# Patent

## Title
Encoding method and apparatus

## Abstract

An encoding method and apparatus are provided. In the encoding method: encoding input information bits with an encoding matrix G and a linear combination formula. The encoding matrix G is an encoding matrix obtained by performing row permutation on an encoding matrix H having a plurality of successive zeroes in one or more columns of the encoding matrix H. Encoding control information with the encoding matrix provided by aspects of the present disclosure, each bit of the control information is distributed on all encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve transmission performance of the control information effectively.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application claims priorities to Chinese Patent Application No. 200910001828.8, entitled “ENCODING METHOD AND APPARATUS” and filed on Jan. 7, 2009, which is hereby incorporated by reference in its entirety.
FIELD OF THE INVENTION
The present disclosure relates to the field of telecommunication technology, and more particularly, to an encoding method and apparatus.
BACKGROUND
In a long term evolution (LTE) system, physical uplink channels may include a physical uplink shared channel (PUSCH), a physical uplink control channel (PUCCH), and a physical random access channel (PRACH). Generally, uplink data is transmitted on the PUSCH, and uplink control signalings are transmitted on the PUCCH. An uplink control signaling may include a channel quality indicator (CQI) signaling, an acknowledged/non-acknowledged (ACK/NACK) message, and a scheduling request message.
When a user equipment (UE) sends control information, for example, a CQI information or a CQI information and an ACK/NACK information, “A” bits control information is encoded with a (20, A) reed-muller (RM) code firstly, where the “A” bits are encoded into 20 bits. Then the 20 bits undergoes a quaternary phase shift keying (QPSK) modulation, which obtains 10 modulated QPSK symbols. The 10 modulated QPSK symbols are mapped to two slots of a PUCCH, in which the first 5 QPSK symbols are mapped to the first slot, and the last 5 symbols are mapped to the second slot, as shown in FIG. 1.
During the implementation of the present disclosure, the inventors find that the prior art has the following defect: When the control information is encoded with the (20, A) RM code matrix aforementioned, some bits of the control information may not have information on some successive modulation symbols, so that sufficient frequency diversity and time diversity gains cannot be obtained.
SUMMARY OF THE INVENTION
Aspects of the present disclosure are directed to encoding methods and apparatuses in a telecommunication system. By encoding with an encoding matrix provided by aspects of the present disclosure, or by performing bit mapping on encoded information, each bit of the control information can be distributed on all encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve transmission performance of the control information effectively.
Accordingly, an encoding method is provided according to an aspect of the present disclosure. The encoding method may include: encoding input information bits with an encoding matrix G and a linear combination formula, where the linear combination formula is




  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ;




in which bi is an encoded output bit, i=0, 1, 2, . . . , B−1; Mi,n is a corresponding element in the encoding matrix G; an is an input information bit, and n=0, . . . A−1; and A and B are positive integers greater than zero. The encoding matrix G is an encoding matrix obtained by performing row permutation on an encoding matrix H having a plurality of successive zeroes in one or more columns of the encoding matrix H.

An encoding method is provided according to another aspect of the present disclosure. The encoding method may include: encoding input information bits with an encoding matrix and a linear combination formula; and interleaving the encoded information bits according to a preset mapping mode, so as to distribute the input information bits on modulated symbols uniformly. In the encoding method, the linear combination formula is




  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ;




in which bi is an output bit after RM encoding, i=0, 1, 2, . . . , B−1; Mi,n is a corresponding element in the encoding matrix; an is an input information bit, n=0, . . . A−1; and A and B are positive integers greater than zero.

An encoding apparatus is provided according to further another aspect of the present disclosure, which may include an encoding unit.
The encoding unit is configured to encode input information bits with the encoding matrix G and the linear combination formula according to claim 1.
An encoding apparatus is provided according to further another aspect of the present disclosure, which may include an encoding unit and an interleaving unit.
The encoding unit is configured to encode input information bits with an encoding matrix and a linear combination formula.
The interleaving unit, connected with the encoding unit, is configured to interleave the encoded information bits according to a preset mapping mode, so as to distribute the input information bits on modulated symbols uniformly.
As can be seen, encoding control information with the encoding matrix provided by aspects of the present disclosure, or performing bit mapping on encoded control information, each bit of the control information can be distributed on all encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve transmission performance of the control information effectively.



BRIEF DESCRIPTION OF THE DRAWINGS
The following drawings are intended for better understanding of embodiments of the present disclosure and constitute part of this application rather than limitation of the present disclosure. In the drawings:
FIG. 1 is a schematic mapping of a PUCCH physical channel in the prior art;
FIG. 2 is a flow chart of an encoding method according to embodiment 3 of the present disclosure;
FIG. 3 to FIG. 6 are performance curves obtained by encoding CQI information bits of 6 bits, 7 bits, 8 bits, and 9 bits with an encoding matrix according to embodiment 2 of the present disclosure;
FIG. 7 is a performance curves of different bits encoded with an encoding matrix in the prior art;
FIG. 8 is a performance curves of different bits encoded with the encoding matrix shown in Table 2 according to an embodiment of the present disclosure;
FIG. 9 is a flow chart of an encoding method according to embodiment 4 of the present disclosure;
FIG. 10 is a flow chart of an encoding method according to embodiment 5 of the present disclosure;
FIG. 11 is a schematic structure of an encoding apparatus according to embodiment 6 of the present disclosure;
FIG. 12 is a schematic structure of an encoding apparatus according to embodiment 7 of the present disclosure;
FIG. 13 is a schematic structure of an encoding apparatus according to embodiment 8 of the present disclosure; and
FIG. 14 is a schematic structure of an encoding apparatus according to embodiment 9 of the present disclosure.



DETAILED DESCRIPTION
In order to make the solution, objectives and merits of the disclosure clearer, a detailed description of the disclosure is given below by reference to accompanying drawings and some exemplary embodiments. The exemplary embodiments of the present disclosure and description thereof are intended for interpreting rather than limiting the present disclosure.
Embodiment 1
In this embodiment, an encoding method for a telecommunication system is provided, which includes: encoding input information bits with an encoding matrix (the encoding matrix is represented as G in this embodiment) and a linear combination formula (or an encoding formula). The linear combination formula is




  
    b
    i
  
  =
  
    
      ∑
      
        n
        =
        0
      
      
        A
        -
        1
      
    
    ⁢
    
      
        (
        
          
            a
            n
          
          ·
          
            M
            
              i
              ,
              n
            
          
        
        )
      
      ⁢
      mod
      ⁢
      
        
      
      ⁢
      2.
    
  




In the above formula, bi is an encoded output information bit, i=0, 1, 2, . . . , B−1; Mi,n is a corresponding element in the encoding matrix G; an is an input information bit, and n=0, . . . A−1; and A and B are positive integers greater than zero.
In this embodiment, the encoding matrix G is obtained by performing row permutation on an encoding matrix having a plurality of successive zeroes in one or more columns of the encoding matrix (in this embodiment, the encoding matrix having a plurality of successive zeroes in one or more columns is represented as encoding matrix H).
In this embodiment, A represents the number of the input information bits, and the B represents the number of the output information bits.
In this embodiment, input information bits a0, a1, a2, a3, . . . , aA-1 of CQI transmitted on a PUCCH channel are encoded by using the encoding matrix G and the encoding formula. The CQI may be sent from a UE. The number of the input information bits A depends on a specific report mode of CQI. The number of the output information bits B depends on the specific encoding mode, for example, in an LTE system, the output information bits B=20. However, a person skilled in the art would understand, B may be set to any proper number as desired according to actual demands.
AS can be seen from the embodiment aforementioned, encoding control information with the encoding matrix G obtained by performing row permutation on the encoding matrix H having a plurality of successive zeroes in one or more columns of the matrix H, each bit of the control information can be distributed on all the decoded output bits as uniformly as possible. Thereby the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve transmission performance of the control information effectively.
Embodiment 2
In this embodiment, an encoding method is provided, in which, the output information bits B=20.
The method may include: encoding input information bits with an encoding matrix and a linear combination formula.
The linear combination formula is




  
    b
    i
  
  =
  
    
      ∑
      
        n
        =
        0
      
      
        A
        -
        1
      
    
    ⁢
    
      
        (
        
          
            a
            n
          
          ·
          
            M
            
              i
              ,
              n
            
          
        
        )
      
      ⁢
      mod
      ⁢
      
        
      
      ⁢
      2.
    
  




In the above formula, bi is an output bit after RM encoding, i=0, 1, 2, . . . , B−1, B=20; Mi,n is a corresponding element in the encoding matrix G; and an is an information bit, and n=0, . . . A−1.
In this embodiment, the number of output information bits B=20. The encoding matrix having a plurality of successive zeroes in one or more columns is, for example, as shown in Table A.




















TABLE A





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
0
0
0
0
0
1
1
1
0


2
1
0
0
1
0
0
1
0
1
1
1
1
1


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
1
1
1
0
0
0
1
0
0
1
1
1


5
1
1
0
0
1
0
1
1
1
0
1
1
1


6
1
0
1
0
1
0
1
0
1
1
1
1
1


7
1
0
0
1
1
0
0
1
1
0
1
1
1


8
1
1
0
1
1
0
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
1
1
0
0
1
1
0
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
0
1
1
0
1
0
0
1
0
1


15
1
1
0
0
1
1
1
1
0
1
1
0
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
1
0
0
1
0
0
1
1


18
1
1
0
1
1
1
1
1
0
0
0
0
0


19
1
0
0
0
0
1
1
0
0
0
0
0
0









For example, in the 6th M column, i.e., column Mi,5, in the encoding matrix as shown in Table A, the first 10 rows are all zeroes. Due to the existence of such successive zeroes, some bits of control information may not have information on successive modulation symbols, so that sufficient time diversity gain cannot be obtained when the channel changes rapidly.
Accordingly, in this embodiment, row permutation may be performed on the encoding matrix as shown in Table A, so as to reduce the number of successive zeroes.
In this embodiment, the encoding matrix obtained after performing row permutation on the encoding matrix shown in Table A may be any one of encoding matrixes as shown in Table 1 to Table 6, but the present disclosure is not limited to these.




















TABLE 1





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
0
1
0
1
0
1
0
1
1
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
0
1
0
0
1
0
1
1
1
1
1


4
1
1
1
0
0
0
0
0
0
1
1
1
0


5
1
0
0
1
1
1
0
0
1
0
0
1
1


6
1
0
1
0
0
1
1
1
0
1
1
1
1


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
0
0
1
1
0
1
0
0
1
0
1


11
1
0
1
1
0
0
0
0
1
0
1
1
1


12
1
1
0
1
1
0
0
1
0
1
1
1
1


13
1
1
0
0
1
1
1
1
0
1
1
0
1


14
1
1
1
0
0
1
1
0
1
0
1
1
1


15
1
0
0
1
0
1
0
1
1
1
1
1
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
0
0
1
1
0
1
1
1


18
1
1
1
1
0
0
0
1
0
0
1
1
1


19
1
0
0
0
0
1
1
0
0
0
0
0
0





























TABLE 2





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
1
1
1
0
0
0
1
0
0
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
1





























TABLE 3





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
1
1
1
0
0
0
1
0
0
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
0
1
0
0
1
1
1
0
1
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
1





























TABLE 4





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
1
1
1
0
0
1
0
1
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
1
0
0
1
1
1
1
0
1
1
0
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
0
1
1
1
1
1
0
0
0
0
0


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
0
0
0
1
1
0
1
0
0
1
0
1


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
1
1
1
0
0
1
0
0
1
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
0
0
0
1
1
0
0
0
0
0
0


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
1
0
0
1
1
1
0
1
1
1
1


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
1





























TABLE 5





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
0
1
1
1
1
0
1
1
0
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
0
0
1
1
1
0
0
1
0
0
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
1
1
1
0
0
1
0
1
1


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
1
0
1
1
1
1
1
0
0
0
0
0


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
0
1
1
0
1
0
0
1
0
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
1
0
0
1
1
1
0
1
1
1
1


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
0
0
0
1
1
0
0
0
0
0
0


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
1





























TABLE 6





i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
0
1
0
0
1
1
1
0
1
1
1
1


1
1
0
0
1
1
0
0
1
1
0
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
0
0
0
0
1
1
0
0
0
0
0
0


5
1
1
0
1
1
0
0
1
0
1
1
1
1


6
1
1
1
0
0
0
0
0
0
1
1
1
0


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
0
1
0
1
0
1
1
1
1
1


10
1
1
0
0
1
1
1
1
0
1
1
0
1


11
1
0
0
1
0
1
0
1
1
1
1
1
1


12
1
0
1
1
1
0
1
0
0
1
1
1
1


13
1
1
1
0
0
1
1
0
1
0
1
1
1


14
1
0
0
1
1
1
0
0
1
0
0
1
1


15
1
1
1
1
0
0
0
1
0
0
1
1
1


16
1
1
0
0
0
0
0
0
0
0
1
1
0


17
1
1
1
0
1
1
1
0
0
1
0
1
1


18
1
0
0
1
0
0
1
0
1
1
1
1
1


19
1
0
0
0
1
1
0
1
0
0
1
0
1









In this embodiment, control information of CQI, for example, a0, a1, a2, a3, . . . , aA-1 transmitted on a PUCCH channel is encoded by using the encoding matrix G obtained after row permutation and an encoding formula aforementioned. The number of the control information is A bits, which depends on a specific report mode of CQI.
In this embodiment, the encoding matrix is an RM encoding matrix, and the control information with A bits may be encoded into 20 bits by using the encoding matrix G aforementioned.
As can be seen from this embodiment, encoding control information with the encoding matrix as shown in Table 1 to Table 6, which are obtained after row permutation according to this embodiment. Due to the number of successive zeroes in the encoding matrix in Table 1 to Table 6 is reduced, each bit of control information can be distributed on all the encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve a transmission performance of the control information effectively.
Embodiment 3
In this embodiment, an encoding method is provided, in which, control information of CQI transmitted on a PUCCH channel is encoded with a (20, A) code. The method may include the following steps as shown in FIG. 2.
In step 201, control information of CQI having A bits, for example, a0, a1, a2, a3, . . . , aA-1, to be transmitted on the PUCCH channel is generated. In this embodiment, the bit number of the CQI, that is, the number of A depends on the specific report mode of the CQI.
In step 202, the generated A bits of CQI information are encoded with a (20, A) code according to any one of encoding matrixes in Table 1 to Table 6 and a linear combination formula. That is to say, the A bits of CQI information are encoded by linear combination so as to generate 20 encoded output information bits. In this embodiment, the used (20, A) code is a linear combination of 13 basic sequences Mi,n in any encoding matrix of Table 1 to Table 6.
The encoding method is illustrated in the following with examples.
As for CQI information having A bits, for example, a0, a1, a2, a3, . . . , aA-1 the encoded output information bits are b0, b1, b2, b3, . . . , bB-1 encoding, in which B=20. The linear combination formula is




  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,




in which i=0, 1, 2, . . . , B−1. Illustration is made in the following by taking the 4-bits CQI information a0, a1, a2, a3 as an example.

For example, the first output information bit b0, after the RM encoding according to the encoding matrix and the linear combination formula, is:

b0=(a0·M0,0+a1·M0,1+a2·M0,2a3·M0,3) mod 2.

Similarly, values of other output information bits b1, b2, b3, . . . , bB-1 may also be obtained, that is:



  
    
      b
      1
    
    =
    
      
        (
        
          
            
              a
              0
            
            ·
            
              M
              
                1
                ,
                0
              
            
          
          +
          
            
              a
              1
            
            ·
            
              M
              
                1
                ,
                1
              
            
          
          +
          
            
              a
              2
            
            ·
            
              M
              
                1
                ,
                2
              
            
          
          +
          
            
              a
              3
            
            ·
            
              M
              
                1
                ,
                3
              
            
          
        
        )
      
      ⁢
      mod
      ⁢
      
        
      
      ⁢
      2
    
  




  ⋮




  
    
      b
      19
    
    =
    
      
        (
        
          
            
              a
              0
            
            ·
            
              M
              
                19
                ,
                0
              
            
          
          +
          
            
              a
              1
            
            ·
            
              M
              
                19
                ,
                1
              
            
          
          +
          
            
              a
              2
            
            ·
            
              M
              
                19
                ,
                2
              
            
          
          +
          
            
              a
              3
            
            ·
            
              M
              
                19
                ,
                3
              
            
          
        
        )
      
      ⁢
      mod
      ⁢
      
        
      
      ⁢
      2
    
  



    
    
        20 encoded output information bits may be obtained after the above calculation.
    
    


In step 203, The 20 encoded output information bits are modulated with QPSK, that is, every two bits form a QPSK symbol, so as to generate 10 QPSK symbols d0, d1, . . . , d9. Then the QPSK symbols are scrambled and mapped to a sub-frame of a PUCCH channel. As shown in FIG. 1, the PUCCH channel is distributed at two sides of an uplink channel in the frequency domain, and two slots is disposed at two different sides of the frequency domain. For example, d0, d1, . . . , d4 are mapped to the first slot of the PUCCH (for example, the m=0 part of the first slot), and d5, d6, . . . , d9 are mapped to the second slot of the PUCCH (for example, the m=0 part of the second slot).
In this embodiment, each encoding matrix shown in Table 1 to Table 6 can be obtained based on the encoding matrix in the prior art, for example shown in Table A.
As shown in Table A, some columns have more successive zeroes. For example, in the 6th column, i.e., Mi,5, the first 10 columns are all zeroes. Suppose the number of bits in the control information is greater or equal to 6, the 6th bit of the control information is only embodied in the last 10 encoded output bits among the 20 encoded output bits after encoding, i.e., the 6th bit of the control information is only embodied on the last 5 QPSK symbols after QPSK modulation. Moreover, the PUCCH is respectively mapped to two sides of the frequency domain in two slots of a sub-frame, so frequency diversity gain is obtain by using incoherence characteristics of the frequency domain as much as possible. According to the mapping rule of the PUCCH, the last 5 symbols are mapped to the second slot of a sub-frame, so that the first slot will not contain any information of the 6th bit, thus the 6th bits cannot obtain sufficient frequency diversity gain. Similarly, although other columns can make information bits embodied on the 2 slots, due to the existence of the successive zeroes, some information bits will not have information on successive modulation symbols, so that sufficient time diversity gain cannot be obtained when the channel changes rapidly.
Therefore, in this embodiment, row transform (or referred to as row permutation) is performed on the encoding matrix in the prior art, for example, the encoding matrix shown in Table A. Row transform can reduce the number of successive zeroes, so that the bits of control information can be distributed on all encoded output bits as uniformly as possible.
The number of successive zeroes in the column having the maximum number of successive zeroes according to the encoding matrix in this embodiment of the present disclosure, for example, the matrix shown in Table 1 to Table 6, is smaller than the number of successive zeroes in the column having the maximum number of successive zeroes according to the encoding matrix in the prior art, for example, the matrix shown in Table A.
Moreover, the number of columns having successive zeroes among several rows mapping to the same modulation symbol according to the encoding matrix as shown in Table 1 to Table 6 is smaller than the number of columns having successive zeroes among several rows mapping to the same modulation symbol according to the encoding matrix in the prior art.
Moreover, the columns having successive zeroes in first B/2 rows and in last B/2 rows are distributed substantially uniformly according to the encoding matrixes shown in Table 1 to Table 6.
In this embodiment, any one of the encoding matrixes in Table 1 to Table 6 can be obtained in the following manner.
Row permutation is performed on the encoding matrix in the prior art as shown in Table A, that is, nth row is displaced with the mth row in the encoding matrix of Table A, so that the number of successive zeroes in each column in the row transformed encoding matrix is reduced as much as possible.
After the row permutation, the encoding matrix as shown in Table 1 to Table 6 may be obtained. Of course, the encoding matrixes as shown in Table 1 to Table 6 are only examples, and other encoding matrixes enabling input information bits distributed on all encoded output information bits as uniformly as possible can also be obtained according to the row permutation manner described above.
Further, if successive zeroes still exist on any column in the encoding matrix obtained after the row permutation or row transform, the successive zeroes may be further distributed to different modulation symbols as much as possible.
Further, after distributing the occurring successive zeroes to different modulation symbols, the encoded information bits is divided into two groups, for example, the first 10 bits are considered as a group, and the last 10 bits are considered as another group. If any column in the two groups has more than one 0 symbol, the symbols are distributed uniformly in the two groups.
The encoding matrix according to this embodiment, for example, the encoding matrix shown in Table 1 to Table 6, may be obtained through the above row permutation method.
The specific implementation process of obtaining the encoding matrix, for example, the encoding matrix shown in Table 1 to Table 6, through the row transform is further illustrated.
In step 1, as for an (B, A) RM encoding matrix X1, in which B represents the output bits of the RM encoder, a row of the encoding matrix X1 is selected to serve as the ith row (for example, the 1st row) of an encoding matrix X2.
In step 2, a row is selected from the rest rows in the encoding matrix X1, and the row satisfies the condition that, after the row is taken as a neighboring row of the ith row of the encoding matrix X2, the number of columns having successive zeroes in the two rows is the minimum.
In step 3, after completion of the step 2, if several rows satisfy the condition defined in the step 2, the row selected in step 2 is determined together with the ith row and the (i−1)th row. Then, the row forming the combination having a column with at least 3 successive zeroes is selected, and the selected row serves as the (i+1)th row of the encoding matrix X2.
In step 4, the (i+1)th row of the encoding matrix X2 is set as the ith row, and the steps 2 and 3 are repeated, until B rows in the encoding matrix X1 are all mapped to the encoding matrix X2.
In step 5, as for the encoding matrix X2, neighboring odd and even rows are considered as a symbol row. If a certain symbol row has a column with two successive zeroes, the column is a zero symbol column. The encoding matrix X2 is processed, in which, a symbol row is selected randomly to serve as the jth row (for example, the 1st row) of an encoding matrix X3.
In step 6, a symbol row is selected from the rest symbol rows in the encoding matrix X2, and the row should satisfy the condition that, after the row is taken as a neighboring row of the jth row of the encoding matrix X3, the number of columns having successive zeroes in the two symbol rows is the minimum. The selected symbol row serves as the (j+1)th symbol row of the encoding matrix X3.
In step 7, the (j+1)th symbol row of the encoding matrix X3 is set as the jth symbol row, and the step 6 is repeated, until all the symbol rows of the encoding matrix X2 are processed.
In step 8, as for the generated encoding matrix X3, the first B/2 rows are considered as a group, and the later B/2 rows are considered as another group. If a certain column has two or more zero symbol columns, symbol row transform is performed on the encoding matrix X3, so that in an encoding matrix X4 obtained after symbol row transform, the zero symbols are distributed in the two groups as uniformly as possible.
In step 9, the encoding matrix X4 is the finally obtained encoding matrix.
In this embodiment, any one of encoding matrixes in Table 1 to Table 6 according to embodiments of the present disclosure can be obtained through the above step 1 to step 9.
The obtained RM encoding matrix, for example, the encoding matrix shown in Table 1, is compared with the encoding matrix in the prior art, i.e., the encoding matrix shown in Table A. The QPSK modulation is performed on the encoded output bits, and particularly, the encoding matrix is divided into 10 groups for consideration, that is to say, every two successive rows are considered as a group, and the group is modulated to one QPSK symbol. When employing the encoding matrix of Table 1, the number of zero symbols is reduced from 32 to 17, and no successive zero on a plurality of symbols exists (two or more successive zero symbols).
In order to view the performance of the encoding matrix according to embodiments of the present disclosure, the RM code is simulated under the simulation conditions in the following: 10 MHz band width, typical urban (TU) channel, UE having a moving speed of 3 km/h, antenna architecture of 2 transmit antennas and 1 received antenna, and estimating by adopting actual channel.
Referring to FIG. 3 to FIG. 6, schematic views showing simulation results of CQI information in different situations of 6 bits, 7 bits, 8 bits, and 9 bits are shown. In the drawings, the horizontal coordinate represents a signal-noise ratio (SNR), and the vertical coordinate represents a block error ratio (BLER), in which solid lines represent RM codes adopted in the existing LTE protocol (current curves), and dashed lines are BLER performance curves corresponding to the encoding matrix of Table 1 (modified curves).
FIG. 7 is a performance curves when performing encoding with the encoding matrix of the prior art, and FIG. 8 is a performance curves when performing encoding with the encoding matrix shown in Table 1 according to embodiments of the present disclosure.
AS can be seen from FIG. 3 to FIG. 6, encoding with the encoding matrix according to embodiments of the present disclosure, the performance is greatly improved.
Relationships between different bits are described in the following.
As shown in FIG. 8, when the encoding matrix according to embodiments of the present disclosure is used, BLER rises uniformly with the increasing of the number of input information bits. However, as shown in FIG. 7, when the encoding matrix as shown in Table A is used, a large gap exists when the number of input information bits is between 5 bits and 6 bits.
It can be seen that, after using the encoding matrix of embodiments of the present disclosure, the transmission quality of the CQI control signaling is greatly improved as compared with that when using the encoding matrix in the prior art. Because the control information is distributed on the control symbols as uniformly as possible, and when a moving speed of a UE is increased, greater gain is obtained with the encoding matrix of embodiments of the present disclosure.
It can be known from the above embodiment that, encoding control information with the encoding matrix shown in Table 1 to Table 6, each bit of the control information can be distributed on all encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve a transmission performance of the control information effectively.
Embodiment 4
In this embodiment, an encoding method is provided, as shown in FIG. 9. The method may include the following steps: Input information bits are encoded with a pre-stored encoding matrix and a linear combination formula (see step 901 of FIG. 9). The encoded output information bits are interleaved, so that the input information bits are distributed uniformly on the modulated symbols (see step 902 of FIG. 9). The linear combination formula is




  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ;




bi is an output information bit after RM encoding; i=0, 1, 2, . . . , B−1; Mi,n is a corresponding element in the encoding matrix; an is an input information bit, and n=0, . . . A−1; and A and B are positive integers greater than zero.

In this embodiment, the used encoding matrix may adopt the encoding matrix in the prior art, for example, as shown in Table A.
In this embodiment, the existing encoding matrix in the prior art needs not to be changed. The encoded output information bits are interleaved, so as to change the sequence of the output information bits, so that the input information bits of the control signaling are distributed on the modulated symbols as uniformly as possible.
It can be seen from the above embodiment that, interleaving the encoded output information bits so as to change the sequence of the output bits, the information bits of the control signaling are distributed on the modulated symbols as uniformly as possible. Thereby, the information bits of the control signaling obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve a transmission performance of control information effectively.
Embodiment 5
In this embodiment, an encoding method is provided, in which, control information of CQI transmitted on a PUCCH channel is encoded with a (20, A) code with encoded output information bits B=20.
As shown in FIG. 10, the method may include the following steps.
In step 1001, control information of CQI having A bits, for example, a0, a1, a2, a3, . . . , aA-1, to be transmitted on the PUCCH channel is generated. In this embodiment, the bit number of the CQI, that is, the number of control information bits A depends on the specific report mode of the CQI.
In step 1002, the generated A bits of CQI are encoded with a (20, A) code according to the encoding matrix shown in Table A and the linear combination formula aforementioned. That is to say, the A bits of CQI information bits are encoded by linear combination so as to generate 20 encoded output information bits. The encoding process is substantially similar to that in embodiment 2.
In step 1003, the 20 encoded bits are interleaved according to a preset mapping mode, so that each encoded output information bit can be distributed uniformly on the modulated symbols. The interleaving process may employ an input-output mapping manner. For example, the mapping relation may be in the following: code indexes of the input 20 encoded bits are [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], and code indexes of the output bits are [0, 18, 14, 6, 2, 1, 8, 11, 3, 15, 10, 7, 12, 16, 4, 17, 5, 9, 19, 13]. A person skilled in the art would understand, the present disclosure is not limited to this example, other manners are also available.
In step 1004, QPSK modulation is performed on the 20 interleaved bits, and the process thereof is similar to that in embodiment 3.
It can be seen from the above embodiment that, by interleaving the encoded output information bits and changing the sequence of the output information bits, the information bits of the control signaling are distributed on the modulated symbols as uniformly as possible. Thereby, the information bits of control signaling obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve a transmission performance of control information effectively.
Embodiment 6
In this embodiment, an encoding apparatus is provided. As shown in FIG. 11, the encoding apparatus includes an encoding unit 1101, and the encoding unit 1101 is configured to encode input information bits with the encoding matrix and the linear combination formula as shown in embodiment 1.
The encoding process executed by the encoding unit 1101 is similar to the encoding process described in embodiment 1.
It can be seen from the above embodiment that, encoding control information with the encoding matrix obtained by performing row permutation on an encoding matrix having a plurality of successive zeroes in one or more columns of the encoding matrix. Because the number of successive zeroes in the obtained encoding matrix is reduced, the bits of the control information are distributed on all encoded output bits as uniformly as possible. Thereby the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve transmission performance of the control information effectively.
Embodiment 7
In this embodiment, an encoding apparatus is provided. As shown in FIG. 12, the encoding apparatus includes an encoding unit 1101, and the process executed by the encoding unit 1101 is similar to the encoding process described in embodiment 5, which is not repeated here.
As shown in FIG. 12, the encoding apparatus may further include a modulation unit 1201 connected to the encoding unit 1101. The modulation unit 1201 is configured to modulate encoded output information bits of control information and map the modulated bits to a PUCCH.
In this embodiment, the encoding matrix may be any one of the encoding matrixes shown in Table 1 to Table 6 according to embodiment 2.
It can be known from above that, encoding control information with the encoding matrix (particularly, any encoding matrix shown in Table 1 to Table 6) obtained by row transform on the encoding matrix in the prior art (for example, the encoding matrix shown in Table A), so that each bit of the control information can be distributed on all encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve a transmission performance of the control information effectively.
Embodiment 8
In this embodiment, an encoding apparatus is provided. As shown in FIG. 13, the apparatus includes an encoding unit 1301 and an interleaving unit 1302. The encoding unit 1301 is configured to encode input information bits with an encoding matrix and a liner combination formula. The interleaving unit 1302, connected to the encoding unit 1301, is configured to interleave the encoded output information bits, so that the input information bits are distributed uniformly on modulated symbols.
In this embodiment, the interleaving process executed by the interleaving unit 1302 is similar to the interleaving process described in embodiment 4, which is not repeated here.
In this embodiment, the used encoding matrix may be the encoding matrix shown in Table A.
It can be seen from the above embodiment that, interleaving the encoded output information bits and changing the sequence of the output information bits, the information bits of control signaling are distributed on the modulated symbols as uniformly as possible. Thereby, the information bits of the control signaling obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve a transmission performance of control information effectively.
Embodiment 9
In this embodiment, an encoding apparatus is provided. As shown in FIG. 14, the apparatus includes an encoding unit 1301 and an interleaving unit 1302. The process executed by the encoding unit 1301 and the interleaving unit 1302 are similar to those in embodiment 7, which are not repeated here.
As shown in FIG. 14, the apparatus may further include a modulation unit 1401 connected to the interleaving unit 1302. The modulation unit 1401 is configured to modulate interleaved information bits of control information and map the interleaved information bits to a PUCCH.
In this embodiment, the operating process of the apparatus is similar to that described in embodiment 5, which is not repeated here.
It can be seen from the above embodiment that, encoding control information with the encoding matrix provided by aspects of the present disclosure, or performing bit mapping on encoded output information bits of control information, each bit of the control information is distributed on all encoded output bits as uniformly as possible. Thereby, the bits of the control information obtain sufficient frequency diversity and time diversity after channel mapping, so as to improve transmission performance of the control information effectively.
The above descriptions are merely preferred embodiments of the present disclosure, but not intended to limit the scope of the present disclosure. Any modification, equivalent replacement, or improvement made without departing from the spirit and principle of the present disclosure should fall within the scope of the present disclosure.

## Claims

1. A method that facilitates sending channel quality indicator (CQI) information in a wireless communication environment, comprising:
encoding CQI information to yield a sequence of coded CQI bits;
modulating the coded CQI bits to yield a sequence of modulated symbols;
mapping the modulated symbols to a physical uplink control channel (PUCCH); and
transmitting the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with





  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,



 A is a positive integer greater than zero, and [Mi,n] is a matrix obtained by performing row permutation on the following matrix:
























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
0
1
0
1
0
1
0
1
1
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
0
1
0
0
1
0
1
1
1
1
1


4
1
1
1
0
0
0
0
0
0
1
1
1
0


5
1
0
0
1
1
1
0
0
1
0
0
1
1


6
1
0
1
0
0
1
1
1
0
1
1
1
1


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
0
0
1
1
0
1
0
0
1
0
1


11
1
0
1
1
0
0
0
0
1
0
1
1
1


12
1
1
0
1
1
0
0
1
0
1
1
1
1


13
1
1
0
0
1
1
1
1
0
1
1
0
1


14
1
1
1
0
0
1
1
0
1
0
1
1
1


15
1
0
0
1
0
1
0
1
1
1
1
1
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
0
0
1
1
0
1
1
1


18
1
1
1
1
0
0
0
1
0
0
1
1
1


19
1
0
0
0
0
1
1
0
0
0
0
0
0.

2. The method according to claim 1, wherein the matrix [Mi,n] is any one of the following:























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
0
1
0
1
0
1
0
1
1
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
0
1
0
0
1
0
1
1
1
1
1


4
1
1
1
0
0
0
0
0
0
1
1
1
0


5
1
0
0
1
1
1
0
0
1
0
0
1
1


6
1
0
1
0
0
1
1
1
0
1
1
1
1


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
0
0
1
1
0
1
0
0
1
0
1


11
1
0
1
1
0
0
0
0
1
0
1
1
1


12
1
1
0
1
1
0
0
1
0
1
1
1
1


13
1
1
0
0
1
1
1
1
0
1
1
0
1


14
1
1
1
0
0
1
1
0
1
0
1
1
1


15
1
0
0
1
0
1
0
1
1
1
1
1
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
0
0
1
1
0
1
1
1


18
1
1
1
1
0
0
0
1
0
0
1
1
1


19
1
0
0
0
0
1
1
0
0
0
0
0
 0,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
1
1
1
0
0
0
1
0
0
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
1
1
1
0
0
0
1
0
0
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
0
1
0
0
1
1
1
0
1
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
1
1
1
0
0
1
0
1
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
1
0
0
1
1
1
1
0
1
1
0
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
0
1
1
1
1
1
0
0
0
0
0


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
0
0
0
1
1
0
1
0
0
1
0
1


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
1
1
1
0
0
1
0
0
1
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
0
0
0
1
1
0
0
0
0
0
0


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
1
0
0
1
1
1
0
1
1
1
1


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
0
1
1
1
1
0
1
1
0
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
0
0
1
1
1
0
0
1
0
0
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
1
1
1
0
0
1
0
1
1


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
1
0
1
1
1
1
1
0
0
0
0
0


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
0
1
1
0
1
0
0
1
0
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
1
0
0
1
1
1
0
1
1
1
1


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
0
0
0
1
1
0
0
0
0
0
0


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
1, and
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
0
1
0
0
1
1
1
0
1
1
1
1


1
1
0
0
1
1
0
0
1
1
0
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
0
0
0
0
1
1
0
0
0
0
0
0


5
1
1
0
1
1
0
0
1
0
1
1
1
1


6
1
1
1
0
0
0
0
0
0
1
1
1
0


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
0
1
0
1
0
1
1
1
1
1


10
1
1
0
0
1
1
1
1
0
1
1
0
1


11
1
0
0
1
0
1
0
1
1
1
1
1
1


12
1
0
1
1
1
0
1
0
0
1
1
1
1


13
1
1
1
0
0
1
1
0
1
0
1
1
1


14
1
0
0
1
1
1
0
0
1
0
0
1
1


15
1
1
1
1
0
0
0
1
0
0
1
1
1


16
1
1
0
0
0
0
0
0
0
0
1
1
0


17
1
1
1
0
1
1
1
0
0
1
0
1
1


18
1
0
0
1
0
0
1
0
1
1
1
1
1


19
1
0
0
0
1
1
0
1
0
0
1
0
 1.

3. The method according to claim 1, wherein the modulated symbols are quaternary phase shift keying (QPSK) modulated symbols.

4. The method according to claim 1, wherein the modulated symbols are mapped to two slots of the PUCCH.

5. A wireless communications apparatus, comprising:
a memory for storing instructions; and
a processor coupled to the memory configured to execute the instructions to allow the apparatus to:
encode channel quality indicator (CQI) information to yield a sequence of coded CQI bits;
modulate the coded CQI bits to yield a sequence of modulated symbols;
map the modulated symbols to a physical uplink control channel (PUCCH); and
transmit the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with






  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,



 A is a positive integer greater than zero, and the matrix [Mi,n] is a matrix obtained by performing row permutation on the following matrix:




























1
1
0
0
0
0
0
0
0
0
1
1
0



1
1
1
0
0
0
0
0
0
1
1
1
0



1
0
0
1
0
0
1
0
1
1
1
1
1



1
0
1
1
0
0
0
0
1
0
1
1
1



1
1
1
1
0
0
0
1
0
0
1
1
1



1
1
0
0
1
0
1
1
1
0
1
1
1



1
0
1
0
1
0
1
0
1
1
1
1
1



1
0
0
1
1
0
0
1
1
0
1
1
1



1
1
0
1
1
0
0
1
0
1
1
1
1



1
0
1
1
1
0
1
0
0
1
1
1
1



1
0
1
0
0
1
1
1
0
1
1
1
1



1
1
1
0
0
1
1
0
1
0
1
1
1



1
0
0
1
0
1
0
1
1
1
1
1
1



1
1
0
1
0
1
0
1
0
1
1
1
1



1
0
0
0
1
1
0
1
0
0
1
0
1



1
1
0
0
1
1
1
1
0
1
1
0
1



1
1
1
0
1
1
1
0
0
1
0
1
1



1
0
0
1
1
1
0
0
1
0
0
1
1



1
1
0
1
1
1
1
1
0
0
0
0
0



1
0
0
0
0
1
1
0
0
0
0
0
0.

6. The wireless communications apparatus according to claim 5, wherein the matrix [Mi,n] is any one of the following:























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
0
1
0
1
0
1
0
1
1
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
0
1
0
0
1
0
1
1
1
1
1


4
1
1
1
0
0
0
0
0
0
1
1
1
0


5
1
0
0
1
1
1
0
0
1
0
0
1
1


6
1
0
1
0
0
1
1
1
0
1
1
1
1


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
0
0
1
1
0
1
0
0
1
0
1


11
1
0
1
1
0
0
0
0
1
0
1
1
1


12
1
1
0
1
1
0
0
1
0
1
1
1
1


13
1
1
0
0
1
1
1
1
0
1
1
0
1


14
1
1
1
0
0
1
I
0
1
0
1
1
1


15
1
0
0
1
0
1
0
1
1
1
1
1
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
0
0
1
1
0
1
1
1


18
1
1
1
1
0
0
0
1
0
0
1
1
1


19
1
0
0
0
0
1
1
0
0
0
0
0
 0,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
1
1
1
0
0
0
1
0
0
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
1
1
1
0
0
0
1
0
0
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
0
1
0
0
1
1
1
0
1
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
1
1
1
0
0
1
0
1
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
1
0
0
1
1
1
1
0
1
1
0
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
0
1
1
1
1
1
0
0
0
0
0


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
0
0
0
1
1
0
1
0
0
1
0
1


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
1
1
1
0
0
1
0
0
1
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
0
0
0
1
1
0
0
0
0
0
0


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
1
0
0
1
1
1
0
1
1
1
1


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
0
1
1
1
1
0
1
1
0
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
0
0
1
1
1
0
0
1
0
0
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
1
1
1
0
0
1
0
1
1


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
1
0
1
1
1
1
1
0
0
0
0
0


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
0
1
1
0
1
0
0
1
0
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
1
0
0
1
1
1
0
1
1
1
1


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
0
0
0
1
1
0
0
0
0
0
0


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
1, and
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
0
1
0
0
1
1
1
0
1
1
1
1


1
1
0
0
1
1
0
0
1
1
0
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
0
0
0
0
1
1
0
0
0
0
0
0


5
1
1
0
1
1
0
0
1
0
1
1
1
1


6
1
1
1
0
0
0
0
0
0
1
1
1
0


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
0
1
0
1
0
1
1
1
1
1


10
1
1
0
0
1
1
1
1
0
1
1
0
1


11
1
0
0
1
0
1
0
1
1
1
1
1
1


12
1
0
1
1
1
0
1
0
0
1
1
1
1


13
1
1
1
0
0
1
1
0
1
0
1
1
1


14
1
0
0
1
1
1
0
0
1
0
0
1
1


15
1
1
1
1
0
0
0
1
0
0
1
1
1


16
1
1
0
0
0
0
0
0
0
0
1
1
0


17
1
1
1
0
1
1
1
0
0
1
0
1
1


18
1
0
0
1
0
0
1
0
1
1
1
1
1


19
1
0
0
0
1
1
0
1
0
0
1
0
 1.

7. A non-transitory computer-readable medium, storing instructions, when executed by a processor, allow the processor to:
encode channel quality indicator (CQI) information to yield a sequence of coded CQI bits;
modulate the coded CQI bits to yield a sequence of modulated symbols;
map the modulated symbols to a physical uplink control channel (PUCCH); and
transmit the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with





  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,



 A is a positive integer greater than zero, and the matrix [Mi,n] is obtained by performing row permutation on the following matrix:




























1
1
0
0
0
0
0
0
0
0
1
1
0



1
1
1
0
0
0
0
0
0
1
1
1
0



1
0
0
1
0
0
1
0
1
1
1
1
1



1
0
1
1
0
0
0
0
1
0
1
1
1



1
1
1
1
0
0
0
1
0
0
1
1
1



1
1
0
0
1
0
1
1
1
0
1
1
1



1
0
1
0
1
0
1
0
1
1
1
1
1



1
0
0
1
1
0
0
1
1
0
1
1
1



1
1
0
1
1
0
0
1
0
1
1
1
1



1
0
1
1
1
0
1
0
0
1
1
1
1



1
0
1
0
0
1
1
1
0
1
1
1
1



1
1
1
0
0
1
1
0
1
0
1
1
1



1
0
0
1
0
1
0
1
1
1
1
1
1



1
1
0
1
0
1
0
1
0
1
1
1
1



1
0
0
0
1
1
0
1
0
0
1
0
1



1
1
0
0
1
1
1
1
0
1
1
0
1



1
1
1
0
1
1
1
0
0
1
0
1
1



1
0
0
1
1
1
0
0
1
0
0
1
1



1
1
0
1
1
1
1
1
0
0
0
0
0



1
0
0
0
0
1
1
0
0
0
0
0
0.

8. The computer-readable medium according to claim 7, wherein the matrix [Mi,n] is any one of the following:























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
0
1
0
1
0
1
0
1
1
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
0
1
0
0
1
0
1
1
1
1
1


4
1
1
1
0
0
0
0
0
0
1
1
1
0


5
1
0
0
1
1
1
0
0
1
0
0
1
1


6
1
0
1
0
0
1
1
1
0
1
1
1
1


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
0
0
1
1
0
1
0
0
1
0
1


11
1
0
1
1
0
0
0
0
1
0
1
1
1


12
1
1
0
1
1
0
0
1
0
1
1
1
1


13
1
1
0
0
1
1
1
1
0
1
1
0
1


14
1
1
1
0
0
1
1
0
1
0
1
1
1


15
1
0
0
1
0
1
0
1
1
1
1
1
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
0
0
1
1
0
1
1
1


18
1
1
1
1
0
0
0
1
0
0
1
1
1


19
1
0
0
0
0
1
1
0
0
0
0
0
 0,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
1
1
1
0
0
0
1
0
0
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
1
1
1
0
0
0
1
0
0
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
0
1
0
0
1
1
1
0
1
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
1
1
1
0
0
1
0
1
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
1
0
0
1
1
1
1
0
1
1
0
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
0
1
1
1
1
1
0
0
0
0
0


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
0
0
0
1
1
0
1
0
0
1
0
1


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
1
1
1
0
0
1
0
0
1
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
0
0
0
1
1
0
0
0
0
0
0


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
1
0
0
1
1
1
0
1
1
1
1


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
0
1
1
1
1
0
1
1
0
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
0
0
1
1
1
0
0
1
0
0
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
1
1
1
0
0
1
0
1
1


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
1
0
1
1
1
1
1
0
0
0
0
0


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
0
1
1
0
1
0
0
1
0
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
1
0
0
1
1
1
0
1
1
1
1


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
0
0
0
1
1
0
0
0
0
0
0


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
1, and
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
0
1
0
0
1
1
1
0
1
1
1
1


1
1
0
0
1
1
0
0
1
1
0
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
0
0
0
0
1
1
0
0
0
0
0
0


5
1
1
0
1
1
0
0
1
0
1
1
1
1


6
1
1
1
0
0
0
0
0
0
1
1
1
0


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
0
1
0
1
0
1
1
1
1
1


10
1
1
0
0
1
1
1
1
0
1
1
0
1


11
1
0
0
1
0
1
0
1
1
1
1
1
1


12
1
0
1
1
1
0
1
0
0
1
1
1
1


13
1
1
1
0
0
1
1
0
1
0
1
1
1


14
1
0
0
1
1
1
0
0
1
0
0
1
1


15
1
1
1
1
0
0
0
1
0
0
1
1
1


16
1
1
0
0
0
0
0
0
0
0
1
1
0


17
1
1
1
0
1
1
1
0
0
1
0
1
1


18
1
0
0
1
0
0
1
0
1
1
1
1
1


19
1
0
0
0
1
1
0
1
0
0
1
0
 1.

9. A wireless communications apparatus, comprising:
a processor configured to:
encode channel quality indicator (CQI) information to yield a sequence of coded CQI bits;
modulate the coded CQI bits to yield a sequence of modulated symbols;
map the modulated symbols to a physical uplink control channel (PUCCH); and
transmit the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with






  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,




 A is a positive integer greater than zero, and [Mi,n] is a matrix obtained by performing row permutation on the following matrix:





























1
1
0
0
0
0
0
0
0
0
1
1
0



1
1
1
0
0
0
0
0
0
1
1
1
0



1
0
0
1
0
0
1
0
1
1
1
1
1



1
0
1
1
0
0
0
0
1
0
1
1
1



1
1
1
1
0
0
0
1
0
0
1
1
1



1
1
0
0
1
0
1
1
1
0
1
1
1



1
0
1
0
1
0
1
0
1
1
1
1
1



1
0
0
1
1
0
0
1
1
0
1
1
1



1
1
0
1
1
0
0
1
0
1
1
1
1



1
0
1
1
1
0
1
0
0
1
1
1
1



1
0
1
0
0
1
1
1
0
1
1
1
1



1
1
1
0
0
1
1
0
1
0
1
1
1



1
0
0
1
0
1
0
1
1
1
1
1
1



1
1
0
1
0
1
0
1
0
1
1
1
1



1
0
0
0
1
1
0
1
0
0
1
0
1



1
1
0
0
1
1
1
1
0
1
1
0
1



1
1
1
0
1
1
1
0
0
1
0
1
1



1
0
0
1
1
1
0
0
1
0
0
1
1



1
1
0
1
1
1
1
1
0
0
0
0
0



1
0
0
0
0
1
1
0
0
0
0
0
0.

10. The wireless communications apparatus according to claim 9, wherein the matrix [Mi,n] is any one of the following:























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
0
1
0
1
0
1
0
1
1
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
0
1
0
0
1
0
1
1
1
1
1


4
1
1
1
0
0
0
0
0
0
1
1
1
0


5
1
0
0
1
1
1
0
0
1
0
0
1
1


6
1
0
1
0
0
1
1
1
0
1
1
1
1


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
0
0
1
1
0
1
0
0
1
0
1


11
1
0
1
1
0
0
0
0
1
0
1
1
1


12
1
1
0
1
1
0
0
1
0
1
1
1
1


13
1
1
0
0
1
1
1
1
0
1
1
0
1


14
1
1
1
0
0
1
1
0
1
0
1
1
1


15
1
0
0
1
0
1
0
1
1
1
1
1
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
0
0
1
1
0
1
1
1


18
1
1
1
1
0
0
0
1
0
0
1
1
1


19
1
0
0
0
0
1
1
0
0
0
0
0
 0,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
1
1
1
0
0
0
1
0
0
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
1
1
1
1
1
0
0
0
0
0


2
1
0
0
0
1
1
0
1
0
0
1
0
1


3
1
0
1
0
1
0
1
0
1
1
1
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
0
0
0
0
0
1
1
1
0


6
1
1
0
1
1
0
0
1
0
1
1
1
1


7
1
1
1
0
0
1
1
0
1
0
1
1
1


8
1
0
1
1
0
0
0
0
1
0
1
1
1


9
1
1
0
0
1
1
1
1
0
1
1
0
1


10
1
1
1
1
0
0
0
1
0
0
1
1
1


11
1
0
0
1
1
0
0
1
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
1
0
1
1
1
0
0
1
0
1
1


14
1
0
1
0
0
1
1
1
0
1
1
1
1


15
1
0
0
1
1
1
0
0
1
0
0
1
1


16
1
1
0
0
1
0
1
1
1
0
1
1
1


17
1
0
1
1
1
0
1
0
0
1
1
1
1


18
1
0
0
0
0
1
1
0
0
0
0
0
0


19
1
1
0
1
0
1
0
1
0
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
1
1
1
0
0
1
0
1
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
1
0
0
1
1
1
1
0
1
1
0
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
0
1
1
1
1
1
0
0
0
0
0


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
0
0
0
1
1
0
1
0
0
1
0
1


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
1
1
1
0
0
1
0
0
1
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
0
0
0
1
1
0
0
0
0
0
0


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
1
0
0
1
1
1
0
1
1
1
1


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
 1,
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
0
0
1
1
1
1
0
1
1
0
1


2
1
1
1
0
0
0
0
0
0
1
1
1
0


3
1
0
0
1
1
1
0
0
1
0
0
1
1


4
1
0
0
1
0
0
1
0
1
1
1
1
1


5
1
1
1
0
1
1
1
0
0
1
0
1
1


6
1
0
1
1
0
0
0
0
1
0
1
1
1


7
1
1
0
1
1
1
1
1
0
0
0
0
0


8
1
1
1
1
0
0
0
1
0
0
1
1
1


9
1
0
0
0
1
1
0
1
0
0
1
0
1


10
1
1
0
0
1
0
1
1
1
0
1
1
1


11
1
0
1
0
0
1
1
1
0
1
1
1
1


12
1
0
1
0
1
0
1
0
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
1
1
0
0
1
1
0
1
1
1


15
1
1
1
0
0
1
1
0
1
0
1
1
1


16
1
1
0
1
1
0
0
1
0
1
1
1
1


17
1
0
0
0
0
1
1
0
0
0
0
0
0


18
1
0
1
1
1
0
1
0
0
1
1
1
1


19
1
0
0
1
0
1
0
1
1
1
1
1
1, and
































i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
0
1
0
0
1
1
1
0
1
1
1
1


1
1
0
0
1
1
0
0
1
1
0
1
1
1


2
1
1
0
1
1
1
1
1
0
0
0
0
0


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
0
0
0
0
1
1
0
0
0
0
0
0


5
1
1
0
1
1
0
0
1
0
1
1
1
1


6
1
1
1
0
0
0
0
0
0
1
1
1
0


7
1
1
0
0
1
0
1
1
1
0
1
1
1


8
1
1
0
1
0
1
0
1
0
1
1
1
1


9
1
0
1
0
1
0
1
0
1
1
1
1
1


10
1
1
0
0
1
1
1
1
0
1
1
0
1


11
1
0
0
1
0
1
0
1
1
1
1
1
1


12
1
0
1
1
1
0
1
0
0
1
1
1
1


13
1
1
1
0
0
1
1
0
1
0
1
1
1


14
1
0
0
1
1
1
0
0
1
0
0
1
1


15
1
1
1
1
0
0
0
1
0
0
1
1
1


16
1
1
0
0
0
0
0
0
0
0
1
1
0


17
1
1
1
0
1
1
1
0
0
1
0
1
1


18
1
0
0
1
0
0
1
0
1
1
1
1
1


19
1
0
0
0
1
1
0
1
0
0
1
0
 1.

11. A method that facilitates sending channel quality indicator (CQI) in a wireless communication environment, comprising:
encoding CQI information to yield a sequence of coded CQI bits with a particular order, wherein the order is denoted as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
interleaving the coded CQI bits to reorder the sequence of coded CQI bits, wherein the order of the reordered sequence is [0, 18, 14, 6, 2, 1, 8, 11, 3, 15, 10, 7, 12, 16, 4, 17, 5, 9, 19, 13];
modulating the reordered coded CQI bits to yield a sequence of modulated symbols;
mapping the modulated symbols to a physical uplink control channel (PUCCH); and
transmitting the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with





  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,



 A is a positive integer greater than zero, and[Mi,n] is the following matrix:
























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
0
0
0
0
0
1
1
1
0


2
1
0
0
1
0
0
1
0
1
1
1
1
1


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
1
1
1
0
0
0
1
0
0
1
1
1


5
1
1
0
0
1
0
1
1
1
0
1
1
1


6
1
0
1
0
1
0
1
0
1
1
1
1
1


7
1
0
0
1
1
0
0
1
1
0
1
1
1


8
1
1
0
1
1
0
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
1
1
0
0
1
1
0
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
0
1
1
0
1
0
0
1
0
1


15
1
1
0
0
1
1
1
1
0
1
1
0
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
1
0
0
1
0
0
1
1


18
1
1
0
1
1
1
1
1
0
0
0
0
0


19
1
0
0
0
0
1
1
0
0
0
0
0
 0.

12. A wireless communications apparatus, comprising:
a memory for storing instructions; and
a processor coupled to the memory configured to execute the instructions to allow the apparatus to:
encode channel quality indicator (CQI) information to yield a sequence of coded CQI bits with a particular order, wherein the order is denoted as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
interleave the coded CQI bits to reorder the sequence of coded CQI bits, wherein the order of the reordered sequence is [0, 18, 14, 6, 2, 1, 8, 11, 3, 15, 10, 7, 12, 16, 4, 17, 5, 9, 19, 13];
modulate the reordered coded CQI bits to yield a sequence of modulated symbols;
map the modulated symbols to a physical uplink control channel (PUCCH); and
transmit the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with






  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,




 A is a positive integer greater than zero, and [Mi,n] is the following matrix:





























1
1
0
0
0
0
0
0
0
0
1
1
0



1
1
1
0
0
0
0
0
0
1
1
1
0



1
0
0
1
0
0
1
0
1
1
1
1
1



1
0
1
1
0
0
0
0
1
0
1
1
1



1
1
1
1
0
0
0
1
0
0
1
1
1



1
1
0
0
1
0
1
1
1
0
1
1
1



1
0
1
0
1
0
1
0
1
1
1
1
1



1
0
0
1
1
0
0
1
1
0
1
1
1



1
1
0
1
1
0
0
1
0
1
1
1
1



1
0
1
1
1
0
1
0
0
1
1
1
1



1
0
1
0
0
1
1
1
0
1
1
1
1



1
1
1
0
0
1
1
0
1
0
1
1
1



1
0
0
1
0
1
0
1
1
1
1
1
1



1
1
0
1
0
1
0
1
0
1
1
1
1



1
0
0
0
1
1
0
1
0
0
1
0
1



1
1
0
0
1
1
1
1
0
1
1
0
1



1
1
1
0
1
1
1
0
0
1
0
1
1



1
0
0
1
1
1
0
0
1
0
0
1
1



1
1
0
1
1
1
1
1
0
0
0
0
0



1
0
0
0
0
1
1
0
0
0
0
0
0.

13. A non-transitory computer-readable medium, storing instructions, when executed by a processor, allow the processor to:
encode channel quality indicator (CQI) information to yield a sequence of coded CQI bits with a particular order, wherein the order is denoted as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
interleave the coded CQI bits to reorder the sequence of coded CQI bits, wherein the order of the reordered sequence is [0, 18, 14, 6, 2, 1, 8, 11, 3, 15, 10, 7, 12, 16, 4, 17, 5, 9, 19, 13];
modulate the reordered coded CQI bits to yield a sequence of modulated symbols;
map the modulated symbols to a physical uplink control channel (PUCCH); and
transmit the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with





  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,



 A is a positive integer greater than zero, and [Mi,n] is the following matrix:
























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
0
0
0
0
0
1
1
1
0


2
1
0
0
1
0
0
1
0
1
1
1
1
1


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
1
1
1
0
0
0
1
0
0
1
1
1


5
1
1
0
0
1
0
1
1
1
0
1
1
1


6
1
0
1
0
1
0
1
0
1
1
1
1
1


7
1
0
0
1
1
0
0
1
1
0
1
1
1


8
1
1
0
1
1
0
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
1
1
0
0
1
1
0
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
0
1
1
0
1
0
0
1
0
1


15
1
1
0
0
1
1
1
1
0
1
1
0
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
1
0
0
1
0
0
1
1


18
1
1
0
1
1
1
1
1
0
0
0
0
0


19
1
0
0
0
0
1
1
0
0
0
0
0
 0.

14. A wireless communications apparatus, comprising:
a processor configured to:
encode channel quality indicator (CQI) information to yield a sequence of coded CQI bits with a particular order, wherein the order is denoted as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
interleave the coded CQI bits to reorder the sequence of coded CQI bits, wherein the order of the reordered sequence is [0, 18, 14, 6, 2, 1, 8, 11, 3, 15, 10, 7, 12, 16, 4, 17, 5, 9, 19, 13];
modulate the reordered coded CQI bits to yield a sequence of modulated symbols;

map the modulated symbols to a physical uplink control channel (PUCCH); and
transmit the CQI information to a base station via the PUCCH, wherein the CQI information is denoted by an, the coded CQI bits are denoted by bi , where i =0, 1, 2, . . . , B-1, B=20, with






  
    
      b
      i
    
    =
    
      
        ∑
        
          n
          =
          0
        
        
          A
          -
          1
        
      
      ⁢
      
        
          (
          
            
              a
              n
            
            ·
            
              M
              
                i
                ,
                n
              
            
          
          )
        
        ⁢
        mod
        ⁢
        
          
        
        ⁢
        2
      
    
  
  ,




 A is a positive integer greater than zero and [Mi,n] is the following matrix:

























i
Mi,0
Mi,1
Mi,2
Mi,3
Mi,4
Mi,5
Mi,6
Mi,7
Mi,8
Mi,9
Mi,10
Mi,11
Mi,12




























0
1
1
0
0
0
0
0
0
0
0
1
1
0


1
1
1
1
0
0
0
0
0
0
1
1
1
0


2
1
0
0
1
0
0
1
0
1
1
1
1
1


3
1
0
1
1
0
0
0
0
1
0
1
1
1


4
1
1
1
1
0
0
0
1
0
0
1
1
1


5
1
1
0
0
1
0
1
1
1
0
1
1
1


6
1
0
1
0
1
0
1
0
1
1
1
1
1


7
1
0
0
1
1
0
0
1
1
0
1
1
1


8
1
1
0
1
1
0
0
1
0
1
1
1
1


9
1
0
1
1
1
0
1
0
0
1
1
1
1


10
1
0
1
0
0
1
1
1
0
1
1
1
1


11
1
1
1
0
0
1
1
0
1
0
1
1
1


12
1
0
0
1
0
1
0
1
1
1
1
1
1


13
1
1
0
1
0
1
0
1
0
1
1
1
1


14
1
0
0
0
1
1
0
1
0
0
1
0
1


15
1
1
0
0
1
1
1
1
0
1
1
0
1


16
1
1
1
0
1
1
1
0
0
1
0
1
1


17
1
0
0
1
1
1
0
0
1
0
0
1
1


18
1
1
0
1
1
1
1
1
0
0
0
0
0


19
1
0
0
0
0
1
1
0
0
0
0
0
0.