Patent Publication Number: US-8542756-B2

Title: Communication method, communication system, transmission device, and receiving device

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a U.S. continuation application filed under 35 USC 111(a) claiming benefit under 35 USC 120 and 365(c) of PCT international application PCT/JP2009/004691, filed Sep. 17, 2009, the disclosure of which is hereby incorporated by reference. 
    
    
     FIELD 
     The embodiment discussed herein is related to a transmission method, a transmission system, a transmission device, and a receiving device. 
     BACKGROUND 
     There has been a known packet communication system in which upon a packet transmitted from a transmission device being not correctly received by a receiving device, the receiving device does not feeds back ACK (reception succeeded) but feeds back NACK (reception failed) to the transmission device, so that the transmission device retransmits the reception-failed packet. For example, International Publication Pamphlet No. WO2003/028314 discloses a technique in which the transmission device transmits plural packets and the receiving device collectively feeds back the ACK/NACK of each of the packets. 
     SUMMARY 
     According to an aspect, a communication method of transmitting plural packets from a first communication device to a second communication device includes associating identification information items with combinations of reception results of the plural packets in the second communication device, a number of the identification information items being less than a number of the plural packets; transmitting, by the first communication device, the plural packets to the second communication device in initial transmission; specifying, by the second communication device, a first of the identification information items based on reception results of the plural packets in initial reception, and transmitting, by the second communication device, the first identification information item to the first communication device; determining, by the first communication device, an encoding method decodable by the second communication device with successfully received packets in the initial reception, encoding, by the first communication device, the plural packets based on the determined encoding method, and retransmitting, by the first communication device, the encoded packets to the second communication device; and decoding, by the second communication device, the encoded packets based on the successfully received packets in the initial reception, and reproducing, by the second communication device, incorrectly received packets in the initial reception. 
     The object and advantage of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention as claimed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a drawing illustrating a wireless communication system according to an embodiment; 
         FIG. 2  is a drawing illustrating a generation of encoded packets according to an embodiment; 
         FIG. 3  is a block diagram illustrating a main part of an internal configuration of a mobile station according to an embodiment; 
         FIG. 4  is a block diagram illustrating a main part of an internal configuration of a base station according to an embodiment; 
         FIG. 5  is a table illustrating corresponding relationships between error patterns and reception indexes; 
         FIG. 6  is a table illustrating corresponding relationships between the reception indexes and encoding methods adapted in the base station; 
         FIG. 7  is a flowchart illustrating transmission of plural packets from the base station to the mobile station; 
         FIG. 8  is a table illustrating encoding matrixes set when the number of transmission packets is eight; 
         FIG. 9  is another table illustrating encoding matrixes set when the number of transmission packets is eight; and 
         FIG. 10  is a table illustrating a result of searching for the number of the encoding methods where feed-back information amount is minimum. 
     
    
    
     DESCRIPTION OF EMBODIMENT 
     In a communication system of the related art, the fed-back information transmitted from the receiving device receiving packets to the transmission device refers to the information of the ACK/NACK (1 bit) for each packet. Therefore, the amount of the information to be fed back to the transmission device refers to the number of bits equal to the number of packets to be transmitted. 
     On the other hand, in a cellular communication system such as LTE (Long Term Evolution) which has been researched by the 3GPP (3rd Generation Partnership Project), in many cases, it may be operated under comparatively higher packet reception error rates due to interference noise and multi-path fading environments; therefore, the retransmission rate of the packets may occur with higher incidence. 
     Further, in the downlink of the cellular communication system, data to be transmitted to many users (mobile stations) may be multiplexed into the same sub frames, and the ACK/NACK information items from many mobiles stations are fed back to the base station. In the communication system, the greater the information amount fed back to the base station, the more radio resources are consumed. Therefore, there is a demand to reduce the feed-back information amount described above. 
     Namely, it may be requested to provide a communication method, a communication system, a transmission device, and a receiving device that may reduce the amount of information to be fed back from the receiving-side transmission device to the transmitting-side communication device. 
     In the following, as a communication system according to an embodiment of the present invention, a wireless communication system including a base station as a first communication device or a transmission device and a mobile station as a second communication device or a receiving device is described. 
     (1) Wireless Communication System in an Embodiment 
       FIG. 1  illustrates a wireless communication system according to an embodiment. As illustrated in  FIG. 1 , the wireless communication system according to this embodiment includes a base station (BS) and a mobile station (MS) in a service area of the wireless base station. In this embodiment, a case is described where plural packets are transmitted from the base station to the mobile station. 
     In this wireless communication system, the packet transmission is performed in a manner such that a predetermined number equal to two or more of packets (i.e., plural packets) are transmitted as a unit of a transmission from the base station to the mobile station. The mobile station determines whether each of the plural packets is received correctly (successfully) (ACK) or fails to be received correctly (incorrectly) (NACK), and feeds back the results to the base station. 
     Here, between the base station and the mobile station, there are provided identification information items which are associated with (assigned to) corresponding combinations of ACK (correctly received or successful reception) and NACK (incorrectly received, or reception failure) results of the plural packets in the mobile station. In the description of this embodiment, the identification information is described as (called) a “reception index”. The mobile station feeds back the reception index corresponding to the reception results of the plural packets to the base station. 
     In this wireless communication system, the base station determines an encoding method decodable by using the packets having been successfully received when the packets are initially received by the second communication device (i.e., the mobile station). Further, based on the determined encoding method, the base station encodes the plural packets to be transmitted (to generate encoded packets). Then, the encoded packets are transmitted to the mobile station. The mobile station reproduces (regenerates) the packets having been incorrectly received in the initial transmission by decoding the encoded packets using correctly received packets in the initial transmission. 
     (2) Generation of Encoded Packets 
     Next, the generation of the encoded packets is described with reference to  FIG. 2 .  FIG. 2  illustrates the generation of the encoded packets in this embodiment. 
     In  FIG. 2 , symbols P 1 , P 2 , . . . , P N  are assumed to be (denote) the plural packets (N packets) in the initial transmission (which refers to the packets that are initially transmitted) from the base station to the mobile station. In the initial transmission, CRC (Cyclic Redundancy Check) codes for error detection are appended to the plural packets and FEC (Forward Error Correction) coding is further performed on the plural packets. 
     After that, the plural packets are transmitted to the mobile station. On the other hand, in the retransmission, the reception index (“R_IDX”) is fed back from the mobile station, and the coding method corresponding to the reception index is selected. 
     Here, in a case where N packets are transmitted and M packets (from among the N packets) have not been correctly received, the encoding method in this case is expressed as in the following formula (1) by using M×N encoding matrix G M,K . Here, the symbol “k” refers to a sequentially assigned number to identify one of the encoding matrixes G M,K  which is relevant to the same number of errors “M” (error number “M”). 
     
       
         
           
             
               
                 
                   
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     In formula (1), symbols P 2 (n), P 2 (n), . . . , and P N (n) denote corresponding nth one bit of N packets P 1 , P 2 , . . . , and P N . Then, the extracted N bits are multiplied by the M×N encoding matrix G M,K  to obtain N bits of R 2 (n), R 2 (n), . . . , and R N (n). By executing this matrix operation on each bit of N packets, M retransmission packets (encoded packets) are generated. 
     In each of the operations in the above formula (1), a “mod-2” operation is performed. 
     (3) Configurations of Base Station and Mobile Station 
     Next, configurations of the base station (transmission device) and the mobile station (receiving device) in the wireless communication system according to this embodiment are described with reference to  FIGS. 3 and 4 . 
       FIG. 3  is a block diagram illustrating a main (relevant) part of an internal configuration of the mobile station, and  FIG. 4  is a block diagram illustrating a main part of an internal configuration of the base station. 
     Configuration of Mobile Station (Receiving Device) 
     As illustrated in  FIG. 3 , the mobile station includes a receiver  31 , a signal separator  32 , an FEC decoder  33 , a packet decoder  34 , an error detector  35 , a buffer  36 , a retransmission controller  37 , a control signal generator  38 , and a transmitter  39 . 
     The signal separator  32  separates (extracts) a data signal and a control signal from a baseband signal acquired by the receiver  31 . For example, when an OFDM (Orthogonal Frequency Division Multiplexing) communication scheme is employed, the signal separator  32  generates a symbol sequence of each of sub carriers based on an FFT process. Then, the data signal and the control signal inserted into a predetermined sub carrier are separated. 
     The data signal and the control signal acquired by the signal separator  32  are output to the FEC decoder  33 . The control signal acquired by the signal separator  32  is decoded and output to the retransmission controller  37 . 
     The FEC decoder  33  sequentially decodes the data signal by the unit of packets, the data signal being from the signal separator  32 . 
     The error detector  35  detects an error by using a CRC bit appended to the packet. As a result of the error detection, an ACK signal (reception succeeded) or a NACK signal (reception failed) for each of the packets is output to the retransmission controller  37 . A successfully (correctly) received packet is output to an upper layer and also stored in the buffer  36 . 
     The packet decoder  34  decodes the encoded packet using the correctly received packet in the buffer  36  under the control of the retransmission controller  37 , the encoded packet being transmitted from the base station when the packet is retransmitted. Details of the decoding process are described below. 
     The retransmission controller  37  determines whether the received packet is an initially received packet (i.e., the packet when the base station initially transmits) or the encoded packet upon being retransmitted based on the received control signal. Then, when determining that the received packet is the encoded packet, the retransmission controller  37  controls the packet decoder  34 . 
     Further, in the wireless communication system, between the mobile station and the base station, the specific reception indexes (identification information items) are associated in advance with corresponding combinations of the ACK (correctly received or successful reception) and the NACK (incorrectly received, or reception failure) results of the plural packets. 
     Further, the retransmission controller  37  specifies the reception index based on the error detection results of the packets by the error detector  35 . The reception index R_IDX is multiplexed with (into) the control signal by the control signal generator  38 , and transmitted to the base station by the transmitter  39 . 
     Configuration of Base Station (Transmission Device) 
     As illustrated in  FIG. 4 , the base station includes a receiver  11 , a control signal extractor  12 , a retransmission controller  13 , a buffer  14 , a CRC appending section  15 , an FEC encoder  16 , a signal multiplexer  17 , and transmitter  18 . 
     The receiver  11  converts a received RF signal into a digital baseband signal. The control signal extractor  12  extracts the control signal by performing a predetermined signal separation process and also demodulation and decoding processes on the baseband signal. 
     The control signal includes the reception index corresponding to the reception results of the plural packets transmitted to the mobile station. The control signal extractor  12  outputs the reception index R_IDX to the retransmission controller  13 . 
     The plural packets to be transmitted to the mobile station are stored in the buffer  14  before being initially transmitted for retransmission control. 
     When the packets are to be retransmitted, based on the reception index from the control signal extractor  12 , the retransmission controller  13  selects one of the plural encoding methods provided. Further, the retransmission controller  13  generates the encoded packets from the plural packets in the buffer  14  based on the selected encoding method. 
     In this case, the retransmission controller  13  determines the encoding method decodable based on the correctly received packets in the mobile station in the initial transmission from among the plural packets to be transmitted in the buffer  14 . Based on the determined encoding method, the retransmission controller  13  encodes the plural packets to be transmitted. Details of the encoding process are described below. 
     The CRC appending section  15  appends CRC bits to newly input packets or the encoded packets from the retransmission controller  13  for error detection. For error correction, the FEC encoder  16  performs encoding on the packets to which the CRC bits are appended, the encoding for the error correction being determined between the base station and the mobile station in advance. 
     The signal multiplexer  17  multiplexes the data signal (packets) from the FEC encoder  16  with the control signal, to generate a baseband signal to be transmitted. For example, when an OFDMA communication scheme is employed, an IFFT (Inverse Fast Fourier Transform) process is performed to convert subcarriers into a time-domain signal. 
     The transmitter  18  upconverts the baseband signal from the signal multiplexer  17  from the baseband frequency to a radio frequency and the like, and emits to air (transmits the RF signal) via an antenna. 
     (4) Example of Packet Encoding Process and Decoding Process in Retransmission 
     Next, a packet encoding process and a decoding process in the retransmission of packets are specifically described by referring to an example where the number of packets to be transmitted is four with reference to  FIGS. 5 and 6 . 
       FIG. 5  is a table illustrating relationships between plural error patterns (combinations of errors) assuming that the number of packets is four and the reception indexes R_IDX correspond to the plural error patterns. 
       FIG. 6  is a table illustrating corresponding relationships between the reception indexes R_IDX and the corresponding encoding methods (encoding matrixes) to be applied by the base station. 
     Further, the operations described below are bit operations (MOD-2 operation). 
     As illustrated in  FIG. 5 , in response to four packets P 1 , P 2 , P 3 , and P 4  from the base station, there are sixteen possible combinations of the reception states (ACK or NACK) (i.e., error patterns  0  through  15 ) in the mobile station. In the mobile station, those sixteen error patterns are associated with corresponding reception indexes in advance as illustrated in  FIG. 5 . 
     When referring to  FIG. 3  again, the retransmission controller  37  of the mobile station determines the reception index R_IDX by referring to the corresponding relationship of  FIG. 5  based on the reception states (ACK or NACK) of the packets, the reception states being given from the error detector  35 , and feeds back the reception index to the base station. 
     The corresponding relationships between the reception indexes R_IDX and the encoding matrixes are assumed to be known to the base station in advance. Here, when referring to  FIG. 2 , the retransmission controller  13  of the base station (see  FIG. 4 ) selects the encoding method (encoding matrix) for the retransmission based on the reception index R_IDX fed back from the mobile station, and generates the encoded packets. 
     Here, it is assumed that N=4 and also M×4 matrixes as the encoding matrix G M,K  are set (established). Further, the number of generated encoded packets is equal to the number of incorrectly received packet in the mobile station. 
     (4-1) In a Case Where the Number of Errors (M) is “0” 
     In this case, as the reception index R_IDX, data “0” is fed back from the mobile station to the base station. By doing this, the base station recognizes that all packets have been correctly received, and no retransmission may have to be performed. 
     (4-2) In a Case Where the Number of Errors (M) is “1” 
     In this case, as illustrated in  FIG. 5 , when any one of the four packets is incorrectly received, a value “1” is fed back from the mobile station to the base station as the reception index R_IDX. Then, as illustrated in  FIG. 6 , the base station selects the encoding matrix G 1,0  corresponding to the fed-back reception index, and generates the encoded packets. 
     Specifically, the selected encoding matrix G 1,0  is expressed in the following formula (2). Therefore, when the encoded packet is given as R 1 , the R 1  is given as illustrated in formula (3). In this case, only the single encoded packet is transmitted as the retransmission packet to the mobile station. 
     Here, the symbols R 1 , P 1 , P 2 , P 3 , and P 4  denote nth bit similar to formula (1). However, in the following, it is assumed that a similar process is performed for each of the (n) bits. Therefore, the description of the factor “n” may be omitted.
 
 G   1,0 =(1 1 1 1)  (2)
 
 R   1   =P   1   +P   2   +P   3   +P   4   (3)
 
     In the mobile station, successfully (correctly) received packets (i.e., three packets) are known. Therefore, when the encoded packet R 1  is received, the three successfully received packets are cancelled (subtracted) from the encoded packet R 1 . Further, as described above, in this embodiment, the mod-2 operation is performed as the operation. Therefore, the same result may be acquired by performing an addition operation as the cancel (subtraction) operation. 
     By doing this, the mobile station may correctly reproduce (decode) the packet which has not been correctly received in the initial transmission of the packet. For example, when assuming that the packet P 4  is the incorrectly received packet, by performing the operation based on following formula (4), it may become possible to reproduce the packet P 4 .
 
 R   1   −P   2   −P   3   =P   4   (4)
 
     The encoded packet R 1  is the sum of all the packets P 1 , P 2 , P 3 , and P 4 . Therefore, even when the incorrectly received packet is any one of those packets in the initial transmission, the incorrectly received packet may be similarly reproduced by cancelling the three successfully received packets from the encoded packet R 1 . 
     Here, it should be noted is that in response to any of the four error patterns where the number of errors is “1”, the same value (“1”) is fed back to the base station as the reception index. Namely, there is no information indicating which of the four packets is the incorrectly received packet among the four packets transmitted from the mobile station to the base station. 
     Namely, when compared with a system where all the reception states (results) (ACK/NACK) of the packets are fed back (i.e., four bits are necessary), it may become possible to reduce an amount of feed-back information (feed-back information amount) in a system according to this embodiment. 
     (4-3) In a Case Where the Number of Errors (M) is “2” 
     In this case, a value “2” or “3” is fed back from the mobile station to the base station as the reception index R_IDX. Further, the base station selects an encoding matrix G 2,0  or G 2,1  in response to the fed-back reception index, and generates the encoded packets. 
     Error Pattern “ 5 ” (NACK, NACK, ACK, ACK) 
     In a case of an error pattern “ 5 ”, as illustrated in  FIGS. 5 and 6 , the reception index R_IDX fed back to the base station is “2”, and the encoding matrix G 2,0  is selected by the base station. In this case, two encoded packets R 1  and R 2  to be retransmitted to the mobile station are acquired based on the following formula (5). 
     
       
         
           
             
               
                 
                   
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     In the mobile station, the successfully (correctly) received packets (i.e., two packets R 3  and R 4 ) are known. Therefore, when the encoded packets R 1  and R 2  are received, by cancelling (subtracting) the two successfully received packets from the encoded packets R 1  and R 2 , as illustrated in the formula (6), the encoded packets R 1 ′ and R 2 ′ after the cancel operation may be obtained. 
     
       
         
           
             
               
                 
                   
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     Based on the formula (6), the packet P 1  is acquired as the encoded packet R 2 ′, and the packet P 2  is acquired by subtracting the packet P 1  (i.e., R 2 ′) from the encoded packet R 1 ′. Namely, the matrix in the right member of formula (6) has an inverse matrix; therefore, P 1  and P 2  may be calculated based on R 1 ′ and R 2 ′. 
     Error Pattern “ 7 ” (NACK, ACK, ACK, NACK) 
     In a case of an error pattern “ 7 ”, as illustrated in  FIGS. 5 and 6 , the reception index R_IDX fed back to the base station is “2”, and the encoding matrix G 2,0  is selected by the base station. In this case, by cancelling the known successfully received packets (i.e., two packets P 2  and P 3 ) from the two encoded packets R 1  and R 2  (see formula (5)), as illustrated in formula (7), the encoded packets R 1 ′ and R 2 ′ after the cancel operation may be acquired (calculated). 
     
       
         
           
             
               
                 
                   
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     In this case similar to the case of the error pattern “ 5 ”, the packets P 1  and P 4  may be reproduced (decoded). 
     Error Pattern “ 8 ” (ACK, NACK, NACK, ACK) 
     In a case of an error pattern “ 8 ”, as illustrated in  FIGS. 5 and 6 , the reception index R_IDX fed back to the base station is “2”, and the encoding matrix G 2,0  is selected by the base station. In this case, by cancelling the known successfully received packets (i.e., two packets P 1  and P 4 ) from the two encoded packets R 1  and R 2  (see formula (5)), as illustrated in formula (8), the encoded packets R 1 ′ and R 2 ′ after the cancel operation may be acquired (calculated). 
     
       
         
           
             
               
                 
                   
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                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In this case, similar to the case of the error pattern “ 5 ”, the packets P 2  and P 3  may be reproduced (decoded). 
     Error Pattern “ 10 ” (ACK, ACK, NACK, NACK) 
     In a case of an error pattern “ 10 ”, as illustrated in  FIGS. 5 and 6 , the reception index R_IDX fed back to the base station is “2”, and the encoding matrix G 2,0  is selected by the base station. In this case, by cancelling the known successfully received packets (i.e., two packets P 1  and P 2 ) from the two encoded packets R 1  and R 2  (see formula (5)), as illustrated in formula (9), the encoded packets R 1 ′ and R 2 ′ after the cancel operation may be acquired (calculated). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 R 
                                 1 
                               
                             
                           
                           
                             
                               
                                 R 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               
                                 1 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   P 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   P 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               1 
                             
                           
                           
                             
                               1 
                             
                             
                               0 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 P 
                                 3 
                               
                             
                           
                           
                             
                               
                                 P 
                                 4 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     In this case, similar to the case of the error pattern “ 5 ”, the packets P 3  and P 4  may be reproduced (decoded). 
     Error Pattern “ 6 ” (NACK, ACK, NACK, ACK) 
     In a case of an error pattern “ 6 ”, as illustrated in  FIGS. 5 and 6 , the reception index R_IDX fed back to the base station is “3”, and the encoding matrix G 2,1  is selected by the base station. In this case, two encoded packets R 1  and R 2  to be retransmitted to the mobile station are given in the following formula (10). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         G 
                         
                           2 
                           , 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               
                                 P 
                                 1 
                               
                             
                           
                           
                             
                               
                                 P 
                                 2 
                               
                             
                           
                           
                             
                               
                                 P 
                                 3 
                               
                             
                           
                           
                             
                               
                                 P 
                                 4 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               1 
                             
                             
                               1 
                             
                             
                               1 
                             
                           
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 P 
                                 1 
                               
                             
                           
                           
                             
                               
                                 P 
                                 2 
                               
                             
                           
                           
                             
                               
                                 P 
                                 3 
                               
                             
                           
                           
                             
                               
                                 P 
                                 4 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     In the mobile station, the successfully (correctly) received packets (two packets R 2  and R 4 ) are known. Therefore, when the encoded packets R 1  and R 2  are received, by cancelling (subtracting) the two successfully received packets from the encoded packets R 1  and R 2 , as illustrated in the formula (11), the encoded packets R 1 ′ and R 2 ′ after the cancel operation may be obtained. This is similar to the case of the error pattern “ 5 ” in that the encoded packets R 1 ′ and R 2 ′ may be reproduced (decoded) based on the formula (11). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 R 
                                 1 
                               
                             
                           
                           
                             
                               
                                 R 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               
                                 1 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   P 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   P 
                                   
                                     4 
                                     ⁢ 
                                     
                                         
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               1 
                             
                           
                           
                             
                               1 
                             
                             
                               0 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 P 
                                 1 
                               
                             
                           
                           
                             
                               
                                 P 
                                 
                                   3 
                                   ⁢ 
                                   
                                       
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Next, a reason why the encoding matrix G 2,1  selected in the case of the error pattern “ 6 ” is different from that selected in the cases the error patterns “ 5 ”, “ 7 ”, “ 8 ”, and “ 10 ” (i.e., a reason why another reception index is selected) is described. 
     In the case of the error pattern “ 6 ”, when it is assumed that not the encoding matrix G 2,1  but the encoding matrix G 2,0  is selected, based on the formula (5), the encoded packets R 1 ′ and R 2 ′ may be given as in the following formula (12). As is apparent from the formula (12), if the encoding matrix G 2,0  is selected, it may not be possible to uniquely determine the packets R 1  and R 2 . 
     This occurs because the matrix in the right member of formula (12) does not have an inverse matrix. Therefore, in the case of the error pattern “ 6 ”, the encoding matrix G 2,1  different from the encoding matrix G 2,0  is set (selected) so that the matrix acquired by cancelling the successfully received packets from the encoded packets has the inverse matrix. 
                     (           R   1   ′               R   2   ′           )     =         (           R   1               R   2           )     -       (         1       1           0       0         )     ⁢     (           P   2               P   4           )         =       (         1       1           1       1         )     ⁢     (           P   1               P   3           )                 (   12   )               
Error Pattern “ 9 ” (ACK, NACK, ACK, NACK)
 
     In a case of an error pattern “ 9 ”, as illustrated in  FIGS. 5 and 6 , the reception index R_IDX fed back to the base station is “3”, and the encoding matrix G 2,1  is selected by the base station. In this case, by cancelling the known successfully received packets (i.e., two packets P 1  and P 3 ) from the two encoded packets R 1  and R 2  (see formula (10)), as illustrated in formula (13), the encoded packets R 1 ′ and R 2 ′ after the cancel operation may be acquired (calculated). Based on the formula (13), the packets P 2  and P 4  may be reproduced (decoded). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 R 
                                 1 
                               
                             
                           
                           
                             
                               
                                 R 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               
                                 1 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   P 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   P 
                                   3 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 P 
                                 2 
                               
                             
                           
                           
                             
                               
                                 P 
                                 4 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     As described above, the encoding process and the decoding process in a case where the number of errors (M) is “2” are described. In a case where the number of errors (M) is “2”, the 2×4 encoding matrix (a first matrix) is set (selected) in a manner such that a 2×2 (2: the number of errors (M)) square matrix (a second matrix) which is decomposed (degenerated) from the 2×4 encoding matrix (the first matrix) has the inverse matrix. 
     The square matrix is acquired after the successfully received packets are cancelled from the encoded packets, and is given as in the following formula (14) or (15) when the number of errors (M) is “2”. (where symbols “I” and “j” denote any value from 1 to 4, respectively) 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             1 
                           
                           
                             0 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               P 
                               i 
                             
                           
                         
                         
                           
                             
                               P 
                               j 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               P 
                               i 
                             
                           
                         
                         
                           
                             
                               P 
                               j 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, with respect to six error patterns when the number of errors is “2”, it may be necessary to provide (prepare) only two reception indexes (“2” and “3”) to be fed back to the base station. Namely, when compared with a system where all the reception states (results) (ACK/NACK) of the packets are fed back (i.e., four bits are necessary), it may become possible to reduce the feed-back information amount in a system according to this embodiment. 
     (4-4) In a Case Where the Number of Errors (M) is “3” 
     In this case, as illustrated in  FIGS. 5 and 6 , a value “4” is fed back from the mobile station to the base station as the reception index R_IDX. Further, the base station selects an encoding matrix G 3,0  in response to the fed-back reception index, and generates three encoded packets. Those encoded packets are given in the following formula (16). 
                     (           R   1               R   2               R   3           )     =       (         1       1       1       1           1       0       1       0           1       0       0       1         )     ⁢     (           P   1               P   2               P   3               P     4   ⁢                     )               (   16   )               
Error Pattern “ 11 ” (NACK, NACK, NACK, ACK)
 
     In a case of an error pattern “ 11 ”, by cancelling (subtracting) one successfully received packet P 4  from the encoded packets transmitted from the base station, the encoded packets R 1 ′, R 2 ′, and R 3 ′ acquired after the cancel operation are given in the following formula (17). Further, as illustrated in the following formula (18), the determinant of the matrix in the right member of formula (17) is not “0”. Therefore, according to the formula (17), the packets P 1 , P 2 , and P 3  may be reproduced (decoded). 
                     (           R   1   ′               R   2   ′               R   3   ′           )     =       (         1       1       1           1       0       1           1       0       0         )     ⁢     (           P   1               P   2               P   3           )               (   17   )                 det   ⁡     (         1       1       1           1       0       1           1       0       0         )       =       det   ⁡     (         0       1       0           0       0       1           1       0       0         )       =   1             (   18   )               
Error Pattern “ 12 ” (NACK, NACK, ACK, NACK)
 
     In a case of an error pattern “ 12 ”, by cancelling (subtracting) one successfully received packet P 3  from the encoded packets transmitted from the base station, the encoded packets R 1 ′, R 2 ′, and R 3 ′ acquired after the cancel operation are given in the following formula (19). Further, as illustrated in the following formula (20), the determinant of the matrix in the right member of formula (19) is not “0”. Therefore, according to the formula (19), the packets P 1 , P 2 , and P 4  may be reproduced (decoded). 
                     (           R   1   ′               R   2   ′               R   3   ′           )     =       (         1       1       1           1       0       0           1       0       1         )     ⁢     (           P   1               P   2               P   4           )               (   19   )                 det   ⁡     (         1       1       1           1       0       0           1       0       1         )       =       det   ⁡     (         0       1       0           1       0       0           0       0       1         )       =   1             (   20   )               
Error pattern “ 13 ” (NACK, ACK, NACK, NACK)
 
     In a case of an error pattern “ 13 ”, by cancelling (subtracting) one successfully received packet P 2  from the encoded packets transmitted from the base station, the encoded packets R 1 ′, R 2 ′, and R 3 ′ acquired after the cancel operation are given in the following formula (21). Further, as illustrated in the following formula (22), the determinant of the matrix in the right member of formula (21) is not “0”. Therefore, according to the formula (21), the packets P 1 , P 3 , and P 4  may be reproduced (decoded). 
                     (           R   1   ′               R   2   ′               R   3   ′           )     =       (         1       1       1           1       1       0           1       0       1         )     ⁢     (           P   1               P   3               P   4           )               (   21   )                 det   ⁡     (         1       1       1           1       1       0           1       0       1         )       =       det   ⁡     (         0       1       0           1       0       0           0       0       1         )       =   1             (   22   )               
Error Pattern “ 14 ” (ACK, NACK, NACK, NACK)
 
     In a case of an error pattern “ 14 ”, by cancelling (subtracting) one successfully received packet P 1  from the encoded packets transmitted from the base station, the encoded packets R 1 ′, R 2 ′, and R 3 ′ acquired after the cancel operation are given in the following formula (23). Further, as illustrated in the following formula (24), the determinant of the matrix in the right member of formula (23) is not “0”. Therefore, according to the formula (23), the packets P 1 , P 3 , and P 4  may be reproduced (decoded). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             R 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             2 
                             ′ 
                           
                         
                       
                       
                         
                           
                             R 
                             3 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               P 
                               2 
                             
                           
                         
                         
                           
                             
                               P 
                               3 
                             
                           
                         
                         
                           
                             
                               P 
                               4 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
                     det 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       det 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     1 
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     In this embodiment, with respect to four error patterns when the number of errors is “3”, it may be necessary to provide (prepare) only one reception index (“4”) to be fed back to the base station. Namely, when compared with a system where all the reception states (results) (ACK/NACK) of the packets are fed back (i.e., four bits are necessary), it may become possible to reduce the feed-back information amount in a system according to this embodiment. 
     (4-5) In a Case Where the Number of Errors (M) is “4” 
     In this case, as illustrated in  FIGS. 5 and 6 , a value “5” is fed back from the mobile station to the base station as the reception index R_IDX. Further, the base station select an encoding matrix G 4,0  in response to the fed-back reception index. 
     The encoding matrix G 4,0  is a 4×4 unit matrix, which is (technically) equivalent to retransmitting all the four packets P 1  through P 4 . 
     (5) Operation When Plural Packets are Transmitted from Base Station to Mobile Station 
     Next, an operation when plural packets are transmitted from the base station to the mobile station is described with reference to  FIG. 7 .  FIG. 7  is a flowchart illustrating an operation of transmitting plural packets from the base station to the mobile station. In the description, the elements illustrated in  FIGS. 3 and 4  may be referred to. 
     First, N packets are transmitted from the base station to the mobile station (in step S 10 ). In the mobile station, the error detector  35  performs error detection on each of the N packets (in step S 12 ). The error detection results are output to the retransmission controller  37 . 
     Based on the error detection results (ACK/NACK) of the packets, the retransmission controller  37  of the mobile station specifies the reception index R_IDX (step S 14 ). Further, the error detection results (ACK/NACK) of the packets (i.e., error patterns) are associated with the corresponding reception indexes in the base station in advance. 
     The mobile station transmits the specified reception index to the base station (in step S 16 ). In the retransmission controller  13  of the base station, the corresponding relationship between the reception indexes and the encoding methods (encoding matrixes) are defined in advance. Therefore, the retransmission controller  13  of the base station determines the encoding method based on the reception index transmitted in step S 16  and performs the encoding (in step S 18 ). 
     Specifically, the retransmission controller  13  multiplies the N transmission packets by the determined M×N (M: the number of errors) encoding matrix by the unit of bits, to generate M encoded packets. The M encoded packets are transmitted to the mobile station (in step S 20 ). 
     The mobile station receives the M encoded packets. Further, the mobile station reproduces (replaces) the incorrectly received packets in step S 12  by decoding the encoded packets (in step S 22 ). Specifically, the packet decoder  34  of the mobile station reproduces the incorrectly received packets by cancelling (subtracting in a bit level) the successfully received packets in step S 12  from the encoded packets. This decoding process is described by exemplifying the case where N=4. 
     (6) Method of Setting Encoding Matrix in Arbitrary Number of Packets 
     In the above (4), with respect to the encoding process and the decoding process of the packets in the retransmission, a case is specifically described where the number of packets to be transmitted is four. However, according to an embodiment, it may also be possible to appropriately set the encoding matrix with respect to an arbitrary number of packets to be transmitted. In the following, a method of setting an appropriate encoding matrix with respect to an arbitrary number of packets with a simple operation is described. 
     In this setting method, when assuming that the number of the packets to be transmitted is N, the encoding matrixes corresponding to the number of errors M (M: 1 to N−1) among N packets are calculated in the following steps. 
     Step A 
     With respect to a specific number of errors M, M×N encoding matrixes are generated in a manner such that the elements of the matrixes are determined by generating random number “0” or “1”. 
     Step B 
     When assuming that M packets among N packets are incorrectly received, the number of error patterns is expressed by  N C M . With respect to each of  N C M  error patterns, it is determined whether the incorrectly received packets may be reproduced (decoded) from (by using) the encoded packets (retransmission packets) based on the encoding matrixes generated in step A. 
     Specifically, an M×M square matrix is generated, the M×M square matrix being a decomposed (degenerated) matrix having remaining M columns corresponding to coefficient columns to be multiplied with the incorrectly received packets in the encoding process. When the determinant of the decomposed (degenerated) matrix is other than zero, it may become possible to reproduce (decode) the incorrectly received packets based on the retransmission packets corresponding to the error pattern. 
     Step C 
     Among the  N C M  error patterns, when there exist P incorrectly received packets which may not be reproduced in step B, a new encoding matrix is generated by generating the random numbers. By doing this, with respect to P incorrectly received packets, the error patterns are classified into a group of reproducible error patterns and a group of unreproducible error patterns. 
     Until all the incorrectly received packets may be reproduced for all the  N C M  error patterns, the new encoding matrix is generated by generating the random numbers. Namely, until all the incorrectly received packets may be reproduced for all the  N C M  error patterns, the number of the encoding matrixes may be increased. 
     By sequentially performing the processes of the above steps A to C with respect to the number of errors “M”, the encoding matrixes corresponding to all the numbers of errors “M” may be acquired. In accordance with the setting method described above, in a case of N=8, the encoding matrixes as illustrated in  FIGS. 8 and 9  may be acquired.  FIG. 8  illustrates the encoding matrixes when the number of errors M among eight transmission packets is in a range from one to four, and  FIG. 9  illustrates the encoding matrixes when the number of errors M among eight transmission packets is in a range from five to eight. 
     Further, it may also be possible to search for the encoding method to minimize the number of the encoding matrixes (i.e., the coding method to minimize the feed-back information amount) by performing the above steps, for example, 10,000,000 times by changing the random numbers.  FIG. 10  illustrates a result of searching for the encoding method to minimize the feed-back information amount based on the above setting method when the number (N) of packets to be transmitted is in a range from 1 to 11. 
     In  FIG. 10 , for example, when assuming that N=11, the number of the encoding matrixes which may be necessary in the communication method according to this embodiment is 45. Further, the reception indexes are associated with the corresponding encoding matrixes. Therefore, the feed-back information amount (i.e., the number of bits that may express the reception indexes) may be six bits only. 
     On the other hand, as for a comparison,  FIG. 10  also illustrates the feed-back information amount in a method of the related art for each of the reception states (ACK/NACK) (one bit) of plural packets. In this method of the related art, when N=11, 11 bits may be necessary. Therefore, according to this embodiment, it may become possible to greatly reduce the feed-back information amount. 
     As described above, in a communication system and a communication method according to this embodiment, the identification information (reception indexes) are previously associated with the corresponding combinations of the reception results (states) of plural packets in the mobile station, the plural packets being transmitted from the base station. The identification information is fed back to the base station. 
     Further, by paying attention to the fact that the successfully received packets in the initial transmission are known in the mobile station, the packets to be retransmitted from the base station are encoded (as the encoded packets) based on the encoding method so that the incorrectly received packets may be reproduced (decoded) based on the encoded packets and the successfully received packets by the mobile station in the initial transmission. The mobile station may reproduce (decode) the incorrectly received packets in the initial transmission by decoding the encoded packets using the successfully received packets in the initial transmission. 
     Here, as described above, when an appropriate encoding method is set, the number of the identification information items (reception information) (i.e., the number of encoding methods) may be reduced and be less than number of packets to be transmitted; therefore the feed-back information amount to the base station may be reduced. 
     According to an embodiment, a communication method of transmitting plural packets from a first communication device to a second communication device includes associating identification information items with combinations of reception results of the plural packets in the second communication device, a number of the identification information items being less than a number of the plural packets; transmitting, by the first communication device, the plural packets to the second communication device in initial transmission; specifying, by the second communication device, a first of the identification information items based on reception results of the plural packets in initial reception, and transmitting, by the second communication device, the first identification information item to the first communication device; determining, by the first communication device, an encoding method decodable by the second communication device with successfully received packets in the initial reception, encoding, by the first communication device, the plural packets based on the determined encoding method, and retransmitting, by the first communication device, the encoded packets to the second communication device; and decoding, by the second communication device, the encoded packets based on the successfully received packets in the initial reception, and reproducing, by the second communication device, incorrectly received packets in the initial reception. 
     According to another embodiment, a communication system includes a first communication device configured to transmit plural packets and a second communication device configured to receive the plural packets from the first communication device. Further the second communication device is configured to store identification information items associated with combinations of reception results of the plural packets in the second communication device, a number of the identification information items being less than a number of the plural packets. Further, the first communication device includes a first transmitter configured to initially transmit the plural packets to the second communication device, a first receiver configured to receive the identification information items from the second communication device, a packet encoder configured to determine an encoding method decodable by the second communication device with successfully received packets in the initial reception, encode the plural packets based on the determined encoding method to generate encoded packets, and a second transmitter configured to retransmit the encoded packets to the second communication device. Further, the second communication device includes a second receiver configured to initially receive the plural packets from the first communication device, an information specifying unit configured to specify a first identification information item based on the reception results of the plural packets, a third transmitter configured to transmit the first identification information item to the first communication device, a third receiver configured to receive the encoded packets from the first communication device, and a packet decoder configured to decode the encoded packets transmitted from the first communication device based on the successfully received packets in the initial reception to reproduce incorrectly received packets in the initial reception. 
     According to another embodiment, a transmission device transmitting plural packets to a receiving device includes a first transmitter configured to initially transmit the plural packets to the receiving device; a first receiver configured to receive identification information items from the receiving device, the identification information items being associated with combinations of reception results of the plural packets in the receiving device; a packet encoder configured to determine an encoding method decodable by the receiving device with successfully received packets in the initial reception of the plural packets, encode the plural packets based on the determined encoding method; and a second transmitter configured to retransmit the encoded packets to the receiving device. 
     According to another embodiment, a receiving device receiving plural packets from a transmission device and storing identification information items associated with combinations of reception results of the plural packets, includes a second receiver configured to initially receive the plural packets from the transmission device; an information specifying unit configured to specify a first of the identification information items based on reception results of the plural packets; a third transmitter configured to transmit the first identification information item to the transmission device; a third receiver configured to receive the encoded packets from the transmission device; and a packet decoder configured to decode the encoded packets transmitted from the transmission device based on the successfully received packets in initial reception to reproduce incorrectly received packets in the initial reception. 
     The communication method, the communication system, the transmission device, and the receiving device according to an embodiment described herein may reduce the amount of information to be fed back from the receiving-side transmission device to the transmitting-side communication device in relation to the success or failure of receiving the plural packets. 
     All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventors to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of superiority or inferiority of the invention. Although the embodiment of the present invention has been described in detail, it should be understood that various changes, substitutions, and alterations could be made hereto without departing from the sprit and scope of the invention.