130 . The sum becomes the variable sum. 
     Step  1130  can be expressed as
 
sum= a   0 + a   1 · W   1 ( j )+ a   2 · W   2 ( j )+ a   3 · W   4 ( j )+ a   4 · W   8 ( j )+ a   5 · W   16 ( j )+ a   6 · M   1 ( j )+ a   7 · M   2 ( j )+ a   8 · M   4 ( j )+ a   9 · M   8 ( j )  (Eq. 9) 
 
     As noted from Eq. 9, the input information bits are multiplied by corresponding symbols of the basis Walsh codes and basis mask sequences, symbol products are summed, and the sum becomes an intended code symbol. 
     In step  1140 , sum indicating the achieved j th  code symbol, is output. j is increased by 1 in step  1150  and then the procedure returns to step  1110 . Meanwhile, if j is 32 in step  1110 , the encoding procedure ends. 
     The encoding apparatus of  FIG. 8  according to the embodiment of the present invention can support extended TFCIs as well as basic TFCIs. Encoders for supporting an extended TFCI include a (32, 10) encoder, a (32, 9) encoder, and a (32, 7) encoder. 
     For the input of 10 input information bits, the (32, 10) encoder outputs a combination of 32 Walsh codes of length 32, 32 bi-orthogonal codes inverted from the Walsh codes, and 15 mask sequences. The 32 Walsh codes can be generated from combinations of 5 basis Walsh Go codes. The 32 bi-orthogonal codes can be obtained by adding 1 to the 32 symbols of each Walsh code. This results has the same effect as multiplication of −1 by the 32 Walsh codes viewed as real numbers. The 15 mask sequences can be achieved through combinations of 5 basis mask sequences. Therefore, a total of 1024 codewords can be produced from the (32, 10) encoder. 
     The (32, 9) encoder receives 9 input information bits and outputs a combination of 32 Walsh codes of length 32, 32 bi-orthogonal codes inverted from the Walsh codes, and 4 mask sequences. The 4 mask sequences are obtained by combing two of 4 basis mask sequences. 
     The (32, 7) encoder receives 7 input information bits and outputs a combination of 32 Walsh codes of length among the 1024 codewords, 32 bi-orthogonal codes inverted from the Walsh codes, and one of 4 basis mask sequences. 
     The above encoders for providing extended TFCIs have a minimum distance  12  and can be implemented by blocking input and output of at least of the 4 basis mask sequences generated from the basis mask sequences  820 . 
     That is, the (32, 9) encoder can be implemented by blocking input and output of one of the four basis mask sequences generated from the basis mask sequence generator  820  shown in FIG.  8 . The (32, 8) encoder can be implemented by blocking input and output of two of the basis mask sequences generated from the basis mask sequence generator  820 . The (32, 7) encoder can be implemented by blocking input and output of three of the basis mask sequences generated from the basis mask sequence generator  820 . As described above, the encoding apparatus according to the embodiment of the present invention can encode flexibly according to the number of input information bits, that is, the number of TFCI bits to be transmitted and maximizes a minimum distance that determined the performance of the encoding apparatus. 
     Codewords in the above encoding apparatus are sequences obtained by combining 32 Walsh codes of length 32, 32 bi-orthogonal codes resulting from adding 1s to the Walsh codes, and 15 mask sequences of length 15. The structure of the codewords is shown in FIG.  13 . 
     For better understanding of the TFC bits encoding procedure, Tables 1a to 1f list code symbols (TFCI codewords) versus  10  TFCI bits. 
     
       
         
               
               
             
           
               
                 TABLE 1a 
               
               
                   
               
             
             
               
                 0000000000:00000000000000000000000000000000 
                 0000000001:11111111111111111111111111111111 
               
               
                 0000000010:01010101010101010101010101010101 
                 0000000011:10101010101010101010101010101010 
               
               
                 0000000100:00110011001100110011001100110011 
                 0000000101:11001100110011001100110011001100 
               
               
                 0000000110:01100110011001100110011001100110 
                 0000000111:10011001100110011001100110011001 
               
               
                 0000001000:00001111000011110000111100001111 
                 0000001001:11110000111100001111000011110000 
               
               
                 0000001010:01011010010110100101101001011010 
                 0000001011:10100101101001011010010110100101 
               
               
                 0000001100:00111100001111000011110000111100 
                 0000001101:11000011110000111100001111000011 
               
               
                 0000001110:01101001011010010110100101101001 
                 0000001111:10010110100101101001011010010110 
               
               
                 0000010000:00000000111111110000000011111111 
                 0000010001:11111111000000001111111100000000 
               
               
                 0000010010:01010101101010100101010110101010 
                 0000010011:10101010010101011010101001010101 
               
               
                 0000010100:00110011110011000011001111001100 
                 0000010101:11001100001100111100110000110011 
               
               
                 0000010110:01100110100110010110011010011001 
                 0000010111:10011001011001101001100101100110 
               
               
                 0000011000:00001111111100000000111111110000 
                 0000011001:11110000000011111111000000001111 
               
               
                 0000011010:01011010101001010101101010100101 
                 0000011011:10100101010110101010010101011010 
               
               
                 0000011100:00111100110000110011110011000011 
                 0000011101:11000011001111001100001100111100 
               
               
                 0000011110:01101001100101100110100110010110 
                 0000011111:10010110011010011001011001101001 
               
               
                 0000100000:00000000000000001111111111111111 
                 0000100001:11111111111111110000000000000000 
               
               
                 0000100010:01010101010101011010101010101010 
                 0000100011:10101010101010100101010101010101 
               
               
                 0000100100:00110011001100111100110011001100 
                 0000100101:11001100110011000011001100110011 
               
               
                 0000100110:01100110011001101001100110011001 
                 0000100111:10011001100110010110011001100110 
               
               
                 0000101000:00001111000011111111000011110000 
                 0000101001:11110000111100000000111100001111 
               
               
                 0000101010:01011010010110101010010110100101 
                 0000101011:10100101101001010101101001011010 
               
               
                 0000101100:00111100001111001100001111000011 
                 0000101101:11000011110000110011110000111100 
               
               
                 0000101110:01101001011010011001011010010110 
                 0000101111:10010110100101100110100101101001 
               
               
                 0000110000:00000000111111111111111100000000 
                 0000110001:11111111000000000000000011111111 
               
               
                 0000110010:01010101101010101010101001010101 
                 0000110011:10101010010101010101010110101010 
               
               
                 0000110100:00110011110011001100110000110011 
                 0000110101:11001100001100110011001111001100 
               
               
                 0000110110:01100110100110011001100101100110 
                 0000110111:10011001011001100110011010011001 
               
               
                 0000111000:00001111111100001111000000001111 
                 0000111001:11110000000011110000111111110000 
               
               
                 0000111010:01011010101001011010010101011010 
                 0000111011:10100101010110100101101010100101 
               
               
                 0000111100:00111100110000111100001100111100 
                 0000111101:11000011001111000011110011000011 
               
               
                 0000111110:01101001100101101001011001101001 
                 0000111111:10010110011010010110100110010110 
               
               
                 0001000000:00101000011000111111000001110111 
                 0001000001:11010111100111000000111110001000 
               
               
                 0001000010:01111101001101101010010100100010 
                 0001000011:10000010110010010101101011011101 
               
               
                 0001000100:00011011010100001100001101000100 
                 0001000101:11100100101011110011110010111011 
               
               
                 0001000110:01001110000001011001011000010001 
                 0001000111:10110001111110100110100111101110 
               
               
                 0001001000:00100111011011001111111101111000 
                 0001001001:11011000100100110000000010000111 
               
               
                 0001001010:01110010001110011010101000101101 
                 0001001011:10001101110001100101010111010010 
               
               
                 0001001100:00010100010111111100110001001011 
                 0001001101:11101011101000000011001110110100 
               
               
                 0001001110:01000001000010101001100100011110 
                 0001001111:10111110111101010110011011100001 
               
               
                 0001010000:00101000100111001111000010001000 
                 0001010001:11010111011000110000111101110111 
               
               
                 0001010010:01111101110010011010010111011101 
                 0001010011:10000010001101100101101000100010 
               
               
                 0001010100:00011011101011111100001110111011 
                 0001010101:11100100010100000011110001000100 
               
               
                 0001010110:01001110111110101001011011101110 
                 0001010111:10110001000001010110100100010001 
               
               
                 0001011000:00100111100100111111111110000111 
                 0001011001:11011000011011000000000001111000 
               
               
                 0001011010:01110010110001101010101011010010 
                 0001011011:10001101001110010101010100101101 
               
               
                 0001011100:00010100101000001100110010110100 
                 0001011101:11101011010111110011001101001011 
               
               
                 0001011110:01000001111101011001100111100001 
                 0001011111:10111110000010100110011000011110 
               
               
                 0001100000:00101000011000110000111110001000 
                 0001100001:11010111100111001111000001110111 
               
               
                 0001100010:01111101001101100101101011011101 
                 0001100011:10000010110010011010010100100010 
               
               
                 0001100100:00011011010100000011110010111011 
                 0001100101:11100100101011111100001101000100 
               
               
                 0001100110:01001110000001010110100111101110 
                 0001100111:10110001111110101001011000010001 
               
               
                 0001101000:00100111011011000000000010000111 
                 0001101001:11011000100100111111111101111000 
               
               
                 0001101010:01110010001110010101010111010010 
                 0001101011:10001101110001101010101000101101 
               
               
                 0001101100:00010100010111110011001110110100 
                 0001101101:11101011101000001100110001001011 
               
               
                 0001101110:01000001000010100110011011100001 
                 0001101111:10111110111101011001100100011110 
               
               
                 0001110000:00101000100111000000111101110111 
                 0001110001:11010111011000111111000010001000 
               
               
                 0001110010:01111101110010010101101000100010 
                 0001110011:10000010001101101010010111011101 
               
               
                 0001110100:00011011101011110011110001000100 
                 0001110101:11100100010100001100001110111011 
               
               
                 0001110110:01001110111110100110100100010001 
                 0001110111:10110001000001011001011011101110 
               
               
                 0001111000:00100111100100110000000001111000 
                 0001111001:11011000011011001111111110000111 
               
               
                 0001111010:01110010110001100101010100101101 
                 0001111011:10001101001110011010101011010010 
               
               
                 0001111100:00010100101000000011001101001011 
                 0001111101:11101011010111111100110010110100 
               
               
                 0001111110:01000001111101010110011000011110 
                 0001111111:10111110000010101001100111100001 
               
               
                 0010000000:00000001110011010110110111000111 
                 0010000001:11111110001100101001001000111000 
               
               
                 0010000010:01010100100110000011100010010010 
                 0010000011:10101011011001111100011101101101 
               
               
                 0010000100:00110010111111100101111011110100 
                 0010000101:11001101000000011010000100001011 
               
               
                 0010000110:01100111101010110000101110100001 
                 0010000111:10011000010101001111010001011110 
               
               
                 0010001000:00001110110000100110001011001000 
                 0010001001:11110001001111011001110100110111 
               
               
                 0010001010:01011011100101110011011110011101 
                 0010001011:10100100011010001100100001100010 
               
               
                 0010001100:00111101111100010101000111111011 
                 0010001101:11000010000011101010111000000100 
               
               
                 0010001110:01101000101001000000010010101110 
                 0010001111:10010111010110111111101101010001 
               
               
                 0010010000:00000001001100100110110100111000 
                 0010010001:11111110110011011001001011000111 
               
               
                 0010010010:01010100011001110011100001101101 
                 0010010011:10101011100110001100011110010010 
               
               
                 0010010100:00110010000000010101111000001011 
                 0010010101:11001101111111101010000111110100 
               
               
                 0010010110:01100111010101000000101101011110 
                 0010010111:10011000101010111111010010100001 
               
               
                 0010011000:00001110001111010110001000110111 
                 0010011001:11110001110000101001110111001000 
               
               
                 0010011010:01011011011010000011011101100010 
                 0010011011:10100100100101111100100010011101 
               
               
                 0010011100:00111101000011100101000100000100 
                 0010011101:11000010111100011010111011111011 
               
               
                 0010011110:01101000010110110000010001010001 
                 0010011111:10010111101001001111101110101110 
               
               
                 0010100000:00000001110011011001001000111000 
                 0010100001:11111110001100100110110111000111 
               
               
                 0010100010:01010100100110001100011101101101 
                 0010100011:10101011011001110011100010010010 
               
               
                 0010100100:00110010111111101010000100001011 
                 0010100101:11001101000000010101111011110100 
               
               
                 0010100110:01100111101010111111010001011110 
                 0010100111:10011000010101000000101110100001 
               
               
                 0010101000:00001110110000101001110100110111 
                 0010101001:11110001001111010110001011001000 
               
               
                 0010101010:01011011100101111100100001100010 
                 0010101011:10100100011010000011011110011101 
               
               
                 0010101100:00111101111100011010111000000100 
                 0010101101:11000010000011100101000111111011 
               
               
                 0010101110:01101000101001001111101101010001 
                 0010101111:10010111010110110000010010101110 
               
               
                 0010110000:00000001001100101001001011000111 
                 0010110001:11111110110011010110110100111000 
               
               
                 0010110010:01010100011001111100011110010010 
                 0010110011:10101011100110000011100001101101 
               
               
                 0010110100:00110010000000011010000111110100 
                 0010110101:11001101111111100101111000001011 
               
               
                 0010110110:01100111010101001111010010100001 
                 0010110111:10011000101010110000101101011110 
               
               
                 0010111000:00001110001111011001110111001000 
                 0010111001:11110001110000100110001000110111 
               
               
                 0010111010:01011011011010001100100010011101 
                 0010111011:10100100100101110011011101100010 
               
               
                 0010111100:00111101000011101010111011111011 
                 0010111101:11000010111100010101000100000100 
               
               
                 0010111110:01101000010110111111101110101110 
                 0010111111:10010111101001000000010001010001 
               
               
                 0011000000:00101001101011101001110110110000 
                 0011000001:11010110010100010110001001001111 
               
               
                 0011000010:01111100111110111100100011100101 
                 0011000011:10000011000001000011011100011010 
               
               
                 0011000100:00011010100111011010111010000011 
                 0011000101:11100101011000100101000101111100 
               
               
                 0011000110:01001111110010001111101111010110 
                 0011000111:10110000001101110000010000101001 
               
               
                 0011001000:00100110101000011001001010111111 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
             
           
               
                 TABLE 1b 
               
               
                   
               
             
             
               
                 0011001001:11011001010111100110110101000000 
                 0011001010:01110011111101001100011111101010 
               
               
                 0011001011:10001100000010110011100000010101 
                 0011001100:00010101100100101010000110001100 
               
               
                 0011001101:11101010011011010101111001110011 
                 0011001110:01000000110001111111010011011001 
               
               
                 0011001111:10111111001110000000101100100110 
                 0011010000:00101001010100011001110101001111 
               
               
                 0011010001:11010110101011100110001010110000 
                 0011010010:01111100000001001100100000011010 
               
               
                 0011010011:10000011111110110011011111100101 
                 0011010100:00011010011000101010111001111100 
               
               
                 0011010101:11100101100111010101000110000011 
                 0011010110:01001111001101111111101100101001 
               
               
                 0011010111:10110000110010000000010011010110 
                 0011011000:00100110010111101001001001000000 
               
               
                 0011011001:11011001101000010110110110111111 
                 0011011010:01110011000010111100011100010101 
               
               
                 0011011011:10001100111101000011100011101010 
                 0011011100:00010101011011011010000101110011 
               
               
                 0011011101:11101010100100100101111010001100 
                 0011011110:01000000001110001111010000100110 
               
               
                 0011011111:10111111110001110000101111011001 
                 0011100000:00101001101011100110001001001111 
               
               
                 0011100001:11010110010100011001110110110000 
                 0011100010:01111100111110110011011100011010 
               
               
                 0011100011:10000011000001001100100011100101 
                 0011100100:00011010100111010101000101111100 
               
               
                 0011100101:11100101011000101010111010000011 
                 0011100110:01001111110010000000010000101001 
               
               
                 0011100111:10110000001101111111101111010110 
                 0011101000:00100110101000010110110101000000 
               
               
                 0011101001:11011001010111101001001010111111 
                 0011101010:01110011111101000011100000010101 
               
               
                 0011101011:10001100000010111100011111101010 
                 0011101100:00010101100100100101111001110011 
               
               
                 0011101101:11101010011011011010000110001100 
                 0011101110:01000000110001110000101100100110 
               
               
                 0011101111:10111111001110001111010011011001 
                 0011110000:00101001010100010110001010110000 
               
               
                 0011110001:11010110101011101001110101001111 
                 0011110010:01111100000001000011011111100101 
               
               
                 0011110011:10000011111110111100100000011010 
                 0011110100:00011010011000100101000110000011 
               
               
                 0011110101:11100101100111011010111001111100 
                 0011110110:01001111001101110000010011010110 
               
               
                 0011110111:10110000110010001111101100101001 
                 0011111000:00100110010111100110110110111111 
               
               
                 0011111001:11011001101000011001001001000000 
                 0011111010:01110011000010110011100011101010 
               
               
                 0011111011:10001100111101001100011100010101 
                 0011111100:00010101011011010101111010001100 
               
               
                 0011111101:11101010100100101010000101110011 
                 0011111110:01000000001110000000101111011001 
               
               
                 0011111111:10111111110001111111010000100110 
                 0100000000:00001010111110010001101100101011 
               
               
                 0100000001:11110101000001101110010011010100 
                 0100000010:01011111101011000100111001111110 
               
               
                 0100000011:10100000010100111011000110000001 
                 0100000100:00111001110010100010100000011000 
               
               
                 0100000101:11000110001101011101011111100111 
                 0100000110:01101100100111110111110101001101 
               
               
                 0100000111:10010011011000001000001010110010 
                 0100001000:00000101111101100001010000100100 
               
               
                 0100001001:11111010000010011110101111011011 
                 0100001010:01010000101000110100000101110001 
               
               
                 0100001011:10101111010111001011111010001110 
                 0100001100:00110110110001010010011100010111 
               
               
                 0100001101:11001001001110101101100011101000 
                 0100001110:01100011100100000111001001000010 
               
               
                 0100001111:10011100011011111000110110111101 
                 0100010000:00001010000001100001101111010100 
               
               
                 0100010001:11110101111110011110010000101011 
                 0100010010:01011111010100110100111010000001 
               
               
                 0100010011:10100000101011001011000101111110 
                 0100010100:00111001001101010010100011100111 
               
               
                 0100010101:11000110110010101101011100011000 
                 0100010110:01101100011000000111110110110010 
               
               
                 0100010111:10010011100111111000001001001101 
                 0100011000:00000101000010010001010011011011 
               
               
                 0100011001:11111010111101101110101100100100 
                 0100011010:01010000010111000100000110001110 
               
               
                 0100011011:10101111101000111011111001110001 
                 0100011100:00110110001110100010011111101000 
               
               
                 0100011101:11001001110001011101100000010111 
                 0100011110:01100011011011110111001010111101 
               
               
                 0100011111:10011100100100001000110101000010 
                 0100100000:00001010111110011110010011010100 
               
               
                 0100100001:11110101000001100001101100101011 
                 0100100010:01011111101011001011000110000001 
               
               
                 0100100011:10100000010100110100111001111110 
                 0100100100:00111001110010101101011111100111 
               
               
                 0100100101:11000110001101010010100000011000 
                 0100100110:01101100100111111000001010110010 
               
               
                 0100100111:10010011011000000111110101001101 
                 0100101000:00000101111101101110101111011011 
               
               
                 0100101001:11111010000010010001010000100100 
                 0100101010:01010000101000111011111010001110 
               
               
                 0100101011:10101111010111000100000101110001 
                 0100101100:00110110110001011101100011101000 
               
               
                 0100101101:11001001001110100010011100010111 
                 0100101110:01100011100100001000110110111101 
               
               
                 0100101111:10011100011011110111001001000010 
                 0100110000:00001010000001101110010000101011 
               
               
                 0100110001:11110101111110010001101111010100 
                 0100110010:01011111010100111011000101111110 
               
               
                 0100110011:10100000101011000100111010000001 
                 0100110100:00111001001101011101011100011000 
               
               
                 0100110101:11000110110010100010100011100111 
                 0100110110:01101100011000001000001001001101 
               
               
                 0100110111:10010011100111110111110110110010 
                 0100111000:00000101000010011110101100100100 
               
               
                 0100111001:11111010111101100001010011011011 
                 0100111010:01010000010111001011111001110001 
               
               
                 0100111011:10101111101000110100000110001110 
                 0100111100:00110110001110101101100000010111 
               
               
                 0100111101:11001001110001010010011111101000 
                 0100111110:01100011011011111000110101000010 
               
               
                 0100111111:10011100100100000111001010111101 
                 0101000000:00100010100110101110101101011100 
               
               
                 0101000001:11011101011001010001010010100011 
                 0101000010:01110111110011111011111000001001 
               
               
                 0101000011:10001000001100000100000111110110 
                 0101000100:00010001101010011101100001101111 
               
               
                 0101000101:11101110010101100010011110010000 
                 0101000110:01000100111111001000110100111010 
               
               
                 0101000111:10111011000000110111001011000101 
                 0101001000:00101101100101011110010001010011 
               
               
                 0101001001:11010010011010100001101110101100 
                 0101001010:01111000110000001011000100000110 
               
               
                 0101001011:10000111001111110100111011111001 
                 0101001100:00011110101001101101011101100000 
               
               
                 0101001101:11100001010110010010100010011111 
                 0101001110:01001011111100111000001000110101 
               
               
                 0101001111:10110100000011000111110111001010 
                 0101010000:00100010011001011110101110100011 
               
               
                 0101010001:11011101100110100001010001011100 
                 0101010010:01110111001100001011111011110110 
               
               
                 0101010011:10001000110011110100000100001001 
                 0101010100:00010001010101101101100010010000 
               
               
                 0101010101:11101110101010010010011101101111 
                 0101010110:01000100000000111000110111000101 
               
               
                 0101010111:10111011111111000111001000111010 
                 0101011000:00101101011010101110010010101100 
               
               
                 0101011001:11010010100101010001101101010011 
                 0101011010:01111000001111111011000111111001 
               
               
                 0101011011:10000111110000000100111000000110 
                 0101011100:00011110010110011101011110011111 
               
               
                 0101011101:11100001101001100010100001100000 
                 0101011110:01001011000011001000001011001010 
               
               
                 0101011111:10110100111100110111110100110101 
                 0101100000:00100010100110100001010010100011 
               
               
                 0101100001:11011101011001011110101101011100 
                 0101100010:01110111110011110100000111110110 
               
               
                 0101100011:10001000001100001011111000001001 
                 0101100100:00010001101010010010011110010000 
               
               
                 0101100101:11101110010101101101100001101111 
                 0101100110:01000100111111000111001011000101 
               
               
                 0101100111:10111011000000111000110100111010 
                 0101101000:00101101100101010001101110101100 
               
               
                 0101101001:11010010011010101110010001010011 
                 0101101010:01111000110000000100111011111001 
               
               
                 0101101011:10000111001111111011000100000110 
                 0101101100:00011110101001100010100010011111 
               
               
                 0101101101:11100001010110011101011101100000 
                 0101101110:01001011111100110111110111001010 
               
               
                 0101101111:10110100000011001000001000110101 
                 0101110000:00100010011001010001010001011100 
               
               
                 0101110001:11011101100110101110101110100011 
                 0101110010:01110111001100000100000100001001 
               
               
                 0101110011:10001000110011111011111011110110 
                 0101110100:00010001010101100010011101101111 
               
               
                 0101110101:11101110101010011101100010010000 
                 0101110110:01000100000000110111001000111010 
               
               
                 0101110111:10111011111111001000110111000101 
                 0101111000:00101101011010100001101101010011 
               
               
                 0101111001:11010010100101011110010010101100 
                 0101111010:01111000001111110100111000000110 
               
               
                 0101111011:10000111110000001011000111111001 
                 0101111100:00011110010110010010100001100000 
               
               
                 0101111101:11100001101001101101011110011111 
                 0101111110:01001011000011000111110100110101 
               
               
                 0101111111:10110100111100111000001011001010 
                 0110000000:00001011001101000111011011101100 
               
               
                 0110000001:11110100110010111000100100010011 
                 0110000010:01011110011000010010001110111001 
               
               
                 0110000011:10100001100111101101110001000110 
                 0110000100:00111000000001110100010111011111 
               
               
                 0110000101:11000111111110001011101000100000 
                 0110000110:01101101010100100001000010001010 
               
               
                 0110000111:10010010101011011110111101110101 
                 0110001000:00000100001110110111100111100011 
               
               
                 0110001001:11111011110001001000011000011100 
                 0110001010:01010001011011100010110010110110 
               
               
                 0110001011:10101110100100011101001101001001 
                 0110001100:00110111000010000100101011010000 
               
               
                 0110001101:11001000111101111011010100101111 
                 0110001110:01100010010111010001111110000101 
               
               
                 0110001111:10011101101000101110000001111010 
                 0110010000:00001011110010110111011000010011 
               
               
                 0110010001:11110100001101001000100111101100 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
             
           
               
                 TABLE 1c 
               
               
                   
               
             
             
               
                 0110010010:01011110100111100010001101000110 
                 0110010011:10100001011000011101110010111001 
               
               
                 0110010100:00111000111110000100010100100000 
                 0110010101:11000111000001111011101011011111 
               
               
                 0110010110:01101101101011010001000001110101 
                 0110010111:10010010010100101110111110001010 
               
               
                 0110011000:00000100110001000111100100011100 
                 0110011001:11111011001110111000011011100011 
               
               
                 0110011010:01010001100100010010110001001001 
                 0110011011:10101110011011101101001110110110 
               
               
                 0110011100:00110111111101110100101000101111 
                 0110011101:11001000000010001011010111010000 
               
               
                 0110011110:01100010101000100001111101111010 
                 0110011111:10011101010111011110000010000101 
               
               
                 0110100000:00001011001101001000100100010011 
                 0110100001:11110100110010110111011011101100 
               
               
                 0110100010:01011110011000011101110001000110 
                 0110100011:10100001100111100010001110111001 
               
               
                 0110100100:00111000000001111011101000100000 
                 0110100101:11000111111110000100010111011111 
               
               
                 0110100110:01101101010100101110111101110101 
                 0110100111:10010010101011010001000010001010 
               
               
                 0110101000:00000100001110111000011000011100 
                 0110101001:11111011110001000111100111100011 
               
               
                 0110101010:01010001011011101101001101001001 
                 0110101011:10101110100100010010110010110110 
               
               
                 0110101100:00110111000010001011010100101111 
                 0110101101:11001000111101110100101011010000 
               
               
                 0110101110:01100010010111011110000001111010 
                 0110101111:10011101101000100001111110000101 
               
               
                 0110110000:00001011110010111000100111101100 
                 0110110001:11110100001101000111011000010011 
               
               
                 0110110010:01011110100111101101110010111001 
                 0110110011:10100001011000010010001101000110 
               
               
                 0110110100:00111000111110001011101011011111 
                 0110110101:11000111000001110100010100100000 
               
               
                 0110110110:01101101101011011110111110001010 
                 0110110111:10010010010100100001000001110101 
               
               
                 0110111000:00000100110001001000011011100011 
                 0110111001:11111011001110110111100100011100 
               
               
                 0110111010:01010001100100011101001110110110 
                 0110111011:10101110011011100010110001001001 
               
               
                 0110111100:00110111111101111011010111010000 
                 0110111101:11001000000010000100101000101111 
               
               
                 0110111110:01100010101000101110000010000101 
                 0110111111:10011101010111010001111101111010 
               
               
                 0111000000:00100011010101111000011010011011 
                 0111000001:11011100101010000111100101100100 
               
               
                 0111000010:01110110000000101101001111001110 
                 0111000011:10001001111111010010110000110001 
               
               
                 0111000100:00010000011001001011010110101000 
                 0111000101:11101111100110110100101001010111 
               
               
                 0111000110:01000101001100011110000011111101 
                 0111000111:10111010110011100001111100000010 
               
               
                 0111001000:00101100010110001000100110010100 
                 0111001001:11010011101001110111011001101011 
               
               
                 0111001010:01111001000011011101110011000001 
                 0111001011:10000110111100100010001100111110 
               
               
                 0111001100:00011111011010111011101010100111 
                 0111001101:11100000100101000100010101011000 
               
               
                 0111001110:01001010001111101110111111110010 
                 0111001111:10110101110000010001000000001101 
               
               
                 0111010000:00100011101010001000011001100100 
                 0111010001:11011100010101110111100110011011 
               
               
                 0111010010:01110110111111011101001100110001 
                 0111010011:10001001000000100010110011001110 
               
               
                 0111010100:00010000100110111011010101010111 
                 0111010101:11101111011001000100101010101000 
               
               
                 0111010110:01000101110011101110000000000010 
                 0111010111:10111010001100010001111111111101 
               
               
                 0111011000:00101100101001111000100101101011 
                 0111011001:11010011010110000111011010010100 
               
               
                 0111011010:01111001111100101101110000111110 
                 0111011011:10000110000011010010001111000001 
               
               
                 0111011100:00011111100101001011101001011000 
                 0111011101:11100000011010110100010110100111 
               
               
                 0111011110:01001010110000011110111100001101 
                 0111011111:10110101001111100001000011110010 
               
               
                 0111100000:00100011010101110111100101100100 
                 0111100001:11011100101010001000011010011011 
               
               
                 0111100010:01110110000000100010110000110001 
                 0111100011:10001001111111011101001111001110 
               
               
                 0111100100:00010000011001000100101001010111 
                 0111100101:11101111100110111011010110101000 
               
               
                 0111100110:01000101001100010001111100000010 
                 0111100111:10111010110011101110000011111101 
               
               
                 0111101000:00101100010110000111011001101011 
                 0111101001:11010011101001111000100110010100 
               
               
                 0111101010:01111001000011010010001100111110 
                 0111101011:10000110111100101101110011000001 
               
               
                 0111101100:00011111011010110100010101011000 
                 0111101101:11100000100101001011101010100111 
               
               
                 0111101110:01001010001111100001000000001101 
                 0111101111:10110101110000011110111111110010 
               
               
                 0111110000:00100011101010000111100110011011 
                 0111110001:11011100010101111000011001100100 
               
               
                 0111110010:01110110111111010010110011001110 
                 0111110011:10001001000000101101001100110001 
               
               
                 0111110100:00010000100110110100101010101000 
                 0111110101:11101111011001001011010101010111 
               
               
                 0111110110:01000101110011100001111111111101 
                 0111110111:10111010001100011110000000000010 
               
               
                 0111111000:00101100101001110111011010010100 
                 0111111001:11010011010110001000100101101011 
               
               
                 0111111010:01111001111100100010001111000001 
                 0111111011:10000110000011011101110000111110 
               
               
                 0111111100:00011111100101000100010110100111 
                 0111111101:11100000011010111011101001011000 
               
               
                 0111111110:01001010110000010001000011110010 
                 0111111111:10110101001111101110111100001101 
               
               
                 1000000000:00011100001101110010111101010001 
                 1000000001:11100011110010001101000010101110 
               
               
                 1000000010:01001001011000100111101000000100 
                 1000000011:10110110100111011000010111111011 
               
               
                 1000000100:00101111000001000001110001100010 
                 1000000101:11010000111110111110001110011101 
               
               
                 1000000110:01111010010100010100100100110111 
                 1000000111:10000101101011101011011011001000 
               
               
                 1000001000:00010011001110000010000001011110 
                 1000001001:11101100110001111101111110100001 
               
               
                 1000001010:01000110011011010111010100001011 
                 1000001011:10111001100100101000101011110100 
               
               
                 1000001100:00100000000010110001001101101101 
                 1000001101:11011111111101001110110010010010 
               
               
                 1000001110:01110101010111100100011000111000 
                 1000001111:10001010101000011011100111000111 
               
               
                 1000010000:00011100110010000010111110101110 
                 1000010001:11100011001101111101000001010001 
               
               
                 1000010010:01001001100111010111101011111011 
                 1000010011:10110110011000101000010100000100 
               
               
                 1000010100:00101111111110110001110010011101 
                 1000010101:11010000000001001110001101100010 
               
               
                 1000010110:01111010101011100100100111001000 
                 1000010111:10000101010100011011011000110111 
               
               
                 1000011000:00010011110001110010000010100001 
                 1000011001:11101100001110001101111101011110 
               
               
                 1000011010:01000110100100100111010111110100 
                 1000011011:10111001011011011000101000001011 
               
               
                 1000011100:00100000111101000001001110010010 
                 1000011101:11011111000010111110110001101101 
               
               
                 1000011110:01110101101000010100011011000111 
                 1000011111:10001010010111101011100100111000 
               
               
                 1000100000:00011100001101111101000010101110 
                 1000100001:11100011110010000010111101010001 
               
               
                 1000100010:01001001011000101000010111111011 
                 1000100011:10110110100111010111101000000100 
               
               
                 1000100100:00101111000001001110001110011101 
                 1000100101:11010000111110110001110001100010 
               
               
                 1000100110:01111010010100011011011011001000 
                 1000100111:10000101101011100100100100110111 
               
               
                 1000101000:00010011001110001101111110100001 
                 1000101001:11101100110001110010000001011110 
               
               
                 1000101010:01000110011011011000101011110100 
                 1000101011:10111001100100100111010100001011 
               
               
                 1000101100:00100000000010111110110010010010 
                 1000101101:11011111111101000001001101101101 
               
               
                 1000101110:01110101010111101011100111000111 
                 1000101111:10001010101000010100011000111000 
               
               
                 1000110000:00011100110010001101000001010001 
                 1000110001:11100011001101110010111110101110 
               
               
                 1000110010:01001001100111011000010100000100 
                 1000110011:10110110011000100111101011111011 
               
               
                 1000110100:00101111111110111110001101100010 
                 1000110101:11010000000001000001110010011101 
               
               
                 1000110110:01111010101011101011011000110111 
                 1000110111:10000101010100010100100111001000 
               
               
                 1000111000:00010011110001111101111101011110 
                 1000111001:11101100001110000010000010100001 
               
               
                 1000111010:01000110100100101000101000001011 
                 1000111011:10111001011011010111010111110100 
               
               
                 1000111100:00100000111101001110110001101101 
                 1000111101:11011111000010110001001110010010 
               
               
                 1000111110:01110101101000011011100100111000 
                 1000111111:10001010010111100100011011000111 
               
               
                 1001000000:00110100010101001101111100100110 
                 1001000001:11001011101010110010000011011001 
               
               
                 1001000010:01100001000000011000101001110011 
                 1001000011:10011110111111100111010110001100 
               
               
                 1001000100:00000111011001111110110000010101 
                 1001000101:11111000100110000001001111101010 
               
               
                 1001000110:01010010001100101011100101000000 
                 1001000111:10101101110011010100011010111111 
               
               
                 1001001000:00111011010110111101000000101001 
                 1001001001:11000100101001000010111111010110 
               
               
                 1001001010:01101110000011101000010101111100 
                 1001001011:10010001111100010111101010000011 
               
               
                 1001001100:00001000011010001110001100011010 
                 1001001101:11110111100101110001110011100101 
               
               
                 1001001110:01011101001111011011011001001111 
                 1001001111:10100010110000100100100110110000 
               
               
                 1001010000:00110100101010111101111111011001 
                 1001010001:11001011010101000010000000100110 
               
               
                 1001010010:01100001111111101000101010001100 
                 1001010011:10011110000000010111010101110011 
               
               
                 1001010100:00000111100110001110110011101010 
                 1001010101:11111000011001110001001100010101 
               
               
                 1001010110:01010010110011011011100110111111 
                 1001010111:10101101001100100100011001000000 
               
               
                 1001011000:00111011101001001101000011010110 
                 1001011001:11000100010110110010111100101001 
               
               
                 1001011010:01101110111100011000010110000011 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
             
           
               
                 TABLE 1d 
               
               
                   
               
             
             
               
                 1001011011:10010001000011100111101001111100 
                 1001011100:00001000100101111110001111100101 
               
               
                 1001011101:11110111011010000001110000011010 
                 1001011110:01011101110000101011011010110000 
               
               
                 1001011111:10100010001111010100100101001111 
                 1001100000:0110100010101000010000011011001 
               
               
                 1001100001:11001011101010111101111100100110 
                 1001100010:1100001000000010111010110001100 
               
               
                 1001100011:10011110111111101000101001110011 
                 1001100100:00000111011001110001001111101010 
               
               
                 1001100101:1111000100110001110110000010101 
                 1001100110:01010010001100100100011010111111 
               
               
                 1001100111:10101101110011011011100101000000 
                 1001101000:00111011010110110010111111010110 
               
               
                 1001101001:1000100101001001101000000101001 
                 1001101010:01101110000011100111101010000011 
               
               
                 1001101011:10010001111100011000010101111100 
                 1001101100:0001000011010000001110011100101 
               
               
                 1001101101:11110111100101111110001100011010 
                 1001101110:01011101001111010100100110110000 
               
               
                 1001101111:10100010110000101011011001001111 
                 1001110000:0110100101010110010000000100110 
               
               
                 1001110001:11001011010101001101111111011001 
                 1001110010:01100001111111100111010101110011 
               
               
                 1001110011:10011110000000011000101010001100 
                 1001110100:0000111100110000001001100010101 
               
               
                 1001110101:11111000011001111110110011101010 
                 1001110110:1010010110011010100011001000000 
               
               
                 1001110111:10101101001100101011100110111111 
                 1001111000:00111011101001000010111100101001 
               
               
                 1001111001:11000100010110111101000011010110 
                 1001111010:01101110111100010111101001111100 
               
               
                 1001111011:0010001000011101000010110000011 
                 1001111100:00001000100101110001110000011010 
               
               
                 1001111101:11110111011010001110001111100101 
                 1001111110:01011101110000100100100101001111 
               
               
                 1001111111:10100010001111011011011010110000 
                 1010000000:00011101111110100100001010010110 
               
               
                 1010000001:1100010000001011011110101101001 
                 1010000010:01001000101011110001011111000011 
               
               
                 1010000011:0110111010100001110100000111100 
                 1010000100:0101110110010010111000110100101 
               
               
                 1010000101:1010001001101101000111001011010 
                 1010000110:01111011100111000010010011110000 
               
               
                 1010000111:10000100011000111101101100001111 
                 1010001000:0010010111101010100110110011001 
               
               
                 1010001001:1101101000010101011001001100110 
                 1010001010:1000111101000000001100011001100 
               
               
                 1010001011:10111000010111111110011100110011 
                 1010001100:00100001110001100111111010101010 
               
               
                 1010001101:1011110001110011000000101010101 
                 1010001110:01110100100100110010101111111111 
               
               
                 1010001111:0001011011011001101010000000000 
                 1010010000:0011101000001010100001001101001 
               
               
                 1010010001:11100010111110101011110110010110 
                 1010010010:1001000010100000001011100111100 
               
               
                 1010010011:10110111101011111110100011000011 
                 1010010100:0101110001101100111000101011010 
               
               
                 1010010101:1010001110010011000111010100101 
                 1010010110:01111011011000110010010000001111 
               
               
                 1010010111:10000100100111001101101111110000 
                 1010011000:0010010000010100100110101100110 
               
               
                 1010011001:11101101111101011011001010011001 
                 1010011010:01000111010111110001100000110011 
               
               
                 1010011011:10111000101000001110011111001100 
                 1010011100:00100001001110010111111001010101 
               
               
                 1010011101:1011110110001101000000110101010 
                 1010011110:01110100011011000010101100000000 
               
               
                 1010011111:10001011100100111101010011111111 
                 1010100000:00011101111110101011110101101001 
               
               
                 1010100001:1100010000001010100001010010110 
                 1010100010:01001000101011111110100000111100 
               
               
                 1010100011:0110111010100000001011111000011 
                 1010100100:0101110110010011000111001011010 
               
               
                 1010100101:1010001001101100111000110100101 
                 1010100110:01111011100111001101101100001111 
               
               
                 1010100111:0000100011000110010010011110000 
                 1010101000:0010010111101011011001001100110 
               
               
                 1010101001:1101101000010100100110110011001 
                 1010101010:01000111101000001110011100110011 
               
               
                 1010101011:0111000010111110001100011001100 
                 1010101100:0100001110001101000000101010101 
               
               
                 1010101101:11011110001110010111111010101010 
                 1010101110:1110100100100111101010000000000 
               
               
                 1010101111:10001011011011000010101111111111 
                 1010110000:00011101000001011011110110010110 
               
               
                 1010110001:1100010111110100100001001101001 
                 1010110010:1001000010100001110100011000011 
               
               
                 1010110011:10110111101011110001011100111100 
                 1010110100:0101110001101101000111010100101 
               
               
                 1010110101:1010001110010010111000101011010 
                 1010110110:01111011011000111101101111110000 
               
               
                 1010110111:0000100100111000010010000001111 
                 1010111000:0010010000010101011001010011001 
               
               
                 1010111001:11101101111101010100110101100110 
                 1010111010:01000111010111111110011111001100 
               
               
                 1010111011:0111000101000000001100000110011 
                 1010111100:0100001001110011000000110101010 
               
               
                 1010111101:11011110110001100111111001010101 
                 1010111110:01110100011011001101010011111111 
               
               
                 1010111111:0001011100100110010101100000000 
                 1011000000:00110101100110011011001011100001 
               
               
                 1011000001:1001010011001100100110100011110 
                 1011000010:01100000110011001110011110110100 
               
               
                 1011000011:0011111001100110001100001001011 
                 1011000100:0000110101010101000000111010010 
               
               
                 1011000101:11111001010101010111111000101101 
                 1011000110:01010011111111111101010010000111 
               
               
                 1011000111:0101100000000000010101101111000 
                 1011001000:00111010100101101011110111101110 
               
               
                 1011001001:1000101011010010100001000010001 
                 1011001010:01101111110000111110100010111011 
               
               
                 1011001011:0010000001111000001011101000100 
                 1011001100:00001001101001011000111011011101 
               
               
                 1011001101:1110110010110100111000100100010 
                 1011001110:01011100111100001101101110001000 
               
               
                 1011001111:10100011000011110010010001110111 
                 1011010000:00110101011001101011001000011110 
               
               
                 1011010001:1001010100110010100110111100001 
                 1011010010:01100000001100111110011101001011 
               
               
                 1011010011:10011111110011000001100010110100 
                 1011010100:0000110010101011000000100101101 
               
               
                 1011010101:11111001101010100111111011010010 
                 1011010110:1010011000000001101010001111000 
               
               
                 1011010111:10101100111111110010101110000111 
                 1011011000:00111010011010011011110100010001 
               
               
                 1011011001:1000101100101100100001011101110 
                 1011011010:01101111001111001110100001000100 
               
               
                 1011011011:10010000110000110001011110111011 
                 1011011100:0001001010110101000111000100010 
               
               
                 1011011101:11110110101001010111000111011101 
                 1011011110:01011100000011111101101101110111 
               
               
                 1011011111:10100011111100000010010010001000 
                 1011100000:00110101100110010100110100011110 
               
               
                 1011100001:11001010011001101011001011100001 
                 1011100010:01100000110011000001100001001011 
               
               
                 1011100011:10011111001100111110011110110100 
                 1011100100:00000110101010100111111000101101 
               
               
                 1011100101:11111001010101011000000111010010 
                 1011100110:01010011111111110010101101111000 
               
               
                 1011100111:10101100000000001101010010000111 
                 1011101000:00111010100101100100001000010001 
               
               
                 1011101001:11000101011010011011110111101110 
                 1011101010:01101111110000110001011101000100 
               
               
                 1011101011:10010000001111001110100010111011 
                 1011101100:00001001101001010111000100100010 
               
               
                 1011101101:11110110010110101000111011011101 
                 1011101110:01011100111100000010010001110111 
               
               
                 1011101111:10100011000011111101101110001000 
                 1011110000:00110101011001100100110111100001 
               
               
                 1011110001:11001010100110011011001000011110 
                 1011110010:01100000001100110001100010110100 
               
               
                 1011110011:10011111110011001110011101001011 
                 1011110100:00000110010101010111111011010010 
               
               
                 1011110101:11111001101010101000000100101101 
                 1011110110:01010011000000000010101110000111 
               
               
                 1011110111:10101100111111111101010001111000 
                 1011111000:00111010011010010100001011101110 
               
               
                 1011111001:11000101100101101011110100010001 
                 1011111010:01101111001111000001011110111011 
               
               
                 1011111011:10010000110000111110100001000100 
                 1011111100:00001001010110100111000111011101 
               
               
                 1011111101:11110110101001011000111000100010 
                 1011111110:01011100000011110010010010001000 
               
               
                 1011111111:10100011111100001101101101110111 
                 1100000000:00010110110011100011010001111010 
               
               
                 1100000001:11101001001100011100101110000101 
                 1100000010:01000011100110110110000100101111 
               
               
                 1100000011:10111100011001001001111011010000 
                 1100000100:00100101111111010000011101001001 
               
               
                 1100000101:11011010000000101111100010110110 
                 1100000110:01110000101010000101001000011100 
               
               
                 1100000111:10001111010101111010110111100011 
                 1100001000:00011001110000010011101101110101 
               
               
                 1100001001:11100110001111101100010010001010 
                 1100001010:01001100100101000110111000100000 
               
               
                 1100001011:10110011011010111001000111011111 
                 1100001100:00101010111100100000100001000110 
               
               
                 1100001101:11010101000011011111011110111001 
                 1100001110:01111111101001110101110100010011 
               
               
                 1100001111:10000000010110001010001011101100 
                 1100010000:00010110001100010011010010000101 
               
               
                 1100010001:11101001110011101100101101111010 
                 1100010010:01000011011001000110000111010000 
               
               
                 1100010011:10111100100110111001111000101111 
                 1100010100:0100101000000100000011110110110 
               
               
                 1100010101:11011010111111011111100001001001 
                 1100010110:01110000010101110101001011100011 
               
               
                 1100010111:10001111101010001010110100011100 
                 1100011000:00011001001111100011101110001010 
               
               
                 1100011001:11100110110000011100010001110101 
                 1100011010:01001100011010110110111011011111 
               
               
                 1100011011:10110011100101001001000100100000 
                 1100011100:0101010000011010000100010111001 
               
               
                 1100011101:11010101111100101111011101000110 
                 1100011110:01111111010110000101110111101100 
               
               
                 1100011111:10000000101001111010001000010011 
                 1100100000:00010110110011101100101110000101 
               
               
                 1100100001:11101001001100010011010001111010 
                 1100100010:01000011100110111001111011010000 
               
               
                 1100100011:10111100011001000110000100101111 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
             
           
               
                 TABLE 1e 
               
               
                   
               
             
             
               
                 1100100100:00100101111111011111100010110110 
                 1100100101:11011010000000100000011101001001 
               
               
                 1100100110:01110000101010001010110111100011 
                 1100100111:10001111010101110101001000011100 
               
               
                 1100101000:00011001110000011100010010001010 
                 1100101001:11100110001111100011101101110101 
               
               
                 1100101010:01001100100101001001000111011111 
                 1100101011:10110011011010110110111000100000 
               
               
                 1100101100:00101010111100101111011110111001 
                 1100101101:11010101000011010000100001000110 
               
               
                 1100101110:01111111101001111010001011101100 
                 1100101111:10000000010110000101110100010011 
               
               
                 1100110000:00111100011000111001101101111010 
                 1100110001:11101001110011100011010010000101 
               
               
                 1100110010:01000011011001001001111000101111 
                 1100110011:10111100100110110110000111010000 
               
               
                 1100110100:00100101000000101111100001001001 
                 1100110101:11011010111111010000011110110110 
               
               
                 1100110110:011100000010101111010110100011100 
                 1100110111:10001111101010000101001011100011 
               
               
                 1100111000:00011001001111101100010001110101 
                 1100111001:11100110110000010011101110001010 
               
               
                 1100111010:01001100011010111001000100100000 
                 1100111011:10110011100101000110111011011111 
               
               
                 1100111100:00101010000011011111011101000110 
                 1100111101:11010101111100100000100010111001 
               
               
                 1100111110:01111111010110001010001000010011 
                 1100111111:10000000101001110101110111101100 
               
               
                 1101000000:00111110101011011100010000001101 
                 1101000001:11000001010100100011101111110010 
               
               
                 1101000010:01101011111110001001000101011000 
                 1101000011:10010100000001110110111010100111 
               
               
                 1101000100:00001101100111101111011100111110 
                 1101000101:11110010011000010000100011000001 
               
               
                 1101000110:01011000110010111010001001101011 
                 1101000111:10100111001101000101110110010100 
               
               
                 1101001000:00110001101000101100101100000010 
                 1101001001:11001110010111010011010011111101 
               
               
                 1101001010:01101100111101111001111001010111 
                 1101001011:10011011000010000110000110101000 
               
               
                 1101001100:00000010100100011111100000110001 
                 1101001101:11111101011011100000011111001110 
               
               
                 1101001110:01010111110001001010110101100100 
                 1101001111:10101000001110110101001010011011 
               
               
                 1101010000:00111110010100101100010011110010 
                 1101010001:11000001101011010011101100001101 
               
               
                 1101010010:01101011000001111001000110100111 
                 1101010011:10010100111110000110111001011000 
               
               
                 1101010100:00001101011000011111011111000001 
                 1101010101:11110010100111100000100000111110 
               
               
                 1101010110:01011000001101001010001010010100 
                 1101010111:10100111110010110101110101101011 
               
               
                 1101011000:00110001010111011100101111111101 
                 1101011001:11001110101000100011010000000010 
               
               
                 1101011010:01100100000010001001111010101000 
                 1101011011:10011011111101110110000101010111 
               
               
                 1101011100:00000010011011101111100011001110 
                 1101011101:11111101100100010000011100110001 
               
               
                 1101011110:01010111001110111010110110011011 
                 1101011111:10101000110001000101001001100100 
               
               
                 1101100000:00111110101011010011101111110010 
                 1101100001:11000001010100101100010000001101 
               
               
                 1101100010:01101011111110000110111010100111 
                 1101100011:10010100000001111001000101011000 
               
               
                 1101100100:00001101100111100000100011000001 
                 1101100101:11110010011000011111011100111110 
               
               
                 1101100110:01011000110010110101110110010100 
                 1101100111:10100111001101001010001001101011 
               
               
                 1101101000:00110001101000100011010011111101 
                 1101101001:11001110010111011100101100000010 
               
               
                 1101101010:01100100111101110110000110101000 
                 1101101011:10011011000010001001111001010111 
               
               
                 1101101100:00000010100100010000011111001110 
                 1101101101:111111010110111011111000000110001 
               
               
                 1101101110:01010111110001000101001010011011 
                 1101101111:10101000001110111010110101100100 
               
               
                 1101110000:00111110010100100011101100001101 
                 1101110001:11000001101011011100010011110010 
               
               
                 1101110010:01101011000001110110111001011000 
                 1101110011:10010100111110001001000110100111 
               
               
                 1101110100;00001101011000010000100000111110 
                 1101110101:11110010100111101111011111000001 
               
               
                 1101110110:01011000001101000101110101101011 
                 1101110111:10100111110010111010001010010100 
               
               
                 1101111000:00110001010111010011010000000010 
                 1101111001:11001110101000101100101111111101 
               
               
                 1101111010:01100100000010000110000101010111 
                 1101111011:10011011111101111001111010101000 
               
               
                 1101111100:00000010011011100000011100110001 
                 1101111101:11111101100100011111100011001110 
               
               
                 1101111110:01010111001110110101001001100100 
                 1101111111:10101000110001001010110110011011 
               
               
                 1110000000:00010111000000110101100110111101 
                 1110000001:11101000111111001010011001000010 
               
               
                 1110000010:01000010010101100000110011101000 
                 1110000011:10111101101010011111001100010111 
               
               
                 1110000100:00100100001100000110101010001110 
                 1110000101:11011011110011111001010101110001 
               
               
                 1110000110:01110001011001010011111111011011 
                 1110000111:10001110100110101100000000100100 
               
               
                 1110001000:00011000000011000101011010110010 
                 1110001001:11100111111100111010100101001101 
               
               
                 1110001010:01001101010110010000001111100111 
                 1110001011:10110010101001101111110000011000 
               
               
                 1110001100:00101011001111110110010110000001 
                 1110001101:1101010011000000100110100111110 
               
               
                 1110001110:01111110011010100011000011010100 
                 1110001111:10000001100101011100111100101011 
               
               
                 1110010000:0001011111111000101100101000010 
                 1110010001:1110100000000111010011010111101 
               
               
                 1110010010:01000010101010010000110000010111 
                 1110010011:10111101010101101111001111101000 
               
               
                 1110010100:00100100110011110110101001110001 
                 1110010101:11011011001100001001010110001110 
               
               
                 1110010110:01110001100110100011111100100100 
                 1110010111:10001110011001011100000011011011 
               
               
                 1110011000:00011000111100110101011001001101 
                 1110011001:11100111000011001010100110110010 
               
               
                 1110011010:01001101101001100000001100011000 
                 1110011011:10110010010110011111110011100111 
               
               
                 1110011100:00101011110000000110010101111110 
                 1110011101:11010100001111111001101010000001 
               
               
                 1110011110:01111110100101010011000000101011 
                 1110011111:10000001011010101100111111010100 
               
               
                 1110100000:00010111000000111010011001000010 
                 1110100001:11101000111111000101100110111101 
               
               
                 11101000010:1000010010101101111001100010111 
                 1110100011:10111101101010010000110011101000 
               
               
                 1110100100:00100100001100001001010101110001 
                 1110100101:11011011110011110110101010001110 
               
               
                 1110100110:01110001011001011100000000100100 
                 1110100111:10001110100110100011111111011011 
               
               
                 1110101000:00011000000011001010100101001101 
                 1110101001:11100111111100110101011010110010 
               
               
                 1110101010:01001101010110011111110000011000 
                 1110101011:10110010101001100000001111100111 
               
               
                 1110101100:00101011001111111001101001111110 
                 1110101101:11010100110000000110010110000001 
               
               
                 1110101110:01111110011010101100111100101011 
                 1110101111:10000001100101010011000011010100 
               
               
                 1110110000:00010111111111001010011010111101 
                 1110110001:11101000000000110101100101000010 
               
               
                 1110110010:01000010101010011111001111101000 
                 1110110011:10111101010101100000110000010111 
               
               
                 1110110100:00100100110011111001010110001110 
                 1110110101:11011011001100000110101001110001 
               
               
                 1110110110:01110001100110101100000011011011 
                 1110110111:10001110011001010011111100100100 
               
               
                 1110111000:00011000111100111010100110110010 
                 1110111001:11100111000011000101011001001101 
               
               
                 1110111010:01001101101001101111110011100111 
                 1110111011:10110010010110010000001100011000 
               
               
                 1110111100:00101011110000001001101010000001 
                 1110111101:11010100001111110110010101111110 
               
               
                 1110111110:01111110100101011100111111010100 
                 1110111111:10000001011010100011000000101011 
               
               
                 1111000000:00111111011000001010100111001010 
                 1111000001:11000000100111110101011000110101 
               
               
                 1111000010:01101010001101011111110010011111 
                 1111000011:1001010111001010000000110110000 
               
               
                 1111000100:00001100010100111001101011111001 
                 1111000101:11110011101011000110010100000110 
               
               
                 1111000110:01011001000001101100111110101100 
                 1111000111:10100110111110010011000001010011 
               
               
                 1111001000:00110000011011111010011011000101 
                 1111001001:11001111100100000101100100111010 
               
               
                 1111001010:01100101001110101111001110010000 
                 1111001011:10011010110001010000110001101111 
               
               
                 1111001100:00000011010111001001010111110110 
                 1111001101:11111100101000110110101000001001 
               
               
                 1111001110:01010110000010011100000010100011 
                 1111001111:101010011111011000011111101011100 
               
               
                 1111010000:00111111100111111010100100110101 
                 1111010001:11000000011000000101011011001010 
               
               
                 1111010010:01101010110010101111110001100000 
                 1111010011:10010101001101010000001110011111 
               
               
                 1111010100:00001100101011001001101000000110 
                 1111010101:11110011010100110110010111111001 
               
               
                 1111010110:01011001111110011100111101010011 
                 1111010111:10100110000001100011000010101100 
               
               
                 1111011000:00110000100100001010011000111010 
                 1111011001:11001111011011110101100111000101 
               
               
                 1111011010:01100101110001011111001101101111 
                 1111011011:10011010001110100000110010010000 
               
               
                 1111011100:00000011101000111001010100001001 
                 1111011101:11111100010111000110101011110110 
               
               
                 1111011110:010101101111011011000000011100 
                 1111011111:10101001000010010011111110100011 
               
               
                 1111100000:00111111011000000101011000110101 
                 1111100001:11000000100111111010100111001010 
               
               
                 1111100010:01101010001101010000001101100000 
                 1111100011:10010101110010101111110010011111 
               
               
                 1111100100:00001100010100110110010100000110 
                 1111100101:11110011101011001001101011111001 
               
               
                 1111100110:01011001000001100011000001010011 
                 1111100111:10100110111110011100111110101100 
               
               
                 1111101000:00110000011011110101100100111010 
                 1111101001:11001111100100001010011011000101 
               
               
                 1111101010:01100101001110100000110001101111 
                 1111101011:10011010110001011111001110010000 
               
               
                 1111101100:00000011010111000110101000001001 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
             
           
               
                   
                 TABLE 1f 
               
               
                   
                   
               
             
             
               
                   
                 1111101101:11111100101000111001010111110110 
               
               
                   
                 1111101110:01010110000010010011111101011100 
               
               
                   
                 1111101111:10101001111101101100000010100011 
               
               
                   
                 1111110000:00111111100111110101011011001010 
               
               
                   
                 1111110001:11000000011000001010100100110101 
               
               
                   
                 1111110010:01101010110010100000001110011111 
               
               
                   
                 1111110011:10010101001101011111110001100000 
               
               
                   
                 1111110100:00001100101011000110010111111001 
               
               
                   
                 1111110101:11110011010100111001101000000110 
               
               
                   
                 1111110110:01011001111110010011000010101100 
               
               
                   
                 1111110111:10100110000001101100111101010011 
               
               
                   
                 1111111000:00110000100100000101100111000101 
               
               
                   
                 1111111001:11001111011011111010011000111010 
               
               
                   
                 1111111010:01100101110001010000110010010000 
               
               
                   
                 1111111011:10011010001110101111001101101111 
               
               
                   
                 1111111100:00000011101000110110101011110110 
               
               
                   
                 1111111101:11111100010111001001010100001001 
               
               
                   
                 1111111110:01010110111101100011111110100011 
               
               
                   
                 1111111111:10101001000010011100000001011100 
               
               
                   
                   
               
             
          
         
       
     
     The decoding apparatus according to the embodiment of the present invention will be described referring to FIG.  9 . An input signal r(t) is applied to 15 multipliers  902  to  906  and a correlation calculator  920 . The input signal r(t) was encoded with a predetermined Walsh code and a predetermined mask sequence in a transmitter. A mask sequence generator  910  generates all possible 15 mask sequences M 1  to M 15 . The multipliers  902  to  906  multiply the mask sequences received from the mask sequence generator  910  by the input signal r(t). The multiplier  902  multiplies the input signal r(t) by the mask sequence M 1  received from the mask sequence generator  910 . The multiplier  904  multiplies the input signal r(t) by the mask sequence M 2  received from the mask sequence generator  910 . The multiplier  906  multiplies the input signal r(t) by the mask sequence M 15  received from the mask sequence generator  910 . If the transmitter encoded TFCI bits with the predetermined mask sequence, one of the outputs of the multipliers  902  to  906  is free of the mask sequence, which means the mask sequence has no effect on the correlations calculated by one of the correlation calculators. For example, if the transmitter used the mask sequence M 2  for encoding the TFCI bits, the output of the multiplier  904  that multiplies the mask sequence M 2  by the input signal r(t) is free of the mask sequence. The mask sequence-free signal is TFCI bits encoded with the predetermined Walsh code. Correlation calculators  920  to  926  calculate the correlations of the input signal r(t) and the outputs of the multipliers  902  to  906  to 64 bi-orthogonal codes. The 64 bi-orthogonal codes have been defined before. The correlation calculator  920  calculates the correlation values of the input signal r(t) to the 64 bi-orthogonal codes of length 32, selects the maximum correlation value from the 64 correlations, and outputs the selected correlation value, a bi-orthogonal code index corresponding to the selected correlation value, and its unique index “0000” to a correlation comparator  940 . 
     The correlation calculator  922  calculates the correlation values of the output of the multiplier  902  to the 64 bi-orthogonal codes, selects the maximum value of the 64 correlations, and outputs the selected correlation value, a bi-orthogonal code index corresponding to the selected correlation, and its unique index “0001” to the correlation comparator  940 . The correlation calculator  924  calculates the correlation values of the output of the multiplier  904  to the 64 bi-orthogonal codes, selects the maximum of the 64 correlation values, and outputs the selected correlation value, a bi-orthogonal code index corresponding to the selected correlation value, and its unique index “0010” to the correlation comparator  940 . Other correlation calculators(not shown) calculate the correlation values of the outputs of the correspondent multipliers to the 64 bi-orthogonal codes and operate similar to the above described correlation calculators, respectively. 
     Finally, the correlation calculator  926  calculates the correlation values of the output of the multiplier  906  to the 64 bi-orthogonal codes, selects the maximum value of the 64 correlations, and outputs the selected correlation value, a bi-orthogonal code index corresponding to the selected correlation value, and its unique index “1111” to the correlation comparator  940 . 
     The unique indexes of the correlation calculators  920  to  926  are the same as the indexes of the mask sequences multiplied by the input signal r(t) in the multipliers  902  to  906 . Table 2 lists the 15 mask indexes multiplied in the multipliers and a mask index assigned to the case that no mask sequence is used, by way of example. 
     
       
         
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 mask sequence 
                   
                 mask sequence 
               
               
                   
                 mask sequence 
                 index 
                 mask sequence 
                 index 
               
               
                   
                   
               
             
             
               
                   
                 not used 
                 0000 
                 M8 
                 1000 
               
               
                   
                 M1 
                 0001 
                 M9 
                 1001 
               
               
                   
                 M2 
                 0010 
                 M10 
                 1010 
               
               
                   
                 M3 
                 0011 
                 M11 
                 1011 
               
               
                   
                 M4 
                 0101 
                 M12 
                 1100 
               
               
                   
                 M5 
                 0101 
                 M13 
                 1101 
               
               
                   
                 M6 
                 0110 
                 M14 
                 1110 
               
               
                   
                 M7 
                 0111 
                 M15 
                 1111 
               
               
                   
                   
               
             
          
         
       
     
     As shown in Table 2, the correlation calculator  922 , which receives the signal which is the product of the input signal r(t) and the mask sequence M 1 , outputs “0001” as its index. The correlation calculator  926 , which receives the signal which is the product of the input signal r(t) and the mask sequence M 15 , outputs “1111” as its index. The correlation calculator  920 , which receives only the input signal r(t), outputs “0000” as its index. 
     Meanwhile, the bi-orthogonal code indexes are expressed in a binary code. For example, if the correlation to {overscore (W 4 )} which is the complement of W 4  is the largest correlation value, a corresponding bi-orthogonal code index (a 0  to a 9 ) is “001001”. 
     The correlation comparator  940  compares the 16 maximum correlation values received from the correlation calculators  920  to  926 , selects the highest correlation value from the 16 received maximum correlation values, and outputs TFCI bits based on the bi-orthogonal code index and the mask sequence index(the unique index) received from the correlation calculator that corresponds to the highest correlation value. The TFCI bits can be determined by combining the bi-orthogonal code index and the mask sequence index. For example, if the mask sequence index is that of M 4 (0100) and the bi-orthogonal code index is that of {overscore (W 4 )} (001001), the TFCI bits(a 9  to a 0 ) are “the M 4  index(0100)+the {overscore (W 4 )} index(001001)”. That is, the TFCI bits(a 9  to a 0 ) are “0100001001” 
     Assuming that the transmitter transmitted code symbols corresponding to TFCI bits (a 0  to a 9 ) “1011000010”, it can be said that the transmitter encoded the TFCI bits with {overscore (W 6 )} and M 4  according to the afore-described encoding procedure. The receiver can determine that the input signal r(t) is encoded with the mask sequence M 4  by multiplying the input signal r(t) by all the mask sequences and that the input signal r(t) is encoded with {overscore (W 6 )} by calculating the correlations of the input signal r(t) to all the bi-orthogonal codes. Based on the above example, the fifth correlation calculator(not shown) will output the largest correlation value, the index of {overscore (W 6 )} (101100) and its unique index(0010). Then, the receiver outputs the decoded TFCI bits(a 0  to a 9 ) “1011000010” by adding the index of {overscore (W 6 )} “101100” and the M 4  index “0010”. 
     In the embodiment of the decoding apparatus, the input signal r(t) is processed in parallel according to the number of mask sequences. It can be further contemplated that the input signal r(t) is sequentially multiplied by the mask sequences and the correlations of the products are sequentially calculated in another embodiment of the decoding apparatus. 
       FIG. 17  illustrates another embodiment of the decoding apparatus. 
     Referring to  FIG. 17 , a memory  1720  stores an input 32-symbol signal r(t). A mask sequence generator  1710  generates 16 mask sequences that were used in the transmitter and outputs them sequentially. A multiplier  1730  multiplies one of the 16 mask sequences received from the mask sequence generator  1710  by the input signal r(t) received from the memory  1720 . A correlation calculator  1740  calculates the output of the multiplier  1730  to 64 biorthogonal codes bi-orthogonal of length 32 and outputs the maximum correlation value and the index of a biorthogonal code corresponding to the largest correlation value to a correlation comparator  1750 . The correlation comparator  1750  stores the maximum correlation value and the biorthogonal code index received from the correlation calculator  1740 , and the index of the mask sequence received from the mask sequence generator  1710 . 
     Upon completion of above processing with the mask sequence, the memory  1720  outputs the stored input signal r(t) to the multiplier  1730 . The multiplier  1730  multiplies the input signal r(t) by one of the other mask sequences. The correlation calculator  1740  calculates correlation of the output of the multiplier  1730  to the 64 biorthogonal codes of length 32 and outputs the maximum correlation value and the index of a biorthogonal code corresponding to the maximum correlation value. The correlation comparator  1750  stores the maximum correlation value, the biorthogonal code index corresponding to the maximum correlation value, and the mask sequence index received from the mask sequence generator  1710 . 
     The above procedure is performed on all of the 16 mask sequences generated from the mask sequence generator  1710 . Then, 16 maximum correlation values the indexes of biorthogonal codes corresponding to the maximum correlation value are stored in the correlation comparator  1750 . The correlation comparator  1750  compares the stored 16 correlation values and selects the one with the highest correlation and outputs TFCI bits by combining the indexes of the biorthogonal code and mask sequence index corresponding to the selected maximum correlation value. When the decoding of the TFCI bits is completed, the input signal r(t) is deleted from the memory  1720  and the next input signal r(t+1) is stored. 
     While the correlation comparator  1750  compares the 16 maximum correlation values at one time in the decoding apparatus of  FIG. 17 , real-time correlation value comparison can be contemplated. That is, the first input maximum correlation value is compared with the next input maximum correlation value and the larger of the two correlation values and a mask sequence index and a biorthogonal code index corresponding to the correlation are stored. Then, the thirdly input maximum correlation is compared with the stored correlation and the larger of the two correlations and a mask sequence index and a biorthogonal code index corresponding to the selected correlation are stored. This comparison operation occurs 15 times which is the number of mask sequences generated from the mask sequence generator  1710 . Upon completion of all the operations, the correlation comparator  1710  output the finally stored biorthogonal index(a 0  to a 6 ) and mask sequence index(a 7  to a 9 ) and outputs the added bits as TFCI bits. 
       FIG. 10  is a flowchart illustrating the operation of the correlation comparator  940  shown in FIG.  9 . The correlation comparator  940  stores the sixteen maximum correlation values, selects a highest correlation value out of the 16 maximum correlation values and output TFCI bits based on the indexes of a bi-orthogonal code and a mask sequence corresponding to the selected highest correlation value. The sixteen correlation values are compared, and TFCI bits are outputted based on the indexes of a bi-orthogonal code and a mask sequence corresponding to the highest correlation value. 
     Referring to  FIG. 10 , a maximum correlation index i is set to 1 and the indices of a maximum correlation value, a biorthogonal code, and a mask sequence to be checked are set to 0s in step  1000 . In step  1010 , the correlation comparator  940  receives a 1 st  maximum correlation value, a 1 st  bi-orthogonal code index, and a 1 st  mask sequence index from the correlation calculator  920 . The correlation comparator  940  compares the 1 st  maximum correlation with an the previous maximum correlation value in step  1020 . If the 1 st  maximum correlation is greater than the previous maximum correlation, the procedure goes to step  1030 . If the 1 st  maximum correlation is equal to or smaller than the previous maximum correlation, the procedure goes to step  1040 . In step  1030 , the correlation comparator  940  designates the 1 st  maximum correlation as a final maximum correlation and stores the 1 st  bi-orthogonal code and mask sequence indexes as final bi-orthogonal code and mask sequence indexes. In step  1040 , the correlation comparator  940  compares the index i with the number 16 of the correlation calculators to determine whether all 16 maximum correlations are completely compared. If i is not 16, the index i is increased by 1 in step  1060  and the procedure returns to step  1010 . Then, the above procedure is repeated. 
     In step  1050 , the correlation comparator  940  outputs the indexes of the bi-orthogonal code and the mask sequence that correspond to the final maximum correlation as decoded bits. The bi-orthogonal code index and the mask sequence index corresponding to the decoded bits are those corresponding to the final maximum correlation among the 16 maximum correlation values received from the 16 correlation calculators. 
     3. Second Embodiment of Encoding/Decoding Apparatus and Method 
     The (32, 10) TFCI encoder that outputs a 32-symbol TFCI codeword in view of 16 slots has been described in the first embodiment of the present invention. Recently, the IMT-2000 standard specification dictates having 15 slots in one frame. Therefore, the second embodiment of the present invention is directed to a (30, 10) TFCI encoder that outputs a 30-symbol TFCI codeword in view of 15 slots. Therefore, the second embodiment of the present invention suggests an encoding apparatus and method for outputting 30 code symbols by puncturing two symbols of 32 coded symbols(codeword) as generated from the (32, 10) TFCI encoder. 
     The encoding apparatuses according to the first and second embodiments of the present invention are the same in configuration except that sequences output from a one-bit generator, a basis Walsh code generator, and a basis mask sequence generator. The encoder apparatus outputs coded symbols of length 30 with symbol #0(1 st  symbol) and symbol #16(17 th  symbol) are punctured in the encoding apparatus of the second embodiment. 
     Referring to  FIG. 8 , 10 input information bits a 0  to a 9  are applied to the input of the  840  to  849 . The one-bit generator  800  outputs symbols 1s(length 32) to the multiplier  840 . The multiplier  840  multiplies the input information bit a 0  by each 32 symbol received from the one-bit generator  800 . The basis Walsh code generator  810  simultaneously generates basis Walsh codes W 1 , W 2 , W 4 , W 8 , and W 16  of length 32. The multiplier  841  multiplies the input information bit a 1  by the basis Walsh code W 1  “01010101010101010101010101010101”. The multiplier  842  multiplies the input information bit a 2  by the basis Walsh code W 2  “00110011001100110011001100110011”. The multiplier  843  multiplies the input information bit a 3  by the basis Walsh code W 4  “00001111000011110000111100001111” The multiplier  844  multiplies the input information bit a 4  by the basis Walsh code W 8  “00000000111111110000000011111111”. The multiplier  845  multiplies the input information bit a 5  by the basis Walsh code W 16  “00000000000000001111111111111111”. 
     The basis mask sequence generator  820  simultaneously generates basis mask sequences M 1 , M 2 , M 4 , and M 8  of length 32. The multiplier  846  multiplies the input information bit a 6  by the basis mask sequence M 1  “00101000011000111111000001110111”. The multiplier  847  multiplies the input information bit a 7  by the basis mask sequence M 2  “00000001110011010110110111000111”. The multiplier  848  multiplies the input information bit a 8  by the basis mask sequence M 4  “00001010111110010001101100101011”. The multiplier  849  multiplies the input information bit a 9  by the basis mask sequence M 8  “00011100001101110010111101010001”. The multipliers  840  to  849  function like switches that control the output of or the generation of the bits from the one-bit generator, each of the basis Walsh codes and each of the basis mask sequences. 
     The adder  860  sums the outputs of the multipliers  840  to  849  symbol by symbol and outputs 32 coded symbols (i.e., a TFCI codeword). Out of the 32 coded symbols, two symbols will be punctured at predetermined positions (i.e. the symbol #0(the first symbol) and symbol #16(the 17 th  symbol) of the adder  860  output are punctured). The remaining 30 symbols will become the 30 TFCI symbols. It will be easy to modify the second embodiment of present invention. For example, the one-bit generator  800 , basis Walsh generator  810 , basis mask sequence generator  820  can generate 30 symbols which excludes the #0 and #16 symbols. The adder  860  then adds the output of the one-bit generator  800 , basis Walsh generator  810  and basis mask sequence generator  820  bit by bit and output 30 encoded symbols as TFCI symbols. 
       FIG. 12  is a encoding method for the second embodiment of present invention. The flowchart illustrating the steps of the encoding apparatus according to the second embodiment of the present invention when the number of slots is 15. 
     Referring to  FIG. 12 , 10 input information bits a 0  to a 9  are received and variables sum and j are set to an initial value 0 in step  1200 . In step  1210 , it is determined whether j is 30. If j is not 30 in step  1210 , the jet symbols W 1 ( j ), W 2 ( j ), W 4 ( j ), W 8 ( j ), and W 16 ( j ) of the basis Walsh codes W 1 , W 2 , W 4 , W 8 , and W 16  (each having two punctured bits) and the j th  symbols M 1 ( j ), M 2 ( j ), M 4 ( j ), and M 8 ( j ) of the basis mask sequences M 1 , M 2 , M 4 , and M 8  (each having two punctured bits) are received in step  1220 . Then, the received symbols are multiplied by the input information bits on a symbol basis and the multiplied symbols are summed in step  1230 . In step  1240 , sum indicating the achieved j th  code symbol is output. j is increased by 1 in step  1250  and then the procedure returns to step  1210 . Meanwhile, if j is 30 in step  1210 , the encoding procedure ends. 
     The (30, 10) encoder outputs  1024  codewords equivalent to the codewords of the (32, 10) encoder with symbols #0 and #16 punctured. Therefore, the total number of information can be expressed is  1024 . 
     The output of a (30, 9) encoder is combinations of 32 Walsh codes of length 30 obtained by puncturing symbols #0 and #16 of each of 32 Walsh codes of length 32, 32 bi-orthogonal codes obtained by adding 1 to each symbol of the punctured Walsh codes (by multiplying −1 to each symbol in the case of a real number), and 8 mask sequences obtained by combining any three of the four punctured basis mask sequences. 
     The output of a (30, 8) encoder is combinations of 32 Walsh codes of length 30 obtained by puncturing #0 and #16 symbols from each of 32 Walsh codes having a length 32 symbols, 32 bi-orthogonal codes obtained by adding 1 to each symbol of the punctured Walsh codes (by multiplying −1 to each symbol in the case of a real number), and 4 mask sequences obtained by combining any two of the four punctured basis mask sequences. 
     The output of a (30, 7) encoder is combinations of 32 Walsh codes of length 30 obtained by puncturing #0 and #16 symbols from each of 32 Walsh codes having a length 32 symbols, 32 bi-orthogonal codes obtained by adding 1 to each symbol of the punctured Walsh codes (by multiplying −1 to each symbol in the case of a real number), and one of the four punctured basis mask sequences. 
     All the above encoders for providing an extended TFCI have a minimum distance of 10. 
     The (30, 9), (30, 8), and (30, 7) encoders can be implemented by blocking input and output of at least one of the four basis mask sequences generated from the basis mask sequence generator  820  shown in FIG.  8 . 
     The above encoders flexibly encode TFCI bits according to the number of the TFCI bits and has a maximized minimum distance that determines encoding performance. 
     A decoding apparatus according to the second embodiment of the present invention is the same in configuration and operation as the decoding apparatus of the first embodiment except for different signal lengths of the encoded symbols. That is, after (32, 10) encoding, two symbols out of the 32 encoded symbols are punctured, or basis Walsh codes with two punctured symbols and basis mask sequences with two punctured symbols are used for generating the 30 encoded symbols. Therefore, except for the received signal r(t) which includes a signal of 30 encoded symbols and insertion of dummy signals at the punctured positions, all decoding operations are equal to the description of the first embodiment of present invention. 
     As  FIG. 17 , this second embodiment of decoding also can be implemented by a single multiplier for multiplying the masks with r(t) and a single correlation calculator for calculating correlation values of bi-orthogonal codes. 
     4. Third Embodiment of Encoding/Decoding Apparatus and Method 
     The third embodiment of the present invention provides an encoding apparatus for blocking the output of a one-bit generator in the (30, 7), (30, 8), (30, 9) or (30, 10) (hereinafter we express (30, 7-10))encoder of the second embodiment and generating another mask sequence instead in order to set a minimum distance to 11. The encoders refer to an encoder that outputs a 30-symbol TFCI codeword for the input of 7, 8, 9 or 10 TFCI bits. 
       FIG. 14  is a block diagram of a third embodiment of the encoding apparatus for encoding a TFCI in the IMT 2000 system. In the drawing, a (30, 7-10) encoder is configured to have a minimum distance of  11 . 
     The encoding apparatus of the third embodiment is similar in structure to that of the second embodiment except that a mask sequence generator  1480  for generating a basis mask sequence M 16  and a switch  1470  for switching the mask sequence generator  1480  and a one-bit generator  1400  to a multiplier  1440  are further provided to the encoding apparatus according to the third embodiment of the present invention. 
     The two bit punctured basis mask sequences M 1 , M 2 , M 4 , M 8 , and M 16  as used in  FIG. 14  are
         M 1 =000001011111000010110100111110   M 2 =000110001100110001111010110111   M 4 =010111100111101010000001100111   M 8 =011011001000001111011100001111   M 16 =100100011110011111000101010011       

     Referring to  FIG. 14 , when a (30, 6) encoder is used, the switch  1470  switches the one-bit generator  1400  to the multiplier  1440  and blocks all the basis mask sequences generated from a basis mask sequence generator  1480 . The multiplier  1440  multiplies the symbols from the one-bit generator  1400  with the input information bit a 0 , symbol by symbol. 
     If a (30, 7-10) encoder is used, the switch  1470  switches the mask sequence generator  1480  to the multiplier  1440  and selectively uses four basis mask sequences generated from a basis mask sequence generator  1420 . In this case, 31 mask sequences M 1  to M 31  can be generated by combining 5 basis mask sequences. 
     The structure and operation of outputting code symbols for the input information bits a 0  to a 9  using multipliers  1440  to  1449  are the same as the first and second embodiments. Therefore, their description will be omitted. 
     As stated above, the switch  1470  switches the mask sequence generator  1480  to the multiplier  1440  to use the (30, 7-10) encoder, whereas the switch  1470  switches the one-bit generator  1400  to the multiplier  1440  to use the (30, 6) encoder. 
     For the input of 6 information bits, the (30, 6) encoder outputs a 30-symbol codeword by combining 32 Walsh codes of length 30 with 32 bi-orthogonal codes obtained by inverting the Walsh codes by the use of the one-bit generator  1400 . 
     For the input of 10 information bits, the (30, 10) encoder outputs a 30-symbol codeword by combining 32 Walsh codes of length 30 and 32 mask sequences generated using five basis mask sequences. Here, the five basis mask sequences are M 1 , M 2 , M 4 , M 8 , and M 16 , as stated above and the basis mask sequence M 16  is output from the mask sequence generator  1480  that is added for the encoding apparatus according to the third embodiment of the present invention. Hence,  1024  codewords can be achieved from the (30, 10) encoder. The (30, 9) encoder outputs a 30-symbol codeword by combining 32 Walsh codes and 16 mask sequences, for the input of 9 information bits. The 16 mask sequences are achieved by combining four of five basis mask sequences. The (30, 8) encoder outputs a 30-symbol codeword by combining 32 Walsh codes and 8 mask sequences, for the input of 8 information bits. The 8 mask sequences are obtained by combining three of five basis mask sequences. For the input of 7 information bits, the (30, 7) encoder outputs a 30-symbol codeword by combining 32 Walsh codes of length 30 and four mask sequences. The four mask sequences are obtained by combining two of five basis mask sequences. 
     All the above (30, 7-10) encoders have a minimum distance of 11 to provide extended TFCIs. The (32, 7-10) encoders can be implemented by controlling use of at least one of the five basis mask sequences generated from the basis mask sequence generator  1420  and the mask sequence generator  1480  shown in FIG.  14 . 
       FIG. 16  is a flowchart illustrating a third embodiment of the TFCI encoding procedure in the IMT 2000 system according to the present invention. 
     Referring to  FIG. 16 ,  10  information bits (TFCI bits) a 0  to a 9  are received and variables sum and j are set to initial values 0s in step  1600 . The variable sum indicates a final code symbol output after symbol-basis addition and the variable j indicates the count number of final code symbols output after the symbol-basis addition. It is determined whether j is 30 in step  1610  in view of the length 30 of punctured Walsh codes and mask sequences used for encoding. The purpose of performing step  1610  is to judge whether the input information bits are encoded with respect to the 30 symbols of each Walsh code and the 30 symbols of each mask sequence. 
     If j is not 30 in step  1610 , which implies that encoding is not completed with respect to all the symbols of the Walsh codes and mask sequences, the j th  symbols W 1 ( j ), W 2 ( j ), W 4 ( j ), W 8 ( j ), and W 16 ( j ) of the basis Walsh codes W 1 , W 2 , W 4 , W 8 , and W 16  and the j th  symbols M 1 ( j ), M 2 ( j ), M 4 ( j ), M 8 ( j ), and M 16 ( j ) of the basis mask sequences M 1 , M 2 , M 4 , M 8 , and M 16  are received in step  1620 . In step  1630 , the input information bits are multiplied by the received symbols symbol by symbol and the symbol products are summed. 
     Step  1630  can be expressed as
 
sum= a   0 · M   16 ( j )+ a   1 · W   1 ( j )+ a   2 · W   2 ( j )+ a   3 · W   4 ( j )+ a   4 · W   8 ( j )+ a   5 · W   16 ( j )+ a   6 · M   1 ( j )+ a   7 · M   2 ( j )+ a   8 · M   4 ( j )+ a   9 · M   8 ( j )  (Eq. 10) 
 
     As noted from Eq. 10, an intended code symbol is obtained by multiplying each input information bit by the symbols of a corresponding basis Walsh code or basis mask sequence and summing the products. 
     In step  1640 , sum indicating the achieved j th  code symbol is output. j is increased by 1 in step  1650  and then the procedure returns to step  1610 . Meanwhile, if j is 30 in step  1610 , the encoding procedure ends. 
     Now there will be given a description of the third embodiment of the decoding apparatus referring to FIG.  15 . An input signal r(t) which includes the 30 encoded symbols signal transmitted by a transmitter and two dummy symbols which have been inserted at the positions that have been punctured by the encoder is applied to 31 multipliers  1502  to  1506  and a correlation calculator  1520 . A mask sequence generator  1500  generates all possible 31 mask sequences of length 32 M 1  to M 31 . The multipliers  1502  to  1506  multiply the mask sequences received from the mask sequence generator  1500  by the input signal r(t). If a transmitter encoded TFCI bits with a predetermined mask sequence, one of the outputs of the multipliers  1502  to  1506  is free of the mask sequence, which means the mask sequence has no effect on the following correlation calculator. For example, if the transmitter used the mask sequence M 31  for encoding the TFCI bits, the output of the multiplier  1506  that multiplies the mask sequence M 31  by the input signal r(t) is free of the mask sequence. However, if the transmitter did not use a mask sequence, the input signal r(t) itself applied to a correlation calculator  1520  is a mask sequence-free signal. Each correlation calculators  1520  to  1526  calculates the correlation values of the outputs of the multipliers  1502  to  1506  with 64 bi-orthogonal codes of length 32, determines maximum correlation value among the 64-correlation sets, and outputs the determined maximum correlation values, the indexes of each bi-orthogonal codes corresponding to the determined maximum correlation values, and each index of the mask sequences to a correlation comparator  1540 , respectively. 
     The correlation comparator  1540  compares the 32 maximum correlation values received a from the correlation calculators  1520  to  1526  and determines the largest of the maximum correlation values as a final maximum correlation. Then, the correlation comparator  1540  outputs the decoded TFCI bits transmitted by the transmitter on the basis of the indexes of the bi-orthogonal code and mask sequence corresponding to the final maximum correlation value. As in  FIG. 17 , the third embodiment of present invention can be also implemented by a single multiplier for multiplying the masks with r(t) and a single correlation calculator for calculating correlation values of bi-orthogonal codes. 
     As described above, the present invention provides an apparatus and method for encoding and decoding a basic TFCI and an extended TFCI variably so that hardware is simplified. Another advantage is that support of both basic TFCI and extended TFCI error correcting coding schemes increases service stability. Furthermore, a minimum distance, a factor that determined the performance of an encoding apparatus, is large enough to satisfy the requirement of an IMT 2000 system, thereby ensuing excellent performance. 
     While the invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.