Abstract:
Disclosed is an apparatus and method for generating a QCTC (Quasi-Complementary Turbo Code) considering a characteristic of a turbo code in a packet communication system or a communication system using an ARQ (Automatic Repeat reQuest) scheme by segmenting a length N of the QCTC into a predetermined number of sections, determining SPIDs (Sub-code Packet Identifications) corresponding to the segmented sections, and specifying one of the SPIDs allocated for initial transmission of the sub-code; calculating a number of remaining symbols represented by N-Fs, where N is a length of the QCTC and Fs is a starting symbol position of the sub-code of the QCTC; determining a last symbol position Ls of the sub-code by comparing the number of the remaining symbols with a length of the sub-code; and sequentially transmitting symbols of the sub-code from the starting symbol position Fs to the last symbol position Ls.

Description:
PRIORITY 
   This application claims priority to an application entitled “Apparatus and Method for Generating Codes in a Communication System” filed in the Korean Industrial Property Office on May 8, 2001 and assigned Serial No. 2001-25025, and to an application entitled “Apparatus and Method for Generating Codes in a Communication System” filed in the Korean Industrial Property Office on Jun. 9, 2001 and assigned Serial No. 2001-32299, the contents of both of which are incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates generally to code generation in a data communications system, and in particular, to an apparatus and method for generating complementary turbo codes, considering the characteristics of turbo codes in a packet communications system or a general communications system that employs a retransmission scheme. 
   2. Description of the Related Art 
   In general, an ARQ (Automatic Repeat Request) system using IR (Incremental Redundancy) is classified into an HARQ (Hybrid Automatic Repeat Request) Type II system and an HARQ Type III system. The HARQ Type II system supports a code rate R higher than 1.0 at each transmission, and variably controls an amount of transmission redundancy according to a channel condition. Here, that the code rate R is higher than 1.0 means that the number of codeword symbols is less than the number of information symbols. The HARQ Type II system combines previously received redundancy with currently received redundancy to create a new low code rate codeword, and repeats this process. However, the HARQ Type III system is designed such that a code rate R of a code used at each transmission or retransmission is less than 1.0. This is to make it possible to perform decoding with only the newly received codes when many packets are missing during transmission due to a bad channel condition or detection error. When all of the codes received at code rate R can be independently decoded, the codes are referred to as “self decodable codes” (SDCs). 
   The HARQ Type II or HARQ Type III system using turbo codes uses quasi-complementary turbo codes (QCTCs) in order to maximize performance of code combining.  FIG. 1  illustrates a block diagram of an apparatus for generating QCTCs. The QCTCs are fully described in U.S. Pat. No. 6,877,130, granted on Apr. 5, 2005 to the same assignee herein, the contents of which are hereby incorporated by reference. 
   Referring to  FIG. 1 , an encoder  301  generates coded symbols by encoding input encoder packet. The encoder  301  uses a mother code with R=1/5 or with any other code rate. A mother code is determined by the system in use. A turbo code with R=1/5 is used herein as a mother code by way of example. A demultiplexer (DEMUX)  302  groups the coded symbols received from the encoder  301  into information symbols X ( 303 ), parity symbols Y 0  ( 313 ), parity symbols Y 1  ( 323 ), parity symbols Y 0 ′ ( 333 ), and parity symbols Y 1 ′ ( 343 ), and outputs the five symbol groups to corresponding sub-block interleavers  304 ,  314 ,  324 ,  334  and  344 , respectively. The sub-block interleavers  304 ,  314 ,  324 ,  334  and  344  randomly permute the sequences output from the demultiplexer  302  by sub-block interleaving, and output the permuted symbols. The codeword symbols randomized by the sub-block interleaving are applied to corresponding blocks. The interleaved coded symbols X ( 306 ) output from the first interleaver  304  are applied directly to the input of a sequence (or symbol) concatenator  307 . The interleaved parity symbols Y 0  and Y 1  from the second and third interleavers  314  and  324  are input to a first multiplexer (MUX)  305  and the interleaved coded symbols Y 0 ′ and Y 1 ′ from the fourth and fifth interleavers  334  and  344  are input to a second MUX  315 . The first MUX  305  multiplexes the interleaved parity symbols Y 0  and Y 1  and feeds the output ( 316 ) to the sequence concatenator  307 . The second MUX  315  multiplexes the interleaved parity symbols Y 0 ′ and Y 1 ′ and feeds the output ( 326 ) to the sequence concatenator  307 . That is, the coded symbols received from the encoder  301  are classified into three sub-groups of the interleaved codeword symbols output from the interleaver  304 , and the parity symbols Y 0  and Y 1  rearranged by the first MUX  305 , and the parity symbols Y 0 ′ and Y 1 ′ rearranged by the second MUX  315 . Next, sequence (or symbol) concatenator  307  generates one symbol sequence [A:B:C] by sequentially concatenating a sub-block-interleaved information symbol sequence A, and multiplexed parity symbol sequences B and C. A concatenated sequence (or symbol) repeater  308  performs symbol repetition on the symbols from the sequence concatenator  307  according to a preset rule. A symbol puncturer (or sub-code C ij  generator)  309  generates sub-codes (i.e., QCTCs) by puncturing the symbols from the concatenated sequence repeater  308  according to a preset rule. An operation of the symbol puncturer  309  will be described in detail. A sub-code generating operation by the sub-code generator  309  is disclosed in Korean Patent Application No. 2001-7357, entitled “Apparatus and Method for Generating Codes in a Communication System”, earlier filed by the applicant, the contents of which are incorporated herein by reference. 
   It is assumed that transmission of a sub-code starts at time k, a sub-code transmitted at time (k+h) is expressed as C ij (k+h), and the coded symbols of a mother code with R=1/5 in  FIG. 1  are defined as C m ( 0 ), C m ( 1 ), . . . , C m (N−1). The number, N, of the coded symbols is defined as N=L_INF×5 since the mother code rate is 1/5. Here, L_INF denotes the size of an interleaved sub-block, or the number of information symbols. 
   Step 1: Determining the Length of an Initial Sub-Code 
   For an initial transmission, one C i0  of the first sub-codes C 00 , C 10 , C 20  of available QCTCs is selected according to a given code rate and the length of the selected sub-code C i0  is stored as a variable L_SC. The code rate or length L_SC of the sub-code is predetermined in the system according to channel environment including transmission channel condition and input data rate. The description is made in the context of three QCTCs shown in  FIG. 3  for better understanding of the present invention, but the number of sub-codes is not limited. 
   Step 2: Selecting and Transmitting a Sub-code for Initial Transmission 
   After the length of a sub-code to be transmitted is determined, C m ( 0 ), C m ( 1 ), . . . , C m (L_SC−1) coded symbols are selected among the coded symbols of the mother code. If L_SC exceeds N, C m ( 0 ), C m ( 1 ), . . . , C m (L_SC−1) are transmitted P times and then C m ( 0 ), C m ( 1 ), . . . , C m (q−1) are transmitted. Here, P and q are the quotient and remainder of L_SC/N, respectively, and P and q are calculated by L 13  SC mod N. Then, the variable q is stored for the next transmission for use in detecting the position of the last symbol of the previous transmitted sub-code with respect to the block of interleaved symbols. 
   Step 3: Determining the Starting Position of a Sub-code for the Next Transmission and the Length of the Sub-code 
   For the next transmission, the code rate R_SC of a new sub-code to be transmitted is determined according to channel environment and the length L_SC of the sub-code is determined according to the determined code rate. The length L_SC and the code rate R_SC are in the relation of
 
 L   —   SC=L   —   INF ×(1 /R   —   SC )  (1)
 
An upper layer system transmits the sub-code length L_SC and the sub-code code rate R_SC to the symbol puncturer  309  for each transmission.
 
   Step 4: Selecting and Transmitting a Sub-code for the Next Transmission 
   After the length L_SC of the sub-code to be transmitted is determined, C m (q), C m (q+1), . . . , C m (q+L_SC−1) coded symbols are selected among the coded symbols of the mother code. In other words, as many symbols as the sub-code length are selected from the mother coded symbols starting with the symbol following the last symbol selected for the previous transmission. If q+L_SC exceeds N, N coded symbols starting with C m (q) are selected recursively and transmitted P times and then the remaining q coded symbols are sequentially transmitted. Here, P and q are the quotient and remainder of (q+L 13  SC)/N, respectively and P and q are calculated by (q+L_SC) mod N. Then, the variable q is stored for the next transmission for use in detecting the position of the last symbol of the previous transmitted sub-code with respect to the block of interleaved symbols. After the generated sub-code is transmitted, the procedure returns to Step 3. 
   A sub-code selection method for the QCTCs is illustrated in detail in a lower part of  FIG. 1  by way of example. Referring to  FIG. 1 , a low rate sub-code with a code rate of 1/7 is initially transmitted in Case 1, and a high rate sub-code with a code rate of 4/7 is initially transmitted in Case 2. As seen from the Cases, a codeword having N codeword symbols is repeated P times, and the repeated codeword symbols are sequentially segmented in a proper size according to a length (or code rate) of the sub-code, at each transmission. In real implementation, a buffer is not used to store P codewords, but a single circular buffer is employed to store N codeword symbols, thereby making it possible to enable iterative transmission by continuous feedback. In addition, any reception buffer for storing received codewords and concatenating the stored codewords is available to a receiver as long as it can store N soft metrics. 
   As described above, the sub code C ij  generator corresponding to the last step segments the coded symbols with R=1/5, rearranged according to a specific rule in the preceding steps, in an arbitrary length according to a sub-code code rate Rs=R_SC. 
   Here, if a starting point Fs for the segmentation is ‘0’, segmentation methods according to respective sub-code code rates are illustrated in  FIG. 2 . Referring to  FIGS. 1  and  2 , if a length of the sub-code to be segmented according to a code rate of the corresponding sub-code is given, the QCTC generator (of  FIG. 1 ) segments as many codeword symbols as the corresponding length in the rearranged codeword sequence with R=1/5. Here, the segmentation is divided into two different methods. A first method is to employ a variable starting point Fs. That is, an initially transmitted sub-code starts at Fs=0, and a starting point Fs of a subsequent sub-code is determined as an (Ls+1) th  symbol position from the last symbol position Ls of the preceding sub-code. In other words, all of the sub-codes are segmented such that the rearranged codewords with R=1/5 are continuously concatenated in the repeated sequence. This is defined as a sequential starting point mode (SSPM). A second method is to employ a fixed starting point Fs. That is, an initially transmitted sub-code starts at Fs=0, and the following sub-codes start at a predefined starting point Fs. Therefore, not all of the sub-codes may be sequentially concatenated in the sequence where the rearranged codewords with R=1/5 are repeated, and segmented in the form that the codeword symbols can be overlapped according to the sub-code code rate. This is defined as a fixed starting point mode (FSPM). 
   In application of the QCTCs, the SSPM becomes an optimal scheme in terms of maximizing decoding performance, and can maximize a code combining gain even when considering the IR However, if a code rate of the sub-code is close to 1.0, there is a probability that sub-codes other than the initial sub-code will undesirably become non self-decodable codes (NSDCs). As stated before, it is assumed that both the HARQ Type II and the HAQR Type III are available in the SSPM. If a code rate of all the transmission sub-codes is less than 1.0, the HARQ Type III is employed, whereas if a code rate of a part of the sub-codes is higher than 1.0, the HARQ Type II is employed. 
   That the currently proposed system employs the HARQ Type III in which a code rate of all of the sub-codes is less than 1.0 means that a receiver performs decoding by sequentially code combining all of the received sub-codes. Further, in the SSPM, a redundancy version (RV) is not exchanged between the transmitter and the receiver. This is because it is not necessary to exchange the redundancy version RV between the transmitter and the receiver in the SSPM. 
   However, when some sub-codes are missing in a very poor channel environment, a phenomenon of awaiting the missing sub-codes may occur in order to continuously perform code combining. In this case, therefore, self-decodable codes (SDCs) capable of independently decoding the respective sub-codes are required as in the HARQ Type III where the RV is provided. This means that an independent RV is transmitted at each sub-code transmission. In this context, the proposed scheme is the FSPM. In this case, a conventionally used 2-bit SPID (sub-packet identification) is used together with an RV indicator, and therefore, it is possible to independently transmit 4 kinds of RVs or starting points (Fs) at each sub-code transmission. Meanwhile, the FSPM cannot become an optimal scheme in terms of maximizing decoding performance, since symbol overlapping occurs. Further, the FSPM cannot maximize a code combining gain even when considering the IR. 
   Therefore, in the following description of the present invention, a difference between the SSPM and the FSPM will first be analyzed, and then advantages and disadvantages of the respective schemes will be analyzed. Thereafter, it will be proven that the SSPM is superior to the FSPM. Accordingly, the present invention will provide a method of enabling the FSPM to have the same performance as that of the SSPM. In particular, the present invention will show that the FSPM has a performance degradation problem due to the symbol overlapping and the symbol puncturing, and provide adaptive SPID selection schemes as a solution to the problem. 
   SUMMARY OF THE INVENTION 
   It is, therefore, an object of the present invention to provide an apparatus and method for minimizing symbol overlapping and symbol puncturing among sub-codes, when generating QCTCs in an SSPM or FSPM mode. 
   It is another object of the present invention to provide an SPID selection apparatus and method for minimizing symbol overlapping and symbol puncturing among sub-codes, when a starting point is designated using an SPID in generating QCTCs in an SSPM or FSPM mode. 
   According to a first aspect of the present invention, there is provided a method for transmitting a sub-code determined by a sub-code rate identical to or different from a code rate of a turbo encoder according to a channel environment from a QCTC generated by the turbo encoder receiving an information stream and operating at the code rate. The method comprises segmenting a length N of the QCTC into a predetermined number of sections, determining SPIDs (Sub-code Packet Identifications) corresponding to the segmented sections, and specifying one of the SPIDs allocated for initial transmission of the sub-code; calculating a number of remaining symbols represented by N−Fs, where N is a length of the QCTC and Fs is a starting symbol position of the sub-code of the QCTC; determining a last symbol position Ls of the sub-code by comparing the number of the remaining symbols with a length of the sub-code; and sequentially transmitting symbols of the sub-code from the starting symbol position Fs to the last symbol position Ls. 
   Preferably, an SPID nearest to the last symbol position Ls among the SPIDs except the specified SPID is chosen as a starting symbol position of a retransmission sub-code in order to respond to a retransmission request for the transmitted sub-code. 
   According to a second aspect of the present invention, there is provided a method for transmitting a sub-code determined by a sub-code rate identical to or different from a code rate of a turbo encoder according to a channel environment from a QCTC generated by the turbo encoder receiving an information stream and operating at the code rate. The method comprises calculating a number of remaining symbols represented by N−Fs, where N is a codeword length of the QCTC and Fs is a starting symbol position of the sub-code of the QCTC; determining a last symbol position Ls of the sub-code by comparing the number of the remaining symbols with a length of the sub-code; and sequentially transmitting symbols of the sub-code from the starting symbol position Fs to the last symbol position Ls. 

   
     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: 
       FIG. 1  illustrates a block diagram of a QCTC (Quasi-Complementary Turbo Code) generating apparatus to which the present invention is applied; 
       FIG. 2  illustrates an operation of generating sub-codes using a turbo encoder with a mother code rate R=1/5 by the QCTC generating apparatus of  FIG. 1 ; 
       FIG. 3  illustrates an operation of generating sub-codes in an FSPM (Fixed Starting Point Mode) mode by the QCTC generating apparatus of  FIG. 1 . 
       FIG. 4  illustrates an operation of generating sub-codes in the FSPM mode by the QCTC generating apparatus of  FIG. 1 ; 
       FIG. 5  illustrates a detailed hardware structure of the QCTC generating apparatus of  FIG. 1  for generating sub-codes with R=2/3 using a turbo encoder with a mother code rate R=1/5; 
       FIG. 6  is a diagram for explaining a symbol overlapping phenomenon occurring when the QCTC generating apparatus of  FIG. 1  generates sub-codes in the FSPM mode; 
       FIG. 7  illustrates decoding performances at a receiver when the QCTC generating apparatus of  FIG. 1  operates in an SSPM mode and an FSPM mode; 
       FIG. 8  illustrates an operation of a receiver for decoding sub-codes generated by the QCTC generating apparatus of  FIG. 1  from a point of address generation; 
       FIG. 9  illustrates an operation of the receiver for decoding sub-codes generated by the QCTC generating apparatus of  FIG. 1 ; 
       FIG. 10  illustrates an SPID selection procedure according to a first embodiment of the present invention; 
       FIG. 11  illustrates a procedure for generating sub-codes in the FSPM mode according to a second embodiment of the present invention; 
       FIG. 12  illustrates an SPID selection procedure according to the second embodiment of the present invention; 
       FIG. 13  illustrates a procedure for generating sub-codes in the FSPM mode according to a third embodiment of the present invention; 
       FIG. 14  illustrates an SPID selection procedure according to the third embodiment of the present invention; 
       FIG. 15  illustrates a procedure for generating sub-codes in an SSPM (Sequential Starting Point Mode) mode according to an embodiment of the present invention; 
       FIG. 16  illustrates an SPID selection procedure according to a fourth embodiment of the present invention (modification of second embodiment); and 
       FIG. 17  illustrates an SPID selection procedure according to a fifth embodiment of the present invention (modification of third embodiment). 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Preferred embodiments of the present invention will be described hereinbelow 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. 
   In the following description, the invention will be applied to a QCTC (or sub-code) generating apparatus illustrated in  FIG. 1 , and provides a method for transmitting sub-codewords determined by a sub-code rate identical to or different from a code rate of a turbo encoder according to a channel environment from QCTC codewords generated using the turbo encoder receiving an information stream and having a given code rate. The sub-code generating apparatus, to which embodiments of the present invention are applied, can generate sub-codewords in the SSPM or FSPM as described before. Herein, the embodiments of the present invention will be divided into an operation of generating sub-codes in the SSPM ( FIG. 15 ) and an operation of generating sub-codes in the FSPM in order to solve a problem of the SSPM (see  FIGS. 10 to 14 , and  FIGS. 16 and 17 ). The operation of selecting an SPID and generating sub-codes in the FSPM according to the present invention can be divided into a first embodiment ( FIG. 10 ), a second embodiment ( FIGS. 11 and 12 ), a third embodiment ( FIGS. 13 and 14 ), a fourth embodiment ( FIG. 16 ), and a fifth embodiment ( FIG. 17 ). 
   A. Fixed Starting Point QCTC Analysis 
   Fixed Starting Point Mode (FSPM) 
   Reference will be made to a problem occurring when QCTCs are generated in the FSPM. The FSPM is a transmission scheme for determining 4 available patterns with same sub packet length by fixing initial position of code symbol of respective sub-codes into a 2-bit message transmitting a redundancy version, call an SPID, and then enabling the 4 available sub-codes to become self-decodable codes (SDC). If sub-codes have different sub packet length or code rate then more redundancy patterns are possible with 2 SPID bits. Of course, the number of the SPID bits is not limited. Herein, the SPID bits are assumed to 2 bits by way of example. This scheme, which is originally proposed regardless of the QCTCs, is constructed to uniformly distribute coded symbols with R=1/5 using a random interleaver, provide four starting points, and then determine positions of the respective starting points according to the SPID. Here, a code rate of the sub-codes may have an arbitrary value as illustrated in  FIG. 3 . 
   Referring to  FIG. 3 , a turbo encoder  401  turbo-encodes input information with a length L (L=4a) at a code rate R=1/5, and outputs a codeword with a length N (N=5L=20a). A random interleaver  402  randomly interleaves the codeword (or coded symbols) from the turbo encoder  401 . A sub-code formation part  403  generates sub-codes based on four starting points previously determined from the interleaved codeword from the random interleaver  402 . As illustrated, the starting points are defined as the positions obtained by dividing the codeword with the length N into four equal parts. 
     FIG. 4  illustrates a block diagram of an apparatus for generating sub-codes with R=2/3 in the FSPM scheme with a mother code rate R=1/5. Referring to  FIG. 4 , a turbo encoder  401  turbo-encodes input information with a length L (L=4a) at a code rate R=1/5, and outputs a codeword with a length N (N=5L=20a). A random interleaver  402  randomly interleaves the codeword (or coded symbols) from the turbo encoder  401 . A sub-code formation part  403  generates sub-codes based on four starting points previously determined from the interleaved codeword from the random interleaver  402 . As illustrated, the starting points are defined as the positions obtained by dividing the codeword with the length N into four equal parts, and each sub-code is a codeword with R=2/3 having 6a coded symbols. 
     FIG. 5  illustrates an apparatus for generating sub-codes with R=2/3, having a turbo encoder with a mother code rate R=1/5. Referring to  FIG. 5 , reference numerals  501  to  503  correspond to a turbo encoder. A first constituent encoder (ENC 1 )  502  encodes input information bits X with a length L (=4a), and outputs parity symbols Y 0  (L bits) and Y 0 ′ (L bits). An interleaver (T 1 )  501  interleaves the input information bits according to a preset rule. A second constituent encoder (ENC 2 )  503  encodes the interleaved symbols from the interleaver  501 , and outputs parity symbols Y 1  (L bits) and Y 1 ′ (L bits). A symbol selector (or symbol puncturer)  504  performs puncturing on the input information bits X (L bits) and the parity symbols Y 0  and Y 1 , Y 0 ′ and Y 1 ′ according to a preset rule, and outputs sub-codes with a code rate R=2/3. 
   Decoding in the FSPM 
   The FSPM has the following problems in decoding. First, as shown in  FIG. 3  in SC 00 , there exist missing (i.e., unused) coded symbols when a code rate of the sub-codes is higher than 0.8. Second, as shown in  FIG. 4 , there exist overlapped coded symbols among the sub-codes SC 00 , SC 01  and SC 10 , when a code rate of the sub-codes is less than 0.8. This relation is illustrated in  FIG. 6 . As illustrated, when a code rate of the sub-codes is less than 0.8, there exist many overlapped coded symbols between the sub-code SC 01  and the sub-code SC 10 . 
   For example, if the maximum sub-code rate Rs is 0.8 (=4/5), there exist no missing symbol caused by the first problem. That is, in all cases, there exits no missing symbol. In contrast, if the maximum sub-code rate Rs is very low, there exist many overlapped coded symbols between the sub-codes, and this means that the decoder performs soft symbol combining before decoding. Average energy Es of the coded symbols should be uniform in order to guarantee performance of the turbo decoder (Uniformity Property), and when the Es is not uniform, a periodic pattern in the regular form is required (Periodicity Property). However, an increase in number of the overlapped symbols makes it difficult to guarantee the property of the overlapped symbols, causing deterioration of decoding performance. In other words, the SSPM has more uniform property than the FSPM in terms of the average energy Es. 
     FIG. 7  illustrates a difference between the SSPM (Case A) and the FSPM (Case B) used in the receiver. In  FIG. 7 , codeword repetition or sequence repetition is 2. In Case A, the sequential starting points show such energy (Es) distribution. That is, if the receiver performs soft symbol combining, the average energy Es is doubled. Alternatively, one part is tripled, and another part is doubled. However, in Case B, the fixed starting points do not show such energy distribution, and instead, show that an energy difference between the symbols may vary up to 9 dB. The non-uniform distribution of the symbol energy combined in the receiver has a direct effect on the decoding performance and causes deterioration of average performance. However, in the SSPM, as much Es increment as a sequence repetition factor is uniformly distributed over the whole coded symbols, and only the remaining repeated symbols have energy higher by +3 dB than Es and this energy is also uniformly distributed in the codeword. That is, that the SSPM guarantees optimal performance by the same sequence repetition. This reason will be described with reference to  FIG. 8 . 
   Referring to  FIG. 8 , the receiver uses N buffers (or an N×Q-bit buffer). The buffers may be realized with a circular buffer. Alternatively, a memory space for the buffers may be designed such that a buffer address generator with a fixed size can generate circular addresses. As illustrated in  FIG. 8 , for C00, the receiver stores N symbols beginning at a starting address ADDR 0 , and from that position, stores 6144 (=21504−15360) symbols in the buffer. Since this is a step of storing the symbols after the first N symbols, the receiver soft combines the currently stored symbols with the previously stored symbols in the above-stated manner, and stores the soft-combined symbols. Here, an address where the soft combining is ended is called “ADDR A”. Next, when C10 is received in the same way, the receiver stores received symbols in the buffer while progressing by 10752 symbols from “ADDR A”. Since this is also a step of storing the symbols after the first N symbols, the receiver soft combines the currently stored symbols with the previously stored symbols in the above-stated manner, and stores the soft-combined symbols. Here, an address where the soft combining is ended is called “ADDR B”. Next, when C20 is received in the same way, the receiver stores received symbols in the buffer while progressing by 5376 symbols from “ADDR B”. Here, an address where the soft combining is ended is called “ADDR C”. Next, when C21 is received in the same way, the receiver stores received symbols in the buffer while progressing by 5376 symbols from “ADDR C”. Here, an address where the soft combining is ended is called “ADDR D”. The receiver finally generates soft metrics for a total of N codeword symbols by continuously performing soft combining on the sub-codes transmitted by one encoding packet in the above manner. Also, this method can be regarded as a method of realizing the sub-code generation scheme for the QCTCs in the transmitter. Summarizing, this method is identical to a method of realizing Step 1 of determining the length of an initial sub-code, Step 2 of selecting and transmitting a sub-code for initial transmission, Step 3 of determining the starting position of a sub-code for the next transmission and the length of the sub-code, and Step 4 of selecting and transmitting a sub-code for the next transmission. Therefore, the receiver can perform soft combining while equally mapping the sub-codes to the codewords with R=1/5 according to sub-code type information transmitted by the transmitter in the circular buffering method. Since the received symbols stored in the circular buffer are regularly accumulated, the sequential starting points have the uniformly combined Es as described in conjunction with  FIG. 7 . 
     FIG. 9  illustrates a block diagram of a scheme for performing decoding in the SSPM according to the present invention. As illustrated, it is assumed that the sub-codes transmitted up to now by the transmitter are C00, C10, C20 and C21. That is, C00 represents a transmitted sub-code having 21504 codeword symbols, C10 represents a transmitted sub-code having 10752 codeword symbols, and C20 and C21 represent transmitted sub-codes each having 5376 codeword symbols. Therefore, up to the present, the receiver has received a total of four sub-codes, and all of these were transmitted as sub-codes having different sub-code rates by an encoding packet (3072 bits were used herein for it by way of example), which is one information block. Therefore, the receiver generates soft metrics for the N codewords by soft combining the sub-codes in the above-stated manner. The receiver performs soft combining by rearranging the four sub-codes such that the positions of 15360 (=3072×5) codeword symbols of a codeword with R=1/5 should be identical to the positions of codeword symbols of the respective sub-codes. Since a length, 21504, of the sub-code C00 is larger than N, the receiver arranges 15360 symbols and then sequentially arranges the remaining 6144 (=21504−15360) codeword symbols from the beginning as in the sequence repetition method, and performs soft symbol combining on the arranged codeword symbols. Likewise, since C10 was transmitted following C00, the receiver also stores C10 following the end of C00, and then performs soft symbol combining on them. Likewise, since C20 and C21 were transmitted following the C10, the receiver stores C20 and C21 following the end of C10, and then performs soft symbol combining on the stored sub-codes. 
   B. EMBODIMENTS 
   SSPM Transmission 
     FIG. 15  illustrates a transmission algorithm for the SSPM according to an embodiment of the present invention. In  FIG. 15 , Lsc represents a size of sub-packets, N represents the number of codeword symbols encoded by a turbo encoder with a code rate R, Fs represents a starting symbol position (or starting point) of each sub-packet, and Ls represents a last symbol position (or last point). Further, N RES  represents a variable calculated by a given formula. In the following algorithm, ‘[x]’ represents a maximum integer less than a given value ‘x’. In addition, N CR  represents a repetition frequency of the whole codeword comprised of N symbols. 
   Referring to  FIG. 15 , a sub-code generator resets a starting point Fs to zero (0) for a new encoder packet in step  1501 . If there is a previously transmitted sub-code, the sub-code generator uses Ls determined from a previously transmitted sub-packet as Fs. Thereafter, in step  1503 , the sub-code generator calculates the number N RES  of the remaining symbols by subtracting the determined starting point Fs from the number N of the codeword symbols. The sub-code generator determines in step  1505  whether the calculated number N RES  of the remaining symbols is greater than or equal to a length Lsc of a current transmission sub-code (or sub-packet). If the number N RES  of the remaining symbols is larger than or equal to the length Lsc of the sub-code, the sub-code generator updates a last point Ls of the sub-code to ‘Fs+Lsc−1’ in step  1507 . Thereafter, in step  1509 , the sub-code generator sequentially transmits coded symbols from the determined starting point Fs to the determined last point Ls. However, if the number N RES  of the remaining symbols is less than the length Lsc of the sub-code, the sub-code generator determines the last point Ls of the sub-code as follows in steps  1511  and  1513  as shown by equations (2) and (3).
 
 N   CR =[( Lsc−N   RES )/ N]   (2)
 
 Ls= ( Lsc−N   RES )− N×N   CR −1  (3)
 
   After the step  1507  or  1513 , the sub-code generator sequentially transmits symbols from the starting point Fs to the (N−1) th  symbol point in step  1509 . Next, the sub-code generator repeats all of the N symbols as many times as N CR  for transmission. Lastly, the sub-code generator transmits symbols from the 0 th  symbol position to the Ls th  symbol position, and then proceeds to step  1515 . After transmitting the symbols corresponding to the sub-code, the sub-code generator updates the starting point Fs to ‘(Ls+1) mod N’ in step  1515 . The sub-code generator determines in step  1517  whether a next sub-packet (or retransmission) is requested. If transmission of the next sub-packet is requested, the sub-code generator returns to step  1503  and repeats the above steps. Otherwise, the sub-code generator returns to step  1501 . 
   As stated above, the disadvantage of the FSPM lies in that there exist many overlapped symbols, and the overlapped symbols cause performance degradation of the decoder. Accordingly, there is a demand for a method of minimizing the number of the overlapped symbols. 
   First Embodiment of FSPM Transmission 
   In the FSPM, SPIDs must be transmitted either sequentially or in a predetermined order. This is to improve error detection capability of preamble and decrease a false alarm rate (FAR). That is, the SPIDs must be transmitted sequentially. If the SPIDs are transmitted irregularly, it is not possible to detect an error of the SPIDs without using CRC. Two examples are given below. In Case 2, there is no way to detect an error of the SPIDs, so it should depend on error detection over the whole transmission preamble including the SPIDs. Therefore, if it is assumed that a system using a forward secondary packet data control channel (F-SPDCCH) transmits the SPIDs without using CRC, the SPIDs must be assigned either sequentially or in a predetermined order.
         Case 1) Sequential SPIDs: 0→1→2→3→0→1→2→3→0 . . .   Case 2) Random SPIDs: 0→3→1→2→1→0→3→2→1 . . .       

   In designing Case 1 and Case 2, importance is placed on error detection rather than symbol overlapping problem. 
     FIG. 10  illustrates an SPID selection procedure according to a first embodiment of the present invention. In  FIG. 10 , P represents the number of bits assigned to the SPID, and M represents a maximum integer expressed with P bits. That is, if P=2, then M=4. Further, N represents the number of coded symbols encoded with a mother code. For example, when a code rate is R=1/5 and a length of input information is L=100, the number of coded symbols encoded with the mother code becomes N=L/R=500. In addition, Lsc represents a size of sub-packets, Fs represents a starting symbol position (or starting point) of each sub-packet, and Ls represents a last symbol position (or last point) of each sub-packet. N RES  is a variable calculated by a given formula. In the following algorithm, ‘[x]’ represents a maximum integer less than a value ‘x’. N CR  represents a repetition frequency of the whole codeword comprised of N symbols. This procedure is performed by the sub-code generator in the QCTC generation apparatus of  FIG. 1 . 
   Referring to  FIG. 10 , in step  1001 , the sub-code generator initializes an SPID to zero (0) for a new encoder packet (EP). Further, the sub-code generator initializes the starting point Fs and the last point Ls of the sub-code. The SPID and the starting point Fs are in the relation of 
   
     
       
         
           
             
               
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                 SIPD 
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                       M 
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   In step  1003 , the sub-code generator calculates the number N RES  of the remaining symbols by subtracting the determined starting point Fs from the number N of the codeword symbols. The sub-code generator determines in step  1005  whether the calculated number N RES  of the remaining symbols is greater than or equal to the length Lsc of the current transmission sub-code (or sub-packet). If the number N RES  of the remaining symbols is greater than or equal to the length Lsc of the sub-code, the sub-code generator updates the last point Ls of the sub-code to ‘Fs+Lsc−1’ in step  1007 . In step  1009 , the sub-code generator sequentially transmits coded symbols from the starting point Fs to the determined last point Ls, and then proceeds to step  1015 . In contrast, if the number N RES  of the remaining symbols is less than the length Lsc of the sub-code, the sub-code generator determines the last point Ls of the sub-code as follows and defined again by equations (2) and (3) in steps  1011  and  1013 .
 
 N   CR =[( Lsc−N   RES )/ N]   (2)
 
 Ls =( Lsc−N   RES )− N×N   CR −1  (3)
 
   After the step  1007  or  1013 , the sub-code generator sequentially transmits symbols from the starting point Fs to the (N−1) th  symbol position in step  1009 . Next, the sub-code generator repeats all of the N symbols as many times as N CR  before transmission. Lastly, the sub-code generator transmits symbols from the 0 th  symbol position to the Ls th  symbol position, and then proceeds to step  1015 . After transmitting the symbols corresponding to the sub-code, the sub-code generator chooses the next one of the determined SPIDs as the starting point Fs of the next sub-packet in step  1015 . The sub-code generator determines in step  1017  whether a next sub-packet (or retransmission) is requested. Here, “the next packet is requested” means that retransmission of the current encoder packet (EP) transmitted by the transmitter is requested due to failure to receive the encoder packet. Thus, the SPID should not be reset, and it should be connected to the next SPID. Therefore, if transmission of the next sub-packet is requested, the sub-code generator returns to step  1003  and repeats the above steps. Otherwise, if transmission of the next sub-packet is not requested, it means that the SPID should be reset. In this case, since the currently transmitted EP is successfully received and thus transmission of a new EP is requested, the sub-code generator returns to step  1001 . 
   Second Embodiment of FSPM Transmission 
   If CRC is used in an SPID transmission message (i.e., CRC is used in F-SPDCCH), an error detection function is provided. In this case, therefore, an order of the SPIDs in the FSPM need not be sequential. Alternatively, if the error detection function is not strongly required in the SPID transmission message, an order of the SPIDs in the FSPM need not be sequential. In this case, it is preferable to select the next transmission sub-code according to the following rule in order to reduce the number of overlapped symbols for optimization of decoding performance. This is because for the maximum code rate 0.8 of the sub-code, if a sub-code rate is less than 0.8 due to the SPID that divides the coded symbols with R=1/5 into four equal parts, symbol overlapping inevitably occurs. Therefore, after transmission of one sub-code, an optimal method minimizes the number of punctured symbols, i.e., symbols pruned instead of being transmitted at transmission of two sub-codes. Accordingly, there is a demand for a method of minimizing the number of overlapped symbols. That is, a starting point Fs of the next sub-packet is determined as a value less than or equal to the last point Ls of the previous sub-packet among the SPID nearest to the last point Ls of the previous sub-packet (or sub-code). When the starting point Fs is selected in this manner, the sub-packets are transmitted as illustrated in  FIG. 11 . As illustrated, after transmitting a sub-packet SC 1 , the sub-code generator selects the nearest SPID=11 among the SPIDs (SPID=00, SPID=01, SPID=10) less than or equal to the last point of the sub-packet SC 1 , and then transmits the next sub-packet SC 2  beginning at the starting point. 
     FIG. 12  illustrates an SPID selection procedure according to a second embodiment of the present invention. In  FIG. 12 , P represents the number of bits assigned to the SPID, and M represents a maximum integer expressed with P bits. That is, if P=2, then M=4. Further, N represents the number of coded symbols encoded with a mother code. For example, when a code rate is R=1/5 and a length of input information is L=100, the number of coded symbols encoded with the mother code becomes N=L/R=500. In addition, Lsc represents a size of sub-packets, Fs represents a starting symbol position (or starting point) of each sub-packet, and Ls represents a last symbol position (or last point) of each sub-packet. N RES  is a variable calculated by a given formula. In the following algorithm, ‘[x]’ represents a maximum integer less than a value ‘x’. N CR  represents a repetition frequency of the whole codeword comprised of N symbols. Meanwhile, the last symbol position Ls can be differently determined according to an algorithm in used. For example, it is also possible to use a method of determining the number of symbols according to a given sub-code rate, perform sequence repetition by comparing the determined number with N, and determine the last symbol position Ls by the number of the remaining symbols, as in the above-stated sequential transmission method. 
   Referring to  FIG. 12 , in step  1201 , the sub-code generator initializes an SPID to zero (0) for a new encoder packet (EP). Further, the sub-code generator initializes the starting point Fs and the last point Ls of the sub-code. The SPID and the starting point Fs are in the relation of 
   
     
       
         
           
             
               
                 SIPD 
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                 SIPD 
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                       M 
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                       1 
                     
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   In step  1203 , the sub-code generator calculates the number N RES  of the remaining symbols by subtracting the determined starting point Fs from the number N of the codeword symbols. The sub-code generator determines in step  1205  whether the calculated number N RES  of the remaining symbols is larger than or equal to the length Lsc of the current transmission sub-code (or sub-packet). If the number N RES  of the remaining symbols is larger than or equal to the length Lsc of the sub-code, the sub-code generator updates the last point Ls of the sub-code to ‘Fs+Lsc−1’ in step  1207 . In step  1209 , the sub-code generator sequentially transmits coded symbols from the starting point Fs to the determined last point Ls, and then proceeds to step  1215 . In contrast, if the number N RES  of the remaining symbols is less than the length Lsc of the sub-code, the sub-code generator determines the last point Ls of the sub-code as follows and defined again by equations (2) and (3) in steps  1211  and  1213 .
 
 N   CR =[( Lsc−N   RES )/ N]   (2)
 
 Ls= ( Lsc−N   RES )− N×N   CR −1  (3)
 
   After the step  1207  or  1213 , the sub-code generator sequentially transmits symbols from the starting point Fs to the (N−1) th  symbol position in step  1209 . Next, the sub-code generator repeats all of the N symbols as many times as N CR  before transmission. Lastly, the sub-code generator transmits symbols from the 0 th  symbol position to the Ls th  symbol position, and then proceeds to step  1215 . After transmitting the symbols corresponding to the sub-code, the sub-code generator chooses the starting point Fs from the determined SPIDs in step  1215 . Here, the sub-code generator chooses, as the starting point Fs of the next sub-packet, a value less than or equal to the last point Ls of the previous sub-packet among the SPID nearest to the last point Ls of the previous sub-packet (or sub-code). The sub-code generator determines in step  1217  whether a next sub-packet (or retransmission) is requested. Here, “the next packet is requested” means that retransmission of the current encoder packet (EP) transmitted by the transmitter is requested due to failure to receive the encoder packet. Thus, the SPID should not be reset, and it should be connected to the next SPID. Therefore, if transmission of the next sub-packet is requested, the sub-code generator returns to step  1203  and repeats the above steps. Otherwise, if transmission of the next sub-packet is not requested, it means that the SPID should be actually reset. In this case, since the currently transmitted EP is successfully received and thus transmission of a new EP is requested, the sub-code generator returns to step  1201 . 
   Third Embodiment of FSPM Transmission 
   The invention provides another method for choosing a starting point of the next sub-code as an SPID nearest to the Ls of the previous sub-code after transmitting one sub-code. That is, the nearest one of the SPIDs greater than or equal to the last point Ls of the previous sub-packet is determined as Fs. This method needs symbol puncturing, but limits the maximum number of overlapped symbols to N/8 (=(N/4)/2). Likewise, the number of punctured symbols is also limited to N/8 (=(N/4)/2). Of course, there is trade-off between a gain caused by the reduction in number of the overlapped symbols and a loss caused by the increase in number of the punctured symbols. That is, for the next sub-packet (or sub-code), the sub-code generator chooses the nearest SPID (or Fs) from the last point Ls of the previous sub-packet (or sub-code). When the starting point Fs is selected in this manner, the sub-packets are transmitted as illustrated in  FIG. 13 . As illustrated, after transmitting a sub-packet SC 1 , the sub-code generator selects the nearest SPID=00 from the last point Ls of the sub-packet SC 1 , and then transmits the next sub-packet SC 2  beginning at the starting point. In this case, there exist punctured symbols between the sub-packet SC 1  and the sub-packet SC 2 . 
     FIG. 14  illustrates an SPID selection procedure according to a third embodiment of the present invention. In  FIG. 14 , P represents the number of bits assigned to the SPID, and M represents a maximum integer expressed with P bits. That is, if P=2, then M=4. Further, N represents the number of coded symbols encoded with a mother code. For example, when a code rate is R=1/5 and a length of input information is L=100, the number of coded symbols encoded with the mother code becomes N=L/R=500. In addition, Lsc represents a size of sub-packets, Fs represents a starting symbol position (or starting point) of each sub-packet, and Ls represents a last symbol position (or last point) of each sub-packet. N RES  is a variable calculated by a given formula. In the following algorithm, ‘[x]’ represents a maximum integer less than a value ‘x’. N CR  represents a repetition frequency of the whole codeword comprised of N symbols. Meanwhile, the last symbol position Ls can be differently determined according to an algorithm in used. 
   Referring to  FIG. 14 , in step  1401 , the sub-code generator initializes an SPID to zero (0) for a new encoder packet (EP). Further, the sub-code generator initializes the starting point Fs and the last point Ls of the sub-code. The SPID and the starting point Fs are in the relation of 
   
     
       
         
           
             
               
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                 SIPD 
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   In step  1403 , the sub-code generator calculates the number N RES  of the remaining symbols by subtracting the determined starting point Fs from the number N of the codeword symbols. The sub-code generator determines in step  1405  whether the calculated number N RES  of the remaining symbols is larger than or equal to the length Lsc of the current transmission sub-code (or sub-packet). If the number N RES  of the remaining symbols is larger than or equal to the length Lsc of the sub-code, the sub-code generator updates the last point Ls of the sub-code to ‘Fs+Lsc−1’ in step  1407 . In step  1409 , the sub-code generator sequentially transmits coded symbols from the starting point Fs to the determined last point Ls, and then proceeds to step  1415 . In contrast, if the number N RES  of the remaining symbols is less than the length Lsc of the sub-code, the sub-code generator determines the last point Ls of the sub-code as follows and again in accordance with equations (2) and (3) in steps  1411  and  1413 .
 
 N   CR =[( Lsc−N   RES )/ N]   (2)
 
 Ls =( Lsc−N   RES )− N×N   CR −1  (3)
 
   After the step  1407  or  1413 , the sub-code generator sequentially transmits symbols from the starting point Fs to the (N−1) th  symbol position in step  1409 . Next, the sub-code generator repeats all of the N symbols as many times as N CR  before transmission. Lastly, the sub-code generator transmits symbols from the 0 th  symbol position to the Ls th  symbol position, and then proceeds to step  1415 . After transmitting the symbols corresponding to the sub-code, the sub-code generator chooses the starting point Fs from the determined SPIDs in step  1415 . Here, the sub-code generator chooses, as the starting point Fs of the next sub-packet, a point corresponding to an SPID (or Fs) equal to or nearest to the last point Ls of the previous sub-packet (sub-code). The sub-code generator determines in step  1417  whether a next sub-packet (or retransmission) is requested. Here, “the next packet is requested” means that retransmission of the current encoder packet (EP) transmitted by the transmitter is requested due to failure to receive the encoder packet. Thus, the SPID should not be reset, and it should be connected to the next SPID. Therefore, if transmission of the next sub-packet is requested, the sub-code generator returns to step  1403  and repeats the above steps. Otherwise, if transmission of the next sub-packet is not requested, it means that the SPID should be reset. In this case, since the currently transmitted EP is successfully received and thus transmission of a new EP is requested, the sub-code generator returns to step  1401 . 
   The invention provides another method applied when the second and third embodiments use a specific SPID for initial transmission. In this case, the methods proposed in the second and third embodiments are equally applied, but the specific SPID for initial transmission cannot be used during retransmission. For example, when SPID=0 is previously determined as an SPID for initial transmission, SPIDs available for retransmission are 1, 2, 3, . . . , (M−1)(N/M). Thus, the sub-code generator selects the SPIDs used for retransmission according to the selection algorithm of the second and third embodiments.  FIGS. 16 and 17  illustrate modifications of the second and third embodiments for the case where the SPID=0 is used for initial transmission. Herein, SPID=0 is used for initial transmission by way of example. When necessary, another SPID can be used for initial transmission. 
   Fourth Embodiment of FSPM Transmission 
     FIG. 16  illustrates an SPID selection procedure according to a fourth embodiment of the present invention. In particular,  FIG. 16  illustrates a modification of the SPID selection procedure according to the second embodiment. In  FIG. 16 , P represents the number of bits assigned to the SPID, and M represents a maximum integer expressed with P bits. That is, if P=2, then M=4. Further, N represents the number of coded symbols encoded with a mother code. For example, when a code rate is R=1/5 and a length of input information is L=100, the number of coded symbols encoded with the mother code becomes N=L/R=500. In addition, Lsc represents a size of sub-packets, Fs represents a starting symbol position (or starting point) of each sub-packet, and Ls represents a last symbol position (or last point) of each sub-packet. N RES  is a variable calculated by a given formula. In the following algorithm, ‘[x]’ represents a maximum integer less than a value ‘x’. N CR  represents a repetition frequency of the whole codeword comprised of N symbols. Meanwhile, the last symbol position Ls can be differently determined according to an algorithm in used. For example, it is also possible to use a method of determining the number of symbols according to a given sub-code rate, perform sequence repetition by comparing the determined number with N, and determine the last symbol position Ls by the number of the remaining symbols, as in the above-stated sequential transmission method. 
   Referring to  FIG. 16 , in step  1601 , the sub-code generator initializes an SPID to zero (0) for a new encoder packet (EP). Further, the sub-code generator initializes the starting point Fs and the last point Ls of the sub-code. The SPID and the starting point Fs are in the relation of 
   
     
       
         
           
             
               
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                 SIPD 
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   In step  1603 , the sub-code generator calculates the number N RES  of the remaining symbols by subtracting the determined starting point Fs from the number N of the codeword symbols. The sub-code generator determines in step  1605  whether the calculated number N RES  of the remaining symbols is larger than or equal to the length Lsc of the current transmission sub-code (or sub-packet). If the number N RES  of the remaining symbols is larger than or equal to the length Lsc of the sub-code, the sub-code generator updates the last point Ls of the sub-code to ‘Fs+Lsc−1’ in step  1607 . In step  1609 , the sub-code generator sequentially transmits coded symbols from the starting point Fs to the determined last point Ls, and then proceeds to step  1615 . In contrast, if the number N RES  of the remaining symbols is less than the length Lsc of the sub-code, the sub-code generator determines the last point Ls of the sub-code as follows and in accordance with equations (2) and (3) in steps  1611  and  1613 .
 
 N   CR =[( Lsc−N   RES )/ N]   (2)
 
 Ls =( Lsc−N   RES )− N×N   CR −1  (3)
 
   After the step  1607  or  1613 , the sub-code generator sequentially transmits symbols from the starting point Fs to the (N−1) th  symbol position in step  1609 . Next, the sub-code generator repeats all of the N symbols as many times as N CR  before transmission. Lastly, the sub-code generator transmits symbols from the 0 th  symbol position to the Ls th  symbol position, and then proceeds to step  1615 . After transmitting the symbols corresponding to the sub-code, the sub-code generator chooses the starting point Fs from the determined SPIDs in step  1615 . Here, the sub-code generator chooses, as the starting point Fs of the next sub-packet, a non-zero value out of the values less than or equal to the last point Ls of the previous sub-packet among the SPID nearest to the last point Ls of the previous sub-packet (or sub-code). That is, the sub-code generator excludes the SPID allocated for initial transmission from retransmission. The sub-code generator determines in step  1617  whether a next sub-packet (or retransmission) is requested. Here, “the next packet is requested” means that retransmission of the current encoder packet (EP) transmitted by the transmitter is requested due to failure to receive the encoder packet. Thus, the SPID should not be reset, and it should be connected to the next SPID. Therefore, if transmission of the next sub-packet is requested, the sub-code generator returns to step  1603  and repeats the above steps. Otherwise, if transmission of the next sub-packet is not requested, it means that the SPID should be actually reset. In this case, since the currently transmitted EP is successfully received and thus transmission of a new EP is requested, the sub-code generator returns to step  1601 . 
   Fifth Embodiment of FSPM Transmission 
     FIG. 17  illustrates an SPID selection procedure according to a fifth embodiment of the present invention. In particular,  FIG. 17  illustrates a modification of the SPID selection procedure according to the third embodiment. In  FIG. 17 , P represents the number of bits assigned to the SPID, and M represents a maximum integer expressed with P bits. That is, if P=2, then M=4. Further, N represents the number of coded symbols encoded with a mother code. For example, when a code rate is R=1/5 and a length of input information is L=100, the number of coded symbols encoded with the mother code becomes N=L/R=500. In addition, Lsc represents a size of sub-packets, Fs represents a starting symbol position (or starting point) of each sub-packet, and Ls represents a last symbol position (or last point) of each sub-packet. N RES  is a variable calculated by a given formula. In the following algorithm, ‘[x]’ represents a maximum integer less than a value ‘x’. N CR  represents a repetition frequency of the whole codeword comprised of N symbols. Meanwhile, the last symbol position Ls can be differently determined according to an algorithm in used. For example, it is also possible to use a method of determining the number of symbols according to a given sub-code rate, perform sequence repetition by comparing the determined number with N, and determine the last symbol position Ls by the number of the remaining symbols, as in the above-stated sequential transmission method. 
   Referring to  FIG. 17 , in step  1701 , the sub-code generator initializes an SPID to zero (0) for a new encoder packet (EP). Further, the sub-code generator initializes the starting point Fs and the last point Ls of the sub-code. The SPID and the starting point Fs are in the relation of 
   
     
       
         
           
             
               
                 SIPD 
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               ⋮ 
             
           
           
             
               
                 SIPD 
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                       M 
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   In step  1703 , the sub-code generator calculates the number N RES  of the remaining symbols by subtracting the determined starting point Fs from the number N of the codeword symbols. The sub-code generator determines in step  1705  whether the calculated number N RES  of the remaining symbols is larger than or equal to the length Lsc of the current transmission sub-code (or sub-packet). If the number N RES  of the remaining symbols is larger than or equal to the length Lsc of the sub-code, the sub-code generator updates the last point Ls of the sub-code to ‘Fs+Lsc−1’ in step  1707 . In step  1709 , the sub-code generator sequentially transmits coded symbols from the starting point Fs to the determined last point Ls, and then proceeds to step  1715 . In contrast, if the number N RES  of the remaining symbols is less than the length Lsc of the sub-code, the sub-code generator determines the last point Ls of the sub-code as follows in accordance with equations (2) and (3) in steps  1711  and  1713 .
 
 N   CR =[( Lsc−N   RES )/ N]   (2)
 
 Ls =( Lsc−N   RES )− N×N   CR −1  (3)
 
   After the step  1707  or  1713 , the sub-code generator sequentially transmits symbols from the starting point Fs to the (N−1) th  symbol position in step  1709 . Next, the sub-code generator repeats all of the N symbols as many times as N CR  before transmission. Lastly, the sub-code generator transmits symbols from the 0 th  symbol position to the Ls th  symbol position, and then proceeds to step  1715 . After transmitting the symbols corresponding to the sub-code, the sub-code generator chooses the starting point Fs from the determined SPIDs in step  1715 . Here, the sub-code generator chooses, as the starting point Fs of the next sub-packet, a non-zero point out of the points corresponding to the SPID (or Fs) equal to or nearest to the last point Ls of the previous sub-packet (or sub-code). That is, the sub-code generator excludes the SPID allocated for initial transmission from retransmission. The sub-code generator determines in step  1717  whether a next sub-packet (or retransmission) is requested. Here, “the next packet is requested” means that retransmission of the current encoder packet (EP) transmitted by the transmitter is requested due to failure to receive the encoder packet. Thus, the SPID should not be reset, and it should be connected to the next SPID. Therefore, if transmission of the next sub-packet is requested, the sub-code generator returns to step  1703  and repeats the above steps. Otherwise, if transmission of the next sub-packet is not requested, it means that the SPID should be reset. In this case, since the currently transmitted EP is successfully received and thus transmission of a new EP is requested, the sub-code generator returns to step  1701 . 
   As described above, the present invention minimizes symbol overlapping and symbol puncturing between sub-codes when generating QCTCs in the SSPM or FSPM, thereby improving throughput. 
   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.