Patent Publication Number: US-2022216885-A1

Title: System and method for processing control information

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of U.S. patent application Ser. No. 16/861,990, filed on Apr. 29, 2020, which is a continuation of PCT/CN2017/111756, filed on Nov. 17, 2017, each of which is incorporated by reference herein in its entirety. 
    
    
     TECHNICAL FIELD 
     The disclosure relates generally to wireless communications and, more particularly, to systems and methods for processing a signal containing control information. 
     BACKGROUND 
     In a communication system, a transmitter may encode a packet of data, also known as information bits, to obtain encoded bits, interleave the encoded bits, and map the interleaved bits to modulation symbols. The transmitter may then process and transmit the modulation symbols via a communication channel. The communication channel may distort the data transmission with a particular channel response and further degrade the data transmission with noise and interference. A receiver may obtain received symbols, which may be distorted and degraded versions of the transmitted modulation symbols. The receiver may process the received symbols to recover the transmitted information bits. 
     The encoding by the transmitter may allow the receiver to reliably recover the transmitted information bits with the degraded received symbols. The transmitter may perform encoding based on a Forward Error Correction (FEC) code that generates redundancy in the code bits, which is typically associated with a Hybrid Automatic Repeat Request (HARQ) technique. The receiver may utilize the redundancy to improve the likelihood of recovering the transmitted information bits. 
     Various types of FEC codes may be used for encoding. Some common types of FEC codes include convolutional code, Turbo code, and Low Density Parity Check (LDPC) code. A convolutional code or a Turbo code can encode a packet of k information bits and generate a coded packet of approximately r times k code bits, where 1/r is the code rate of the convolutional or Turbo code. A convolutional code can readily encode a packet of any size by passing each information bit through an encoder that can operate on one information bit at a time. A Turbo code can also support different packet sizes by employing two constituent encoders that can operate on one information bit at a time and a code interleaver that can support different packet sizes. An LDPC code may have better performance than convolutional and Turbo codes under certain operating conditions. An example of the LDPC code, typically known as a quasi-cyclic LDPC (QC-LDPC) code, that presents a constructive characteristic thereby allowing low-complexity encoding has gained particular attention. 
     In a New Radio (NR) communication system, when the transmitter and receiver respectively use the QC-LDPC code for encoding and decoding information bits, two predefined base graphs (BG&#39;s), typically known as BG1 (Base Graph 1) and BG2 (Base Graph 2), would be used, wherein the BG1 and BG2 correspond to respective base matrixes. For example, the transmitter selects one of BG1 and BG2 to be used based on various conditions (e.g., a code rate, a modulation order, etc.), lifts the selected BG to retrieve a parity check matrix, and uses the retrieved parity check matrix to encode the information bits to obtain an LDPC codeword. The receiver, on the other end, generally follows the similar operations (e.g., using one of BG1 and BG2) to decode and obtain the information bits. 
     In some cases, however, the transmitter and receiver may not use a same BG to encode and decode the information bits, respectively. For example, due to distortion or delay of the communication channel, when the receiver misses first transmitted information bits, the receiver may mistakenly treat retransmitted information bits as the first transmitted information bits. As such, the receiver may determine a wrong BG to decode the information bits, which may wrongly decode the information bits. Thus, existing systems and methods to encode and decode information bits using the QC-LDPC code are not entirely satisfactory. 
     SUMMARY OF THE INVENTION 
     The exemplary embodiments disclosed herein are directed to solving the issues relating to one or more of the problems presented in the prior art, as well as providing additional features that will become readily apparent by reference to the following detailed description when taken in conjunction with the accompany drawings. In accordance with various embodiments, exemplary systems, methods, devices and computer program products are disclosed herein. It is understood, however, that these embodiments are presented by way of example and not limitation, and it will be apparent to those of ordinary skill in the art who read the present disclosure that various modifications to the disclosed embodiments can be made while remaining within the scope of the invention. 
     In one embodiment, a method includes: determining a redundancy version and a new data indicator indicated by control information; determining a base graph of a low density parity check code based on which of a plurality of predefined conditions the redundancy version, and/or the new data indicator satisfy; and sending a signal comprising information bits that are encoded based on the determined base graph of the low density parity check code. 
     In yet another embodiment, a method includes: receiving control information indicative of a redundancy version and a current logic state of a new data indicator; determining a base graph of a low density parity check code based on which of a plurality of predefined conditions the redundancy version, and/or the new data indicator satisfy; and retrieving information bits from a received signal using the determined base graph of the low density parity check code. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various exemplary embodiments of the invention are described in detail below with reference to the following Figures. The drawings are provided for purposes of illustration only and merely depict exemplary embodiments of the invention to facilitate the reader&#39;s understanding of the invention. Therefore, the drawings should not be considered limiting of the breadth, scope, or applicability of the invention. It should be noted that for clarity and ease of illustration these drawings are not necessarily drawn to scale. 
         FIG. 1  illustrates an exemplary cellular communication network in which techniques disclosed herein may be implemented, in accordance with an embodiment of the present disclosure. 
         FIG. 2  illustrates block diagrams an exemplary base station and a user equipment device, in accordance with some embodiments of the present disclosure. 
         FIG. 3  illustrates a flow chart of an exemplary method to transmit information bits encoded by a QC-LDPC code, in accordance with some embodiments of the present disclosure. 
         FIG. 4  illustrates an exemplary diagram showing how a base graph  1  and a base graph each corresponds to a transport block size and a code rate, in accordance with some embodiments of the present disclosure. 
         FIG. 5  illustrates a flow chart of an exemplary method to retrieve information bits from a signal encoded by a QC-LDPC code, in accordance with some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Various exemplary embodiments of the invention are described below with reference to the accompanying figures to enable a person of ordinary skill in the art to make and use the invention. As would be apparent to those of ordinary skill in the art, after reading the present disclosure, various changes or modifications to the examples described herein can be made without departing from the scope of the invention. Thus, the present invention is not limited to the exemplary embodiments and applications described and illustrated herein. Additionally, the specific order or hierarchy of steps in the methods disclosed herein are merely exemplary approaches. Based upon design preferences, the specific order or hierarchy of steps of the disclosed methods or processes can be re-arranged while remaining within the scope of the present invention. Thus, those of ordinary skill in the art will understand that the methods and techniques disclosed herein present various steps or acts in a sample order, and the invention is not limited to the specific order or hierarchy presented unless expressly stated otherwise. 
       FIG. 1  illustrates an exemplary wireless communication network  100  in which techniques disclosed herein may be implemented, in accordance with an embodiment of the present disclosure. The exemplary communication network  100  includes a base station  102  (hereinafter “BS  102 ”) and a user equipment device  104  (hereinafter “UE  104 ”) that can communicate with each other via a communication link  110  (e.g., a wireless communication channel), and a cluster of notional cells  126 ,  130 ,  132 ,  134 ,  136 ,  138  and  140  overlaying a geographical area  101 . In  FIG. 1 , the BS  102  and UE  104  are contained within the geographic boundary of cell  126 . Each of the other cells  130 ,  132 ,  134 ,  136 ,  138  and  140  may include at least one base station operating at its allocated bandwidth to provide adequate radio coverage to its intended users. For example, the base station  102  may operate at an allocated channel transmission bandwidth to provide adequate coverage to the UE  104 . The base station  102  and the UE  104  may communicate via a downlink radio frame  118 , and an uplink radio frame  124  respectively. Each radio frame  118 / 124  may be further divided into sub-frames  120 / 127  which may include data symbols  122 / 128 . In the present disclosure, the BS  102  and UE  104  are described herein as non-limiting examples of “communication nodes,” generally, which can practice the methods disclosed herein. Such communication nodes may be capable of wireless and/or wired communications, in accordance with various embodiments of the invention. 
       FIG. 2  illustrates a block diagram of an exemplary wireless communication system  200  for transmitting and receiving wireless communication signals, e.g., OFDM/OFDMA signals, in accordance with some embodiments of the invention. The system  200  may include components and elements configured to support known or conventional operating features that need not be described in detail herein. In one exemplary embodiment, system  200  can be used to transmit and receive data symbols in a wireless communication environment such as the wireless communication environment  100  of  FIG. 1 , as described above. 
     System  200  generally includes a base station  202  (hereinafter “BS  202 ”) and a user equipment device  204  (hereinafter “UE  204 ”). The BS  202  includes a BS (base station) transceiver module  210 , a BS antenna  212 , a BS processor module  214 , a BS memory module  216 , and a network communication module  218 , each module being coupled and interconnected with one another as necessary via a data communication bus  220 . The UE  204  includes a UE (user equipment) transceiver module  230 , a UE antenna  232 , a UE memory module  234 , and a UE processor module  236 , each module being coupled and interconnected with one another as necessary via a data communication bus  240 . The BS  202  communicates with the UE  204  via a communication channel  250 , which can be any wireless channel or other medium known in the art suitable for transmission of data as described herein. 
     As would be understood by persons of ordinary skill in the art, system  200  may further include any number of modules other than the modules shown in  FIG. 2 . Those skilled in the art will understand that the various illustrative blocks, modules, circuits, and processing logic described in connection with the embodiments disclosed herein may be implemented in hardware, computer-readable software, firmware, or any practical combination thereof. To clearly illustrate this interchangeability and compatibility of hardware, firmware, and software, various illustrative components, blocks, modules, circuits, and steps are described generally in terms of their functionality. Whether such functionality is implemented as hardware, firmware, or software depends upon the particular application and design constraints imposed on the overall system. Those familiar with the concepts described herein may implement such functionality in a suitable manner for each particular application, but such implementation decisions should not be interpreted as limiting the scope of the present invention. 
     In accordance with some embodiments, the UE transceiver  230  may be referred to herein as an “uplink” transceiver  230  that includes a RF transmitter and receiver circuitry that are each coupled to the antenna  232 . A duplex switch (not shown) may alternatively couple the uplink transmitter or receiver to the uplink antenna in time duplex fashion. Similarly, in accordance with some embodiments, the BS transceiver  210  may be referred to herein as a “downlink” transceiver  210  that includes RF transmitter and receiver circuitry that are each coupled to the antenna  212 . A downlink duplex switch may alternatively couple the downlink transmitter or receiver to the downlink antenna  212  in time duplex fashion. The operations of the two transceivers  210  and  230  are coordinated in time such that the uplink receiver is coupled to the uplink antenna  232  for reception of transmissions over the wireless transmission link  250  at the same time that the downlink transmitter is coupled to the downlink antenna  212 . Preferably there is close time synchronization with only a minimal guard time between changes in duplex direction. 
     The UE transceiver  230  and the base station transceiver  210  are configured to communicate via the wireless data communication link  250 , and cooperate with a suitably configured RF antenna arrangement  212 / 232  that can support a particular wireless communication protocol and modulation scheme. In some exemplary embodiments, the UE transceiver  608  and the base station transceiver  602  are configured to support industry standards such as the Long Term Evolution (LTE) and emerging 5G standards, and the like. It is understood, however, that the invention is not necessarily limited in application to a particular standard and associated protocols. Rather, the UE transceiver  230  and the base station transceiver  210  may be configured to support alternate, or additional, wireless data communication protocols, including future standards or variations thereof. 
     In accordance with various embodiments, the BS  202  may be an evolved node B (eNB), a serving eNB, a target eNB, a femto station, or a pico station, for example. In some embodiments, the UE  204  may be embodied in various types of user devices such as a mobile phone, a smart phone, a personal digital assistant (PDA), tablet, laptop computer, wearable computing device, etc. The processor modules  214  and  236  may be implemented, or realized, with a general purpose processor, a content addressable memory, a digital signal processor, an application specific integrated circuit, a field programmable gate array, any suitable programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof, designed to perform the functions described herein. In this manner, a processor may be realized as a microprocessor, a controller, a microcontroller, a state machine, or the like. A processor may also be implemented as a combination of computing devices, e.g., a combination of a digital signal processor and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a digital signal processor core, or any other such configuration. 
     Furthermore, the steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in firmware, in a software module executed by processor modules  214  and  236 , respectively, or in any practical combination thereof. The memory modules  216  and  234  may be realized as RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. In this regard, memory modules  216  and  234  may be coupled to the processor modules  210  and  230 , respectively, such that the processors modules  210  and  230  can read information from, and write information to, memory modules  216  and  234 , respectively. The memory modules  216  and  234  may also be integrated into their respective processor modules  210  and  230 . In some embodiments, the memory modules  216  and  234  may each include a cache memory for storing temporary variables or other intermediate information during execution of instructions to be executed by processor modules  210  and  230 , respectively. Memory modules  216  and  234  may also each include non-volatile memory for storing instructions to be executed by the processor modules  210  and  230 , respectively. 
     The network communication module  218  generally represents the hardware, software, firmware, processing logic, and/or other components of the base station  202  that enable bi-directional communication between base station transceiver  602  and other network components and communication nodes configured to communication with the base station  202 . For example, network communication module  218  may be configured to support internet or WiMAX traffic. In a typical deployment, without limitation, network communication module  218  provides an 802.3 Ethernet interface such that base station transceiver  210  can communicate with a conventional Ethernet based computer network. In this manner, the network communication module  218  may include a physical interface for connection to the computer network (e.g., Mobile Switching Center (MSC)). The terms “configured for,” “configured to” and conjugations thereof, as used herein with respect to a specified operation or function, refer to a device, component, circuit, structure, machine, signal, etc., that is physically constructed, programmed, formatted and/or arranged to perform the specified operation or function. 
     Referring again to  FIG. 1 , as discussed above, when a transmitter (e.g., the BS  102 ) uses a BG (base graph) of a QC-LDPC code to encode information bits and transmit to a receiver (e.g., the UE  104 ), the UE  104  may mistakenly use a wrong (e.g., inconsistent) BG to decode the information bits, wherein such encoded information bits has been retransmitted as the UE  104  misses a first transmission. In this regard, the present disclosure provides various embodiments of systems and methods to use downlink control information (DCI), which is transmitted from a BS and received by a UE, to cause the BS and UE to use a consistent BG to encode and decode information bits, respectively. More specifically, in accordance with some embodiments, the BS and UE may respectively use various information contained in the DCI to accurately determine the correct BG by checking whether the various information satisfies either a first or second predefined condition. 
       FIG. 3  illustrates a flow chart of an exemplary method  300  performed by a BS to transmit information bits encoded by a QC-LDPC code, in accordance with some embodiments. The illustrated embodiment of the method  300  is merely an example. Therefore, it should be understood that any of a variety of operations may be omitted, re-sequenced, and/or added while remaining within the scope of the present disclosure. 
     In some embodiments, the method  300  starts with operation  302  in which downlink control information (DCI) is provided. According to some embodiments, the DCI includes various information such as, for example, a modulation and coding scheme (MCS) index (hereinafter “I MCS ”), a new data indicator (hereinafter “NDI”), a redundancy version (hereinafter “RV”), a number of physical resource blocks (hereinafter “PRB”), etc. The RV as used herein is typically referred to redundancy bits when HARQ is used to retransmit information bits. Next, the method  300  proceeds to determination operation  304  in which the BS determines whether a first or second predefined condition is satisfied. In some embodiments, the first predefined condition includes at least one of the following: whether the RV is equal to RV0, whether a current logic state of the NDI is equal to a logic “0,” and whether the NDI presents a transition to a different logic state (e.g., whether the NDI has been toggled to a value different from a previously transmitted value, which indicates a first transmission); and the second predefined condition includes at least one of the following: whether the RV is equal to RV1, RV2, or RV3, whether a current logic state of the NDI is equal to a logic “1,” and whether the NDI lacks a transition to a different logic state (e.g., whether the NDI has not been toggled to a value different from a previously transmitted value, which indicates a retransmission). In some embodiments, the presence of the NDI transition is typically referred to as a “toggled NDI,” and the lack of the NDI transition is typically referred to as a “non-toggled NDI.” When the first predefined condition is satisfied, the method  300  proceeds to operation  306 ; and when the second predefined condition is satisfied, the method  300  proceeds to operation  308 . In some embodiments, in operation  306 , the BS is configured to process the various information contained in the DCI to select one from the above-mentioned BG1 and BG2 that are predefined by the QC-LDPC code; and on the other hand, in operation  308 , the BS is configured to use the various information contained in the DCI to directly select one from the above-mentioned BG1 and BG2 (i.e., no further processing on the various information). After the BG is selected either at operation  306  or  308 , the method  300  continues to operation  310  in which the BS uses the selected BG to encode information bits. In some embodiments, in operation  310 , in addition to at least one encoding process using the selected BG being performed, one or more further steps (e.g., a rate matching step, a interleaving step, a symbol modulation step, etc.) may be performed after the information bits have been encoded. The method  300  continues to operation  312  in which the BS sends the encoded information bits. As mentioned above, since one or more further steps are performed after the information bits are encoded, in some embodiments, the BS may send the encoded information bits as one or more symbols. 
     In some embodiments, when the first predefined condition is satisfied (operation  306 ), i.e., the RV being equal to RV0, the current logic state of the NDI being equal to a logic 0, and/or the NDI transitioning to a different logic state, the BS uses the I MCS  (indicated by the DCI) to determine a modulation order (Q m ) and a code rate (R). More specifically, the BS may refer to a predefined table (e.g., Table 1 as shown below) to determine which modulation order and code rate that the I MCS  corresponds to. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 Code Rate R × 
               
               
                 I MCS   
                 Q m   
                 [1024] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 2 
                 121 
               
               
                 1 
                 2 
                 171 
               
               
                 2 
                 2 
                 120 
               
               
                 3 
                 2 
                 156.5 
               
               
                 4 
                 2 
                 193 
               
               
                 5 
                 2 
                 250.5 
               
               
                 6 
                 2 
                 308 
               
               
                 7 
                 2 
                 378.5 
               
               
                 8 
                 2 
                 449 
               
               
                 9 
                 2 
                 525.5 
               
               
                 10 
                 4 
                 602 
               
               
                 11 
                 4 
                 679 
               
               
                 12 
                 4 
                 756 
               
               
                 13 
                 4 
                 378 
               
               
                 14 
                 4 
                 434 
               
               
                 15 
                 4 
                 490 
               
               
                 16 
                 4 
                 553 
               
               
                 17 
                 6 
                 616 
               
               
                 18 
                 6 
                 657.5 
               
               
                 19 
                 6 
                 699 
               
               
                 20 
                 6 
                 774.75 
               
               
                 21 
                 6 
                 850.5 
               
               
                 22 
                 6 
                 924.75 
               
               
                 23 
                 6 
                 616.5 
               
               
                 24 
                 6 
                 666 
               
               
                 25 
                 6 
                 719 
               
               
                 26 
                 6 
                 772 
               
               
                 27 
                 6 
                 822.5 
               
               
                 28 
                 6 
                 873 
               
               
                 29 
                 2 
                 reserved 
               
               
                 30 
                 4 
               
               
                 31 
                 6 
               
               
                   
               
            
           
         
       
     
     As shown in Table 1, there are a total of 32 different values of I MCS . In some embodiments, such 32 different values of I MCS  may be grouped into a plurality of subsets: I MCS Set0 and I MCS Set1. For example, I MCS Set0 may be presented as I MCS Set0={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28} and I MCS Set1 may be presented as I MCS Set1={29, 30, 31}. It is noted that I MCS Set0 and I MCS Set1 have no intersection, and I MCS Set0 and I MCS Set1 form a union. In some embodiments, I MCS Set1 may be grouped for retransmission data or for reserved use. 
     According to I MCS  (indicated by the DCI), a single combination of the modulation order (Q m ) and code rate (R) can be determined. Accordingly, the BS uses the PRB (also indicated by the DCI) to estimate a number of Resource Elements (N RE ), and determine a layer parameter “v,” wherein such v is synonymous with “stream.” In particular, for a Multiple-Input-Multiple-Output (MIMO) BS, at least two layers (i.e., v=2) may be used, and such v is always less than or equal to a number of antennas of the MIMO BS. In some embodiments, the BS can use Q m , R, N RE , and v to determine a transport block size (TBS). More specifically, TBS=floor (TBS′/8)×8, wherein TBS&#39;=N RE ×v×Q m ×R, and “floor” represents a floor function [x] that gives the largest integer less than or equal to x. After the BS estimates TBS, in some embodiments, the BS can use R and TBS to select either BG1 or BG2, which will be discussed below with respect to  FIG. 4 . 
       FIG. 4  illustrates an exemplary diagram showing how BG1 and BG2 each corresponds to the TBS and R, in accordance with various embodiments. As shown in  FIG. 4 , the BS may determine the BG to be used as BG1 when estimated TBS is between 292 and 3824 and estimated R is greater than ⅔, or when estimated TBS is greater than 3824 and estimated R is greater than ¼; and the BS may determine the BG to be used as BG2 when estimated TBS is less than 292, when estimated TBS is between 292 and 3824 and estimated R is less than ⅔, or when estimated TBS is greater than 3824 and estimated R is less than ¼. 
     On the other hand, in some embodiments, when the second predefined condition is satisfied (operation  308 ), i.e., the RV being equal to RV1, RV2, or RV3, the current logic state of the NDI being equal to a logic 1, and/or the NDI not transitioning to a different logic state, the BS uses the I MCS  (indicated by the DCI) to directly select either BG1 or BG2. 
     In an embodiment, the BS groups the 32 different values of I MCS  into a plurality of subsets: I MCS Set2, I MCS Set3, and I MCS Set4. When the I MCS  (indicated by the DCI) belongs to I MCS Set2, the BS selects the BG1; and when the I MCS  (indicated by the DCI) belongs to I MCS Set3, the BS selects the BG2, wherein I MCS Set4 may be grouped for retransmission data or for reserved use. 
     In an example, I MCS Set2 may be grouped as each I MCS  in I MCS Set2 being an even integer, i.e., I MCS Set2={0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}, I MCS Set3 may be grouped as each I MCS  in I MCS Set3 being an odd integer, i.e., I MCS Set3={1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27}, and the reserved I MCS Set4={29, 30, 31}. Alternatively, I MCS Set3 may be grouped as each I MCS  in I MCS Set3 being an even integer, i.e., I MCS Set3={0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}, I MCS Set2 may be grouped as each I MCS  in I MCS Set2 being an odd integer, i.e., I MCS Set2={1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27}, and the reserved I MCS Set4={29, 30, 31}. It is noted that any two of I MCS Set2, I MCS Set3, and I MCS Set4 have no intersection, and I MCS Set2, I MCS Set3, and I MCS Set4 form a union. 
     In another example, the grouped subsets I MCS Set2 and I MCS Set3 may satisfy the following criterion: at least b 0 % of I MCS  in I MCS Set2 that each has a remainder after a division of the respective I MCS  by an even integer “a” being less than “a/2”, and at least b 1 % of I MCS  in I MCS Set3 that each has a remainder after a division of the respective I MCS  by the even integer “a” being greater than or equal to “a/2”, and wherein b 0  is a real number greater than 75 and less than 100 and b 1  is a real number greater than 75 and less than 100. In yet another example, the grouped subsets I MCS Set2 and I MCS Set3 may satisfy the following criterion: at least 60% of a total number of I MCS  in I MCS Set2 is greater than “N′,” and at least 60% of a total number of I MCS  in I MCS Set3 is less than “N′,” and wherein N′ is equal to a sum of the total number of I MCS  in I MCS Set2 and the total number of I MCS  in I MCS Set3. 
     In another embodiment, the BS may refer to a predefined table (e.g., Table 2 as shown below) to determine which BG (either BG1 or BG2) that the I MCS  corresponds to. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 Code Rate R × 
                 Base Graph 
               
               
                 I MCS   
                 Q m   
                 [1024] 
                 Index 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 0 
                 2 
                 121 
                 1 
               
               
                 1 
                 2 
                 171 
                 2 
               
               
                 2 
                 2 
                 120 
                 1 
               
               
                 3 
                 2 
                 156.5 
                 2 
               
               
                 4 
                 2 
                 193 
                 1 
               
               
                 5 
                 2 
                 250.5 
                 2 
               
               
                 6 
                 2 
                 308 
                 1 
               
               
                 7 
                 2 
                 378.5 
                 2 
               
               
                 8 
                 2 
                 449 
                 1 
               
               
                 9 
                 2 
                 525.5 
                 2 
               
               
                 10 
                 4 
                 602 
                 1 
               
               
                 11 
                 4 
                 679 
                 2 
               
               
                 12 
                 4 
                 756 
                 1 
               
               
                 13 
                 4 
                 378 
                 2 
               
               
                 14 
                 4 
                 434 
                 1 
               
               
                 15 
                 4 
                 490 
                 2 
               
               
                 16 
                 4 
                 553 
                 1 
               
               
                 17 
                 6 
                 616 
                 2 
               
               
                 18 
                 6 
                 657.5 
                 1 
               
               
                 19 
                 6 
                 699 
                 2 
               
               
                 20 
                 6 
                 774.75 
                 1 
               
               
                 21 
                 6 
                 850.5 
                 2 
               
               
                 22 
                 6 
                 924.75 
                 1 
               
               
                 23 
                 6 
                 616.5 
                 2 
               
               
                 24 
                 6 
                 666 
                 1 
               
               
                 25 
                 6 
                 719 
                 2 
               
               
                 26 
                 6 
                 772 
                 1 
               
               
                 27 
                 6 
                 822.5 
                 2 
               
               
                 28 
                 6 
                 873 
                 1 
               
            
           
           
               
               
               
            
               
                 29 
                 2 
                 reserved 
               
               
                 30 
                 4 
               
               
                 31 
                 6 
               
               
                   
               
            
           
         
       
     
     As shown in Table 2, each I MCS  not only corresponds to a single combination of modulation order (Q m ) and a code rate (R) but also to a respective BG index (either 1 or 2). In some embodiments, BG index 1 is associated with BG1, and BG index 2 is associated with BG2. It is noted that the above-described criteria that I MCS Set2 and I MCS Set3 follow may be applied to Table 2, in accordance with some embodiments. 
     Referring still to operation  308  of the method  300  in  FIG. 3  (i.e., the second predefined condition is satisfied), in some embodiments, the BS may use the I MCS  (indicated by the DCI) and the code rate (R), corresponding to the indicated I MCS , to directly select either BG1 or BG2. More specifically, when R is greater than R 1 , the BS selects BS1; and when R is less than or equal to R 2 , the BS selects BS2, wherein R 1  and R 2  are each a real number less than 1, and R 1  is greater than R 2 . 
     Referring still to operation  308  of the method  300  in  FIG. 3  (i.e., the second predefined condition is satisfied), in some embodiments, the BS may use the I MCS  and the number of physical resource blocks (PRB), both indicated by the DCI, to directly select either BG1 or BG2. More specifically, the BS selects BG1, when a remainder after division of I MCS  by 2 is equal to a remainder after division of PRB by 2; and the BS selects BG2, when a remainder after division of I MCS  by 2 is not equal to a remainder after division of PRB by 2. Alternatively, the BS selects BG2, when a remainder after division of I MCS  by 2 is equal to a remainder after division of PRB by 2; and the BS selects BG1, when a remainder after division of I MCS  by 2 is not equal to a remainder after division of PRB by 2. 
     Referring still to operation  308  of the method  300  in  FIG. 3  (i.e., the second predefined condition is satisfied), in some embodiments, the BS may use a relationship between a first efficiency value derived from a MCS table, which will be shown below, and a second efficiency value indicated in a channel quality indicator (CQI) table, which will be shown below, to directly select either BG1 or BG2. More specifically, the first efficiency value is calculated as a product of a modulation order (Q m ) and a code rate (R) that correspond to a single I MCS , which is indicated by the DCI, and the second efficiency value is listed as one of a plurality of pre-calculated efficiency values in the CQI table. Accordingly, the BS may group the 32 different values of I MCS  into another plurality of subsets: I MCS Set5, I MCS Set6, I MCS Set7, and I MCS Set8, wherein each I MCS &#39;s corresponding first efficiency value in I MCS Set5 is equal to any of the plurality of pre-calculated efficiency values in the CQI table (i.e., the second efficiency value), each I MCS &#39;s corresponding first efficiency value in I MCS Set6 is equal to an average of any two adjacent ones of the plurality of pre-calculated efficiency values (i.e., the respective pre-calculated efficiency values of two adjacent CQI indexes) in the CQI table, each I MCS &#39;s corresponding first efficiency value in I MCS Set7 is not equal to any first efficiency values included in I MCS Set5 and I MCS Set6, and I MCS Set8 is reserved for retransmission or for future use. 
     In some embodiments, an exemplary CQI table with a maximum modulation order of 256QAM is shown in Table 3 and an exemplary MCS table for the use of sending a PDSCH (Physical Downlink Shared Channel) signal with a maximum modulation order of 8 (256QAM) is shown in Table 4. According to the above-discussed grouping principles, in some embodiments, I MCS Set5={1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27}, I MCS Set6={2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}, I MCS Set7={0}, and I MCS Set8={28, 29, 30, 31}. Further, a maximum code rate in such an MCS table (e.g., Table 4) is equal to 0.95+Δx wherein Δx is a real number between −0.01 and +0.01. For example, as listed in Table 4, the maximum code rate indicated in the MCS table is equal to 972/1024=0.9492 wherein Δx=0.008. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 CQI 
                 Modulation 
                 code rate × 
                   
               
               
                   
                 index 
                 order 
                 1024 
                 efficiency 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 0 
                 out of range 
               
            
           
           
               
               
               
               
               
            
               
                   
                 1 
                 QPSK 
                 78 
                 0.1523 
               
               
                   
                 2 
                 QPSK 
                 193 
                 0.3770 
               
               
                   
                 3 
                 QPSK 
                 449 
                 0.8770 
               
               
                   
                 4 
                 16QAM 
                 378 
                 1.4766 
               
               
                   
                 5 
                 16QAM 
                 490 
                 1.9141 
               
               
                   
                 6 
                 16QAM 
                 616 
                 2.4063 
               
               
                   
                 7 
                 64QAM 
                 466 
                 2.7305 
               
               
                   
                 8 
                 64QAM 
                 567 
                 3.3223 
               
               
                   
                 9 
                 64QAM 
                 666 
                 3.9023 
               
               
                   
                 10 
                 64QAM 
                 772 
                 4.5234 
               
               
                   
                 11 
                 64QAM 
                 873 
                 5.1152 
               
               
                   
                 12 
                 256QAM 
                 711 
                 5.5547 
               
               
                   
                 13 
                 256QAM 
                 797 
                 6.2266 
               
               
                   
                 14 
                 256QAM 
                 885 
                 6.9141 
               
               
                   
                 15 
                 256QAM 
                 972 
                 7.5938 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 code rate × 
               
               
                 I MCS   
                 Q m   
                 1024 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 2 
                 120 
               
               
                 1 
                 2 
                 193 
               
               
                 2 
                 2 
                 321 
               
               
                 3 
                 2 
                 449 
               
               
                 4 
                 2 
                 603 
               
               
                 5 
                 4 
                 378 
               
               
                 6 
                 4 
                 434 
               
               
                 7 
                 4 
                 490 
               
               
                 8 
                 4 
                 553 
               
               
                 9 
                 4 
                 616 
               
               
                 10 
                 4 
                 658 
               
               
                 11 
                 6 
                 466 
               
               
                 12 
                 6 
                 517 
               
               
                 13 
                 6 
                 567 
               
               
                 14 
                 6 
                 617 
               
               
                 15 
                 6 
                 666 
               
               
                 16 
                 6 
                 719 
               
               
                 17 
                 6 
                 772 
               
               
                 18 
                 6 
                 823 
               
               
                 19 
                 6 
                 873 
               
               
                 20 
                 8 
                 683 
               
               
                 21 
                 8 
                 711 
               
               
                 22 
                 8 
                 754 
               
               
                 23 
                 8 
                 797 
               
               
                 24 
                 8 
                 841 
               
               
                 25 
                 8 
                 885 
               
               
                 26 
                 8 
                 929 
               
               
                 27 
                 8 
                 972 
               
               
                 28 
                 2 
                 reserved 
               
               
                 29 
                 4 
               
               
                 30 
                 6 
               
               
                 31 
                 8 
               
               
                   
               
            
           
         
       
     
     In some embodiments, another exemplary CQI table with a maximum modulation order of 64QAM is shown in Table 5. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 CQI 
                 Modulation 
                 code rate × 
                   
               
               
                   
                 index 
                 order 
                 1024 
                 efficiency 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 0 
                 out of range 
               
            
           
           
               
               
               
               
               
            
               
                   
                 1 
                 QPSK 
                 78 
                 0.1523 
               
               
                   
                 2 
                 QPSK 
                 120 
                 0.2344 
               
               
                   
                 3 
                 QPSK 
                 193 
                 0.3770 
               
               
                   
                 4 
                 QPSK 
                 308 
                 0.6016 
               
               
                   
                 5 
                 QPSK 
                 449 
                 0.8770 
               
               
                   
                 6 
                 QPSK 
                 602 
                 1.1758 
               
               
                   
                 7 
                 16QAM 
                 378 
                 1.4766 
               
               
                   
                 8 
                 16QAM 
                 490 
                 1.9141 
               
               
                   
                 9 
                 16QAM 
                 616 
                 2.4063 
               
               
                   
                 10 
                 64QAM 
                 466 
                 2.7305 
               
               
                   
                 11 
                 64QAM 
                 567 
                 3.3223 
               
               
                   
                 12 
                 64QAM 
                 666 
                 3.9023 
               
               
                   
                 13 
                 64QAM 
                 772 
                 4.5234 
               
               
                   
                 14 
                 64QAM 
                 873 
                 5.1152 
               
               
                   
                 15 
                 64QAM 
                 948 
                 5.5547 
               
               
                   
                   
               
            
           
         
       
     
     In some embodiments, another exemplary MCS table for the use of sending a PDSCH (Physical Downlink Shared Channel) signal with a maximum modulation order of 6 (64QAM) is shown in Table 6. 
     
       
         
           
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 code rate × 
               
               
                 I MCS   
                 Q m   
                 1024 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 2 
                 120 
               
               
                 1 
                 2 
                 157 
               
               
                 2 
                 2 
                 193 
               
               
                 3 
                 2 
                 251 
               
               
                 4 
                 2 
                 308 
               
               
                 5 
                 2 
                 379 
               
               
                 6 
                 2 
                 449 
               
               
                 7 
                 2 
                 526 
               
               
                 8 
                 2 
                 602 
               
               
                 9 
                 2 
                 679 
               
               
                 10 
                 4 
                 340 
               
               
                 11 
                 4 
                 378 
               
               
                 12 
                 4 
                 434 
               
               
                 13 
                 4 
                 490 
               
               
                 14 
                 4 
                 553 
               
               
                 15 
                 4 
                 616 
               
               
                 16 
                 4 
                 658 
               
               
                 17 
                 6 
                 438 
               
               
                 18 
                 6 
                 466 
               
               
                 19 
                 6 
                 517 
               
               
                 20 
                 6 
                 567 
               
               
                 21 
                 6 
                 617 
               
               
                 22 
                 6 
                 666 
               
               
                 23 
                 6 
                 719 
               
               
                 24 
                 6 
                 772 
               
               
                 25 
                 6 
                 823 
               
               
                 26 
                 6 
                 873 
               
               
                 27 
                 6 
                 911 
               
               
                 28 
                 6 
                 948 
               
               
                 29 
                 2 
                 reserved 
               
               
                 30 
                 4 
               
               
                 31 
                 6 
               
               
                   
               
            
           
         
       
     
     In some embodiments, an exemplary MCS table for the use of sending a PUSCH (Physical Uplink Shared Channel) signal with a maximum modulation order of 6 (64QAM) using CP-OFDM (Cyclic Prefix Orthogonal Frequency Division Multiplexing) is shown in Table 7. 
     
       
         
           
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 code rate × 
               
               
                 I MCS   
                 Q m   
                 1024 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 2 
                 100 
               
               
                 1 
                 2 
                 130 
               
               
                 2 
                 2 
                 161 
               
               
                 3 
                 2 
                 209 
               
               
                 4 
                 2 
                 257 
               
               
                 5 
                 2 
                 315 
               
               
                 6 
                 2 
                 374 
               
               
                 7 
                 2 
                 438 
               
               
                 8 
                 2 
                 502 
               
               
                 9 
                 2 
                 566 
               
               
                 10 
                 2 
                 630 
               
               
                 11 
                 4 
                 315 
               
               
                 12 
                 4 
                 362 
               
               
                 13 
                 4 
                 408 
               
               
                 14 
                 4 
                 461 
               
               
                 15 
                 4 
                 513 
               
               
                 16 
                 4 
                 548 
               
               
                 17 
                 4 
                 583 
               
               
                 18 
                 4 
                 646 
               
               
                 19 
                 4 
                 709 
               
               
                 20 
                 4 
                 771 
               
               
                 21 
                 6 
                 514 
               
               
                 22 
                 6 
                 555 
               
               
                 23 
                 6 
                 599 
               
               
                 24 
                 6 
                 643 
               
               
                 25 
                 6 
                 685 
               
               
                 26 
                 6 
                 727 
               
               
                 27 
                 6 
                 759 
               
               
                 28 
                 6 
                 790 
               
               
                 29 
                 2 
                 reserved 
               
               
                 30 
                 4 
               
               
                 31 
                 6 
               
               
                   
               
            
           
         
       
     
     In some embodiments, yet another MCS table for the use of sending a PUSCH (Physical Uplink Shared Channel) signal with a maximum modulation order of 8 (256QAM) using CP-OFDM (Cyclic Prefix Orthogonal Frequency Division Multiplexing) is shown in Table 8. 
     
       
         
           
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 code rate × 
               
               
                 I MCS   
                 Q m   
                 1024 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 2 
                 100 
               
               
                 1 
                 2 
                 161 
               
               
                 2 
                 2 
                 268 
               
               
                 3 
                 2 
                 374 
               
               
                 4 
                 2 
                 502 
               
               
                 5 
                 2 
                 630 
               
               
                 6 
                 4 
                 362 
               
               
                 7 
                 4 
                 408 
               
               
                 8 
                 4 
                 461 
               
               
                 9 
                 4 
                 513 
               
               
                 10 
                 4 
                 583 
               
               
                 11 
                 4 
                 646 
               
               
                 12 
                 4 
                 709 
               
               
                 13 
                 4 
                 771 
               
               
                 14 
                 6 
                 555 
               
               
                 15 
                 6 
                 599 
               
               
                 16 
                 6 
                 643 
               
               
                 17 
                 6 
                 685 
               
               
                 18 
                 6 
                 727 
               
               
                 19 
                 6 
                 790 
               
               
                 20 
                 6 
                 838 
               
               
                 21 
                 6 
                 886 
               
               
                 22 
                 8 
                 701 
               
               
                 23 
                 8 
                 738 
               
               
                 24 
                 8 
                 764 
               
               
                 25 
                 8 
                 821 
               
               
                 26 
                 8 
                 895 
               
               
                 27 
                 8 
                 949 
               
               
                 28 
                 2 
                 reserved 
               
               
                 29 
                 4 
               
               
                 30 
                 6 
               
               
                 31 
                 8 
               
               
                   
               
            
           
         
       
     
     In some embodiments, yet another exemplary MCS table for the use of sending a PUSCH (Physical Uplink Shared Channel) signal with a maximum modulation order of 6 (64QAM) using DFT-S-OFDM (Discrete Fourier Transformation Spread Orthogonal Frequency Division Multiplexing) is shown in Table 9. 
     
       
         
           
               
               
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 code rate × 
               
               
                 I MCS   
                 Q m   
                 1024 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 1 
                 200 
               
               
                 1 
                 1 
                 260 
               
               
                 2 
                 2 
                 161 
               
               
                 3 
                 2 
                 209 
               
               
                 4 
                 2 
                 257 
               
               
                 5 
                 2 
                 315 
               
               
                 6 
                 2 
                 374 
               
               
                 7 
                 2 
                 438 
               
               
                 8 
                 2 
                 502 
               
               
                 9 
                 2 
                 566 
               
               
                 10 
                 2 
                 630 
               
               
                 11 
                 4 
                 315 
               
               
                 12 
                 4 
                 362 
               
               
                 13 
                 4 
                 408 
               
               
                 14 
                 4 
                 461 
               
               
                 15 
                 4 
                 513 
               
               
                 16 
                 4 
                 548 
               
               
                 17 
                 4 
                 583 
               
               
                 18 
                 4 
                 646 
               
               
                 19 
                 4 
                 709 
               
               
                 20 
                 4 
                 771 
               
               
                 21 
                 6 
                 555 
               
               
                 22 
                 6 
                 599 
               
               
                 23 
                 6 
                 643 
               
               
                 24 
                 6 
                 685 
               
               
                 25 
                 6 
                 727 
               
               
                 26 
                 6 
                 759 
               
               
                 27 
                 6 
                 790 
               
               
                 28 
                 1 
                 reserved 
               
               
                 29 
                 2 
               
               
                 30 
                 4 
               
               
                 31 
                 6 
               
               
                   
               
            
           
         
       
     
     In some embodiments, yet another exemplary MCS table for the use of sending a PUSCH (Physical Uplink Shared Channel) signal with a maximum modulation order of 8 (256QAM) using DFT-S-OFDM (Discrete Fourier Transformation Spread Orthogonal Frequency Division Multiplexing) is shown in Table 10. 
     
       
         
           
               
               
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 MCS Index 
                 Modulation Order 
                 code rate × 
               
               
                 I MCS   
                 Q m   
                 1024 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 0 
                 1 
                 200 
               
               
                 1 
                 2 
                 161 
               
               
                 2 
                 2 
                 268 
               
               
                 3 
                 2 
                 374 
               
               
                 4 
                 2 
                 502 
               
               
                 5 
                 2 
                 630 
               
               
                 6 
                 4 
                 362 
               
               
                 7 
                 4 
                 461 
               
               
                 8 
                 4 
                 513 
               
               
                 9 
                 4 
                 583 
               
               
                 10 
                 4 
                 646 
               
               
                 11 
                 4 
                 709 
               
               
                 12 
                 4 
                 771 
               
               
                 13 
                 6 
                 555 
               
               
                 14 
                 6 
                 599 
               
               
                 15 
                 6 
                 643 
               
               
                 16 
                 6 
                 685 
               
               
                 17 
                 6 
                 727 
               
               
                 18 
                 6 
                 790 
               
               
                 19 
                 6 
                 838 
               
               
                 20 
                 6 
                 886 
               
               
                 21 
                 8 
                 701 
               
               
                 22 
                 8 
                 738 
               
               
                 23 
                 8 
                 764 
               
               
                 24 
                 8 
                 821 
               
               
                 25 
                 8 
                 895 
               
               
                 26 
                 8 
                 949 
               
               
                 27 
                 1 
                 reserved 
               
               
                 28 
                 2 
               
               
                 29 
                 4 
               
               
                 30 
                 6 
               
               
                 31 
                 8 
               
               
                   
               
            
           
         
       
     
     In some embodiments, once the BS selects the BG (either BG1 or BG2), the BG can use the QC-LDPC code, as known in the art, to encode the to-be transmitted information bits. Thus, steps performed by the BS to use the BG to encode the information bits will be herein briefly described: 
     Step 1. Calculate an intermediate parameter kb (when BG1 is selected, kb=22; when BG2 is selected and TBS is equal to or less than 192, kb=6; when BG2 is selected and TBS is greater than 192 and less than or equal to 560, kb=8; when BG2 is selected and TBS is greater than 560 and less than or equal to 640, kb=9; and when BG2 is selected and TBS is greater than 640, kb=10). 
     Step 2. Calculate a lifting value Z. The lifting value Z is selected as a minimum integer greater than or equal to TBS/kb. 
     Step 3. Based on a plurality of predefined tables (e.g., Tables 3, 4, and 5 provided below), retrieve a parity check matrix H using the lifting value Z, which will be discussed as follows. 
     In general, each BG is associated with a base graph matrix, H BG . For BG1, the H BG  includes 46 rows and with row indexes i=0, 1, 2, . . . , 45 and 68 columns with column indexes j=0, 1, 2, . . . , 67. For BG2, the H BG  includes 42 rows with row indexes i=0, 1, 2, . . . , 41 and 52 columns with column indexes j=0, 1, 2, . . . , 51. The elements in the H BG  with row and column indexes given in Table 11 (for BG1) and Table 12 (fof BG 2) are of value 1, and all other elements in H BG  are of value 0. Then, The matrix H is obtained by replacing each element of H BG  with a Z×Z matrix, according to the following: each element of value 0 in H BG  is replaced by an all zero matrix 0 of size Z×Z; each element of value 1 in H BG  is replaced by a circular permutation matrix I(P i,j ) of size Z×Z, where i and j are the row and column indexes of the element, and I(P i,j  is obtained by circularly shifting an identity matrix I of size Z×Z to the right P i,j  times. The value of P i,j  is given by P i,j =mod(V i,j ,Z). The value of V i,j  is given by Tables 3 and 4 according to a set index i IS , which corresponds to a set of lifting values Z as shown in Table 13, and the base graph index (i.e., which BG is selected). 
     
       
         
           
               
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 H BG   
                   
               
            
           
           
               
               
               
            
               
                 Row 
                 Column 
                 V i,j   
               
               
                 index 
                 index 
                 Set index i LS   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 i 
                 j 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 0 
                 0 
                 250 
                 307 
                 73 
                 223 
                 211 
                 294 
                 0 
                 135 
               
               
                   
                 1 
                 69 
                 19 
                 15 
                 16 
                 198 
                 118 
                 0 
                 227 
               
               
                   
                 2 
                 226 
                 50 
                 103 
                 94 
                 188 
                 167 
                 0 
                 126 
               
               
                   
                 3 
                 159 
                 369 
                 49 
                 91 
                 186 
                 330 
                 0 
                 134 
               
               
                   
                 5 
                 100 
                 181 
                 240 
                 74 
                 219 
                 207 
                 0 
                 84 
               
               
                   
                 6 
                 10 
                 216 
                 39 
                 10 
                 4 
                 165 
                 0 
                 83 
               
               
                   
                 9 
                 59 
                 317 
                 15 
                 0 
                 29 
                 243 
                 0 
                 53 
               
               
                   
                 10 
                 229 
                 288 
                 162 
                 205 
                 144 
                 250 
                 0 
                 225 
               
               
                   
                 11 
                 110 
                 109 
                 215 
                 216 
                 116 
                 1 
                 0 
                 205 
               
               
                   
                 12 
                 191 
                 17 
                 164 
                 21 
                 216 
                 339 
                 0 
                 128 
               
               
                   
                 13 
                 9 
                 357 
                 133 
                 215 
                 115 
                 201 
                 0 
                 75 
               
               
                   
                 15 
                 195 
                 215 
                 298 
                 14 
                 233 
                 53 
                 0 
                 135 
               
               
                   
                 16 
                 23 
                 106 
                 110 
                 70 
                 144 
                 347 
                 0 
                 217 
               
               
                   
                 18 
                 190 
                 242 
                 113 
                 141 
                 95 
                 304 
                 0 
                 220 
               
               
                   
                 19 
                 35 
                 180 
                 16 
                 198 
                 216 
                 167 
                 0 
                 90 
               
               
                   
                 20 
                 239 
                 330 
                 189 
                 104 
                 73 
                 47 
                 0 
                 105 
               
               
                   
                 21 
                 31 
                 346 
                 32 
                 81 
                 261 
                 188 
                 0 
                 137 
               
               
                   
                 22 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
               
               
                   
                 23 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 1 
                 0 
                 2 
                 76 
                 303 
                 141 
                 179 
                 77 
                 22 
                 96 
               
               
                   
                 2 
                 239 
                 76 
                 294 
                 45 
                 162 
                 225 
                 11 
                 236 
               
               
                   
                 3 
                 117 
                 73 
                 27 
                 151 
                 223 
                 96 
                 124 
                 136 
               
               
                   
                 4 
                 124 
                 288 
                 261 
                 46 
                 256 
                 338 
                 0 
                 221 
               
               
                   
                 5 
                 71 
                 144 
                 161 
                 119 
                 160 
                 268 
                 10 
                 128 
               
               
                   
                 7 
                 222 
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                 255 
                 74 
                 141 
               
               
                   
                 7 
                 116 
                 383 
                 96 
                 65 
                 0 
                 111 
                 16 
                 11 
               
               
                   
                 14 
                 182 
                 312 
                 46 
                 81 
                 183 
                 54 
                 28 
                 181 
               
               
                   
                 47 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 26 
                 0 
                 195 
                 71 
                 270 
                 107 
                 0 
                 325 
                 21 
                 163 
               
               
                   
                 2 
                 243 
                 81 
                 110 
                 176 
                 0 
                 326 
                 142 
                 131 
               
               
                   
                 4 
                 215 
                 76 
                 318 
                 212 
                 0 
                 226 
                 192 
                 169 
               
               
                   
                 15 
                 61 
                 136 
                 67 
                 127 
                 277 
                 99 
                 197 
                 98 
               
               
                   
                 48 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 27 
                 1 
                 25 
                 194 
                 210 
                 208 
                 45 
                 91 
                 98 
                 165 
               
               
                   
                 6 
                 104 
                 194 
                 29 
                 141 
                 36 
                 326 
                 140 
                 232 
               
               
                   
                 8 
                 194 
                 101 
                 304 
                 174 
                 72 
                 268 
                 22 
                 9 
               
               
                   
                 49 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 28 
                 0 
                 128 
                 222 
                 11 
                 146 
                 275 
                 102 
                 4 
                 32 
               
               
                   
                 4 
                 165 
                 19 
                 293 
                 153 
                 0 
                 1 
                 1 
                 43 
               
               
                   
                 19 
                 181 
                 244 
                 50 
                 217 
                 155 
                 40 
                 40 
                 200 
               
               
                   
                 21 
                 63 
                 274 
                 234 
                 114 
                 62 
                 167 
                 93 
                 205 
               
               
                   
                 50 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 29 
                 1 
                 86 
                 252 
                 27 
                 150 
                 0 
                 273 
                 92 
                 232 
               
               
                   
                 14 
                 236 
                 5 
                 308 
                 11 
                 180 
                 104 
                 136 
                 32 
               
               
                   
                 18 
                 84 
                 147 
                 117 
                 53 
                 0 
                 243 
                 106 
                 118 
               
               
                   
                 25 
                 6 
                 78 
                 29 
                 68 
                 42 
                 107 
                 6 
                 103 
               
               
                   
                 51 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 30 
                 0 
                 216 
                 159 
                 91 
                 34 
                 0 
                 171 
                 2 
                 170 
               
               
                   
                 10 
                 73 
                 229 
                 23 
                 130 
                 90 
                 16 
                 88 
                 199 
               
               
                   
                 13 
                 120 
                 260 
                 105 
                 210 
                 252 
                 95 
                 112 
                 26 
               
               
                   
                 24 
                 9 
                 90 
                 135 
                 123 
                 173 
                 212 
                 20 
                 105 
               
               
                   
                 52 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 31 
                 1 
                 95 
                 100 
                 222 
                 175 
                 144 
                 101 
                 4 
                 73 
               
               
                   
                 7 
                 177 
                 215 
                 308 
                 49 
                 144 
                 297 
                 49 
                 149 
               
               
                   
                 22 
                 172 
                 258 
                 66 
                 177 
                 166 
                 279 
                 125 
                 175 
               
               
                   
                 25 
                 61 
                 256 
                 162 
                 128 
                 19 
                 222 
                 194 
                 108 
               
               
                   
                 53 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 32 
                 0 
                 221 
                 102 
                 210 
                 192 
                 0 
                 351 
                 6 
                 103 
               
               
                   
                 12 
                 112 
                 201 
                 22 
                 209 
                 211 
                 265 
                 126 
                 110 
               
               
                   
                 14 
                 199 
                 175 
                 271 
                 58 
                 36 
                 338 
                 63 
                 151 
               
               
                   
                 24 
                 121 
                 287 
                 217 
                 30 
                 162 
                 83 
                 20 
                 211 
               
               
                   
                 54 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 33 
                 1 
                 2 
                 323 
                 170 
                 114 
                 0 
                 56 
                 10 
                 199 
               
               
                   
                 2 
                 187 
                 8 
                 20 
                 49 
                 0 
                 304 
                 30 
                 132 
               
               
                   
                 11 
                 41 
                 361 
                 140 
                 161 
                 76 
                 141 
                 6 
                 172 
               
               
                   
                 21 
                 211 
                 105 
                 33 
                 137 
                 18 
                 101 
                 92 
                 65 
               
               
                   
                 55 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 34 
                 0 
                 127 
                 230 
                 187 
                 82 
                 197 
                 60 
                 4 
                 161 
               
               
                   
                 7 
                 167 
                 148 
                 296 
                 186 
                 0 
                 320 
                 153 
                 237 
               
               
                   
                 15 
                 164 
                 202 
                 5 
                 68 
                 108 
                 112 
                 197 
                 142 
               
               
                   
                 17 
                 159 
                 312 
                 44 
                 150 
                 0 
                 54 
                 155 
                 180 
               
               
                   
                 56 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 35 
                 1 
                 161 
                 320 
                 207 
                 192 
                 199 
                 100 
                 4 
                 231 
               
               
                   
                 6 
                 197 
                 335 
                 158 
                 173 
                 278 
                 210 
                 45 
                 174 
               
               
                   
                 12 
                 207 
                 2 
                 55 
                 26 
                 0 
                 195 
                 168 
                 145 
               
               
                   
                 22 
                 103 
                 266 
                 285 
                 187 
                 205 
                 268 
                 185 
                 100 
               
               
                   
                 57 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 36 
                 0 
                 37 
                 210 
                 259 
                 222 
                 216 
                 135 
                 6 
                 11 
               
               
                   
                 14 
                 105 
                 313 
                 179 
                 157 
                 16 
                 15 
                 200 
                 207 
               
               
                   
                 15 
                 51 
                 297 
                 178 
                 0 
                 0 
                 35 
                 177 
                 42 
               
               
                   
                 18 
                 120 
                 21 
                 160 
                 6 
                 0 
                 188 
                 43 
                 100 
               
               
                   
                 58 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 37 
                 1 
                 198 
                 269 
                 298 
                 81 
                 72 
                 319 
                 82 
                 59 
               
               
                   
                 13 
                 220 
                 82 
                 15 
                 195 
                 144 
                 236 
                 2 
                 204 
               
               
                   
                 23 
                 122 
                 115 
                 115 
                 138 
                 0 
                 85 
                 135 
                 161 
               
               
                   
                 59 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 38 
                 0 
                 167 
                 185 
                 151 
                 123 
                 190 
                 164 
                 91 
                 121 
               
               
                   
                 9 
                 151 
                 177 
                 179 
                 90 
                 0 
                 196 
                 64 
                 90 
               
               
                   
                 10 
                 157 
                 289 
                 64 
                 73 
                 0 
                 209 
                 198 
                 26 
               
               
                   
                 12 
                 163 
                 214 
                 181 
                 10 
                 0 
                 246 
                 100 
                 140 
               
               
                   
                 60 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 39 
                 1 
                 173 
                 258 
                 102 
                 12 
                 153 
                 236 
                 4 
                 115 
               
               
                   
                 3 
                 139 
                 93 
                 77 
                 77 
                 0 
                 264 
                 28 
                 188 
               
               
                   
                 7 
                 149 
                 346 
                 192 
                 49 
                 165 
                 37 
                 109 
                 168 
               
               
                   
                 19 
                 0 
                 297 
                 208 
                 114 
                 117 
                 272 
                 188 
                 52 
               
               
                   
                 61 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 40 
                 0 
                 157 
                 175 
                 32 
                 67 
                 216 
                 304 
                 10 
                 4 
               
               
                   
                 8 
                 137 
                 37 
                 80 
                 45 
                 144 
                 237 
                 84 
                 103 
               
               
                   
                 17 
                 149 
                 312 
                 197 
                 96 
                 2 
                 135 
                 12 
                 30 
               
               
                   
                 62 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 41 
                 1 
                 167 
                 52 
                 154 
                 23 
                 0 
                 123 
                 2 
                 53 
               
               
                   
                 3 
                 173 
                 314 
                 47 
                 215 
                 0 
                 77 
                 75 
                 189 
               
               
                   
                 9 
                 139 
                 139 
                 124 
                 60 
                 0 
                 25 
                 142 
                 215 
               
               
                   
                 18 
                 151 
                 288 
                 207 
                 167 
                 183 
                 272 
                 128 
                 24 
               
               
                   
                 63 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 42 
                 0 
                 149 
                 113 
                 226 
                 114 
                 27 
                 288 
                 163 
                 222 
               
               
                   
                 4 
                 157 
                 14 
                 65 
                 91 
                 0 
                 83 
                 10 
                 170 
               
               
                   
                 24 
                 137 
                 218 
                 126 
                 78 
                 35 
                 17 
                 162 
                 71 
               
               
                   
                 64 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 43 
                 1 
                 151 
                 113 
                 228 
                 206 
                 52 
                 210 
                 1 
                 22 
               
               
                   
                 16 
                 163 
                 132 
                 69 
                 22 
                 243 
                 3 
                 163 
                 127 
               
               
                   
                 18 
                 173 
                 114 
                 176 
                 134 
                 0 
                 53 
                 99 
                 49 
               
               
                   
                 25 
                 139 
                 168 
                 102 
                 161 
                 270 
                 167 
                 98 
                 125 
               
               
                   
                 65 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 44 
                 0 
                 139 
                 80 
                 234 
                 84 
                 18 
                 79 
                 4 
                 191 
               
               
                   
                 7 
                 157 
                 78 
                 227 
                 4 
                 0 
                 244 
                 6 
                 211 
               
               
                   
                 9 
                 163 
                 163 
                 259 
                 9 
                 0 
                 293 
                 142 
                 187 
               
               
                   
                 22 
                 173 
                 274 
                 260 
                 12 
                 57 
                 272 
                 3 
                 148 
               
               
                   
                 66 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 45 
                 1 
                 149 
                 135 
                 101 
                 184 
                 168 
                 82 
                 181 
                 177 
               
               
                   
                 6 
                 151 
                 149 
                 228 
                 121 
                 0 
                 67 
                 45 
                 114 
               
               
                   
                 10 
                 167 
                 15 
                 126 
                 29 
                 144 
                 235 
                 153 
                 93 
               
               
                   
                 67 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 H BG   
                   
               
            
           
           
               
               
               
            
               
                 Row 
                 Column 
                 V i,j   
               
               
                 index 
                 index 
                 Set index i LS   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 i 
                 j 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 0 
                 0 
                 9 
                 174 
                 0 
                 72 
                 3 
                 156 
                 143 
                 145 
               
               
                   
                 1 
                 117 
                 97 
                 0 
                 110 
                 26 
                 143 
                 19 
                 131 
               
               
                   
                 2 
                 204 
                 166 
                 0 
                 23 
                 53 
                 14 
                 176 
                 71 
               
               
                   
                 3 
                 26 
                 66 
                 0 
                 181 
                 35 
                 3 
                 165 
                 21 
               
               
                   
                 6 
                 189 
                 71 
                 0 
                 95 
                 115 
                 40 
                 196 
                 23 
               
               
                   
                 9 
                 205 
                 172 
                 0 
                 8 
                 127 
                 123 
                 13 
                 112 
               
               
                   
                 10 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                   
                 11 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 1 
                 0 
                 167 
                 27 
                 137 
                 53 
                 19 
                 17 
                 18 
                 142 
               
               
                   
                 3 
                 166 
                 36 
                 124 
                 156 
                 94 
                 65 
                 27 
                 174 
               
               
                   
                 4 
                 253 
                 48 
                 0 
                 115 
                 104 
                 63 
                 3 
                 183 
               
               
                   
                 5 
                 125 
                 92 
                 0 
                 156 
                 66 
                 1 
                 102 
                 27 
               
               
                   
                 6 
                 226 
                 31 
                 88 
                 115 
                 84 
                 55 
                 185 
                 96 
               
               
                   
                 7 
                 156 
                 187 
                 0 
                 200 
                 98 
                 37 
                 17 
                 23 
               
               
                   
                 8 
                 224 
                 185 
                 0 
                 29 
                 69 
                 171 
                 14 
                 9 
               
               
                   
                 9 
                 252 
                 3 
                 55 
                 31 
                 50 
                 133 
                 180 
                 167 
               
               
                   
                 11 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 12 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 2 
                 0 
                 81 
                 25 
                 20 
                 152 
                 95 
                 98 
                 126 
                 74 
               
               
                   
                 1 
                 114 
                 114 
                 94 
                 131 
                 106 
                 168 
                 163 
                 31 
               
               
                   
                 3 
                 44 
                 117 
                 99 
                 46 
                 92 
                 107 
                 47 
                 3 
               
               
                   
                 4 
                 52 
                 110 
                 9 
                 191 
                 110 
                 82 
                 183 
                 53 
               
               
                   
                 8 
                 240 
                 114 
                 108 
                 91 
                 111 
                 142 
                 132 
                 155 
               
               
                   
                 10 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
               
               
                   
                 12 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 13 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 3 
                 1 
                 8 
                 136 
                 38 
                 185 
                 120 
                 53 
                 36 
                 239 
               
               
                   
                 2 
                 58 
                 175 
                 15 
                 6 
                 121 
                 174 
                 48 
                 171 
               
               
                   
                 4 
                 158 
                 113 
                 102 
                 36 
                 22 
                 174 
                 18 
                 95 
               
               
                   
                 5 
                 104 
                 72 
                 146 
                 124 
                 4 
                 127 
                 111 
                 110 
               
               
                   
                 6 
                 209 
                 123 
                 12 
                 124 
                 73 
                 17 
                 203 
                 159 
               
               
                   
                 7 
                 54 
                 118 
                 57 
                 110 
                 49 
                 89 
                 3 
                 199 
               
               
                   
                 8 
                 18 
                 28 
                 53 
                 156 
                 128 
                 17 
                 191 
                 43 
               
               
                   
                 9 
                 128 
                 186 
                 46 
                 133 
                 79 
                 105 
                 160 
                 75 
               
               
                   
                 10 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                   
                 13 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 4 
                 0 
                 179 
                 72 
                 0 
                 200 
                 42 
                 86 
                 43 
                 29 
               
               
                   
                 1 
                 214 
                 74 
                 136 
                 16 
                 24 
                 67 
                 27 
                 140 
               
               
                   
                 11 
                 71 
                 29 
                 157 
                 101 
                 51 
                 83 
                 117 
                 180 
               
               
                   
                 14 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 5 
                 0 
                 231 
                 10 
                 0 
                 185 
                 40 
                 79 
                 136 
                 121 
               
               
                   
                 1 
                 41 
                 44 
                 131 
                 138 
                 140 
                 84 
                 49 
                 41 
               
               
                   
                 5 
                 194 
                 121 
                 142 
                 170 
                 84 
                 35 
                 36 
                 169 
               
               
                   
                 7 
                 159 
                 80 
                 141 
                 219 
                 137 
                 103 
                 132 
                 88 
               
               
                   
                 11 
                 103 
                 48 
                 64 
                 193 
                 71 
                 60 
                 62 
                 207 
               
               
                   
                 15 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 6 
                 0 
                 155 
                 129 
                 0 
                 123 
                 109 
                 47 
                 7 
                 137 
               
               
                   
                 5 
                 228 
                 92 
                 124 
                 55 
                 87 
                 154 
                 34 
                 72 
               
               
                   
                 7 
                 45 
                 100 
                 99 
                 31 
                 107 
                 10 
                 198 
                 172 
               
               
                   
                 9 
                 28 
                 49 
                 45 
                 222 
                 133 
                 155 
                 168 
                 124 
               
               
                   
                 11 
                 158 
                 184 
                 148 
                 209 
                 139 
                 29 
                 12 
                 56 
               
               
                   
                 16 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 7 
                 1 
                 129 
                 80 
                 0 
                 103 
                 97 
                 48 
                 163 
                 86 
               
               
                   
                 5 
                 147 
                 186 
                 45 
                 13 
                 135 
                 125 
                 78 
                 186 
               
               
                   
                 7 
                 140 
                 16 
                 148 
                 105 
                 35 
                 24 
                 143 
                 87 
               
               
                   
                 11 
                 3 
                 102 
                 96 
                 150 
                 108 
                 47 
                 107 
                 172 
               
               
                   
                 13 
                 116 
                 143 
                 78 
                 181 
                 65 
                 55 
                 58 
                 154 
               
               
                   
                 17 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 8 
                 0 
                 142 
                 118 
                 0 
                 147 
                 70 
                 53 
                 101 
                 176 
               
               
                   
                 1 
                 94 
                 70 
                 65 
                 43 
                 69 
                 31 
                 177 
                 169 
               
               
                   
                 12 
                 230 
                 152 
                 87 
                 152 
                 88 
                 161 
                 22 
                 225 
               
               
                   
                 18 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 9 
                 1 
                 203 
                 28 
                 0 
                 2 
                 97 
                 104 
                 186 
                 167 
               
               
                   
                 8 
                 205 
                 132 
                 97 
                 30 
                 40 
                 142 
                 27 
                 238 
               
               
                   
                 10 
                 61 
                 185 
                 51 
                 184 
                 24 
                 99 
                 205 
                 48 
               
               
                   
                 11 
                 247 
                 178 
                 85 
                 83 
                 49 
                 64 
                 81 
                 68 
               
               
                   
                 19 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 10 
                 0 
                 11 
                 59 
                 0 
                 174 
                 46 
                 111 
                 125 
                 38 
               
               
                   
                 1 
                 185 
                 104 
                 17 
                 150 
                 41 
                 25 
                 60 
                 217 
               
               
                   
                 6 
                 0 
                 22 
                 156 
                 8 
                 101 
                 174 
                 177 
                 208 
               
               
                   
                 7 
                 117 
                 52 
                 20 
                 56 
                 96 
                 23 
                 51 
                 232 
               
               
                   
                 20 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 11 
                 0 
                 11 
                 32 
                 0 
                 99 
                 28 
                 91 
                 39 
                 178 
               
               
                   
                 7 
                 236 
                 92 
                 7 
                 138 
                 30 
                 175 
                 29 
                 214 
               
               
                   
                 9 
                 210 
                 174 
                 4 
                 110 
                 116 
                 24 
                 35 
                 168 
               
               
                   
                 13 
                 56 
                 154 
                 2 
                 99 
                 64 
                 141 
                 8 
                 51 
               
               
                   
                 21 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 12 
                 1 
                 63 
                 39 
                 0 
                 46 
                 33 
                 122 
                 18 
                 124 
               
               
                   
                 3 
                 111 
                 93 
                 113 
                 217 
                 122 
                 11 
                 155 
                 122 
               
               
                   
                 11 
                 14 
                 11 
                 48 
                 109 
                 131 
                 4 
                 49 
                 72 
               
               
                   
                 22 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 13 
                 0 
                 83 
                 49 
                 0 
                 37 
                 76 
                 29 
                 32 
                 48 
               
               
                   
                 1 
                 2 
                 125 
                 112 
                 113 
                 37 
                 91 
                 53 
                 57 
               
               
                   
                 8 
                 38 
                 35 
                 103 
                 143 
                 62 
                 27 
                 95 
                 167 
               
               
                   
                 13 
                 222 
                 166 
                 26 
                 140 
                 47 
                 127 
                 186 
                 219 
               
               
                   
                 23 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 14 
                 1 
                 115 
                 19 
                 0 
                 36 
                 143 
                 11 
                 91 
                 82 
               
               
                   
                 6 
                 145 
                 118 
                 138 
                 95 
                 51 
                 145 
                 20 
                 232 
               
               
                   
                 11 
                 3 
                 21 
                 57 
                 40 
                 130 
                 8 
                 52 
                 204 
               
               
                   
                 13 
                 232 
                 163 
                 27 
                 116 
                 97 
                 166 
                 109 
                 162 
               
               
                   
                 24 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 15 
                 0 
                 51 
                 68 
                 0 
                 116 
                 139 
                 137 
                 174 
                 38 
               
               
                   
                 10 
                 175 
                 63 
                 73 
                 200 
                 96 
                 103 
                 108 
                 217 
               
               
                   
                 11 
                 213 
                 81 
                 99 
                 110 
                 128 
                 40 
                 102 
                 157 
               
               
                   
                 25 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 16 
                 1 
                 203 
                 87 
                 0 
                 75 
                 48 
                 78 
                 125 
                 170 
               
               
                   
                 9 
                 142 
                 177 
                 79 
                 158 
                 9 
                 158 
                 31 
                 23 
               
               
                   
                 11 
                 8 
                 135 
                 111 
                 134 
                 28 
                 17 
                 54 
                 175 
               
               
                   
                 12 
                 242 
                 64 
                 143 
                 97 
                 8 
                 165 
                 176 
                 202 
               
               
                   
                 26 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 17 
                 1 
                 254 
                 158 
                 0 
                 48 
                 120 
                 134 
                 57 
                 196 
               
               
                   
                 5 
                 124 
                 23 
                 24 
                 132 
                 43 
                 23 
                 201 
                 173 
               
               
                   
                 11 
                 114 
                 9 
                 109 
                 206 
                 65 
                 62 
                 142 
                 195 
               
               
                   
                 12 
                 64 
                 6 
                 18 
                 2 
                 42 
                 163 
                 35 
                 218 
               
               
                   
                 27 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 18 
                 0 
                 220 
                 186 
                 0 
                 68 
                 17 
                 173 
                 129 
                 128 
               
               
                   
                 6 
                 194 
                 6 
                 18 
                 16 
                 106 
                 31 
                 203 
                 211 
               
               
                   
                 7 
                 50 
                 46 
                 86 
                 156 
                 142 
                 22 
                 140 
                 210 
               
               
                   
                 28 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 19 
                 0 
                 87 
                 58 
                 0 
                 35 
                 79 
                 13 
                 110 
                 39 
               
               
                   
                 1 
                 20 
                 42 
                 158 
                 138 
                 28 
                 135 
                 124 
                 84 
               
               
                   
                 10 
                 185 
                 156 
                 154 
                 86 
                 41 
                 145 
                 52 
                 88 
               
               
                   
                 29 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 20 
                 1 
                 26 
                 76 
                 0 
                 6 
                 2 
                 128 
                 196 
                 117 
               
               
                   
                 4 
                 105 
                 61 
                 148 
                 20 
                 103 
                 52 
                 35 
                 227 
               
               
                   
                 11 
                 29 
                 153 
                 104 
                 141 
                 78 
                 173 
                 114 
                 6 
               
               
                   
                 30 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 21 
                 0 
                 76 
                 157 
                 0 
                 80 
                 91 
                 156 
                 10 
                 238 
               
               
                   
                 8 
                 42 
                 175 
                 17 
                 43 
                 75 
                 166 
                 122 
                 13 
               
               
                   
                 13 
                 210 
                 67 
                 33 
                 81 
                 81 
                 40 
                 23 
                 11 
               
               
                   
                 31 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 22 
                 1 
                 222 
                 20 
                 0 
                 49 
                 54 
                 18 
                 202 
                 195 
               
               
                   
                 2 
                 63 
                 52 
                 4 
                 1 
                 132 
                 163 
                 126 
                 44 
               
               
                   
                 32 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 23 
                 0 
                 23 
                 106 
                 0 
                 156 
                 68 
                 110 
                 52 
                 5 
               
               
                   
                 3 
                 235 
                 86 
                 75 
                 54 
                 115 
                 132 
                 170 
                 94 
               
               
                   
                 5 
                 238 
                 95 
                 158 
                 134 
                 56 
                 150 
                 13 
                 111 
               
               
                   
                 33 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 24 
                 1 
                 46 
                 182 
                 0 
                 153 
                 30 
                 113 
                 113 
                 81 
               
               
                   
                 2 
                 139 
                 153 
                 69 
                 88 
                 42 
                 108 
                 161 
                 19 
               
               
                   
                 9 
                 8 
                 64 
                 87 
                 63 
                 101 
                 61 
                 88 
                 130 
               
               
                   
                 34 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 25 
                 0 
                 228 
                 45 
                 0 
                 211 
                 128 
                 72 
                 197 
                 66 
               
               
                   
                 5 
                 156 
                 21 
                 65 
                 94 
                 63 
                 136 
                 194 
                 95 
               
               
                   
                 35 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 26 
                 2 
                 29 
                 67 
                 0 
                 90 
                 142 
                 36 
                 164 
                 146 
               
               
                   
                 7 
                 143 
                 137 
                 100 
                 6 
                 28 
                 38 
                 172 
                 66 
               
               
                   
                 12 
                 160 
                 55 
                 13 
                 221 
                 100 
                 53 
                 49 
                 190 
               
               
                   
                 13 
                 122 
                 85 
                 7 
                 6 
                 133 
                 145 
                 161 
                 86 
               
               
                   
                 36 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 27 
                 0 
                 8 
                 103 
                 0 
                 27 
                 13 
                 42 
                 168 
                 64 
               
               
                   
                 6 
                 151 
                 50 
                 32 
                 118 
                 10 
                 104 
                 193 
                 181 
               
               
                   
                 37 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 28 
                 1 
                 98 
                 70 
                 0 
                 216 
                 106 
                 64 
                 14 
                 7 
               
               
                   
                 2 
                 101 
                 111 
                 126 
                 212 
                 77 
                 24 
                 186 
                 144 
               
               
                   
                 5 
                 135 
                 168 
                 110 
                 193 
                 43 
                 149 
                 46 
                 16 
               
               
                   
                 38 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 29 
                 0 
                 18 
                 110 
                 0 
                 108 
                 133 
                 139 
                 50 
                 25 
               
               
                   
                 4 
                 28 
                 17 
                 154 
                 61 
                 25 
                 161 
                 27 
                 57 
               
               
                   
                 39 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 30 
                 2 
                 71 
                 120 
                 0 
                 106 
                 87 
                 84 
                 70 
                 37 
               
               
                   
                 5 
                 240 
                 154 
                 35 
                 44 
                 56 
                 173 
                 17 
                 139 
               
               
                   
                 7 
                 9 
                 52 
                 51 
                 185 
                 104 
                 93 
                 50 
                 221 
               
               
                   
                 9 
                 84 
                 56 
                 134 
                 176 
                 70 
                 29 
                 6 
                 17 
               
               
                   
                 40 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 31 
                 1 
                 106 
                 3 
                 0 
                 147 
                 80 
                 117 
                 115 
                 201 
               
               
                   
                 13 
                 1 
                 170 
                 20 
                 182 
                 139 
                 148 
                 189 
                 46 
               
               
                   
                 41 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 32 
                 0 
                 242 
                 84 
                 0 
                 108 
                 32 
                 116 
                 110 
                 179 
               
               
                   
                 5 
                 44 
                 8 
                 20 
                 21 
                 89 
                 73 
                 0 
                 14 
               
               
                   
                 12 
                 166 
                 17 
                 122 
                 110 
                 71 
                 142 
                 163 
                 116 
               
               
                   
                 42 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 33 
                 2 
                 132 
                 165 
                 0 
                 71 
                 135 
                 105 
                 163 
                 46 
               
               
                   
                 9 
                 10 
                 61 
                 185 
                 51 
                 184 
                 24 
                 99 
                 205 
               
               
                   
                 7 
                 164 
                 179 
                 88 
                 12 
                 6 
                 137 
                 173 
                 2 
               
               
                   
                 10 
                 235 
                 124 
                 13 
                 109 
                 2 
                 29 
                 179 
                 106 
               
               
                   
                 43 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 34 
                 0 
                 147 
                 173 
                 0 
                 29 
                 37 
                 11 
                 197 
                 184 
               
               
                   
                 12 
                 85 
                 177 
                 19 
                 201 
                 25 
                 41 
                 191 
                 135 
               
               
                   
                 13 
                 36 
                 12 
                 78 
                 69 
                 114 
                 162 
                 193 
                 141 
               
               
                   
                 44 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 35 
                 1 
                 57 
                 77 
                 0 
                 91 
                 60 
                 126 
                 157 
                 85 
               
               
                   
                 5 
                 40 
                 184 
                 157 
                 165 
                 137 
                 152 
                 167 
                 225 
               
               
                   
                 11 
                 63 
                 18 
                 6 
                 55 
                 93 
                 172 
                 181 
                 175 
               
               
                   
                 45 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 36 
                 0 
                 140 
                 25 
                 0 
                 1 
                 121 
                 73 
                 197 
                 178 
               
               
                   
                 2 
                 38 
                 151 
                 63 
                 175 
                 129 
                 154 
                 167 
                 112 
               
               
                   
                 7 
                 154 
                 170 
                 82 
                 83 
                 26 
                 129 
                 179 
                 106 
               
               
                   
                 46 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 37 
                 10 
                 219 
                 37 
                 0 
                 40 
                 97 
                 167 
                 181 
                 154 
               
               
                   
                 13 
                 151 
                 31 
                 144 
                 12 
                 56 
                 38 
                 193 
                 114 
               
               
                   
                 47 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 38 
                 1 
                 31 
                 84 
                 0 
                 37 
                 1 
                 112 
                 157 
                 42 
               
               
                   
                 5 
                 66 
                 151 
                 93 
                 97 
                 70 
                 7 
                 173 
                 41 
               
               
                   
                 11 
                 38 
                 190 
                 19 
                 46 
                 1 
                 19 
                 191 
                 105 
               
               
                   
                 48 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 39 
                 0 
                 239 
                 93 
                 0 
                 106 
                 119 
                 109 
                 181 
                 167 
               
               
                   
                 7 
                 172 
                 132 
                 24 
                 181 
                 32 
                 6 
                 157 
                 45 
               
               
                   
                 12 
                 34 
                 57 
                 138 
                 154 
                 142 
                 105 
                 173 
                 189 
               
               
                   
                 49 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 40 
                 2 
                 0 
                 103 
                 0 
                 98 
                 6 
                 160 
                 193 
                 78 
               
               
                   
                 10 
                 75 
                 107 
                 36 
                 35 
                 73 
                 156 
                 163 
                 67 
               
               
                   
                 13 
                 120 
                 163 
                 143 
                 36 
                 102 
                 82 
                 179 
                 180 
               
               
                   
                 50 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 41 
                 1 
                 129 
                 147 
                 0 
                 120 
                 48 
                 132 
                 191 
                 53 
               
               
                   
                 5 
                 229 
                 7 
                 2 
                 101 
                 47 
                 6 
                 197 
                 215 
               
               
                   
                 11 
                 118 
                 60 
                 55 
                 81 
                 19 
                 8 
                 167 
                 230 
               
               
                   
                 51 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 13 
               
               
                   
               
               
                 Set index (i LS ) 
                 Set of lifting sizes (Z) 
               
               
                   
               
             
            
               
                 1 
                 {2, 4, 8, 16, 32, 64, 128, 256} 
               
               
                 2 
                 {3, 6, 12, 24, 48, 96, 192, 384} 
               
               
                 3 
                 {5, 10, 20, 40, 80, 160, 320} 
               
               
                 4 
                 {7, 14, 28, 56, 112, 224} 
               
               
                 5 
                 {9, 18, 36, 72, 144, 288} 
               
               
                 6 
                 {11, 22, 44, 88, 176, 352} 
               
               
                 7 
                 {13, 26, 52, 104, 208} 
               
               
                 8 
                 {15, 30, 60, 120, 240} 
               
               
                   
               
            
           
         
       
     
     After the parity check matrix H is determined, the information bits can be encoded as an QC-LDPC codeword. Next, as discussed above, the rate matching step, the interleaving step, and the symbol modulation step are respectively performed on the QC-LDPC codeword to generate one or more modulated symbols for transmission. 
       FIG. 5  illustrates a flow chart of an exemplary method  500  performed by a UE to retrieve information bits from a signal encoded by a QC-LDPC code, in accordance with some embodiments. The illustrated embodiment of the method  500  is merely an example. Therefore, it should be understood that any of a variety of operations may be omitted, re-sequenced, and/or added while remaining within the scope of the present disclosure. Since the method  500  performed by the UE is substantially similar to the method  300  performed by the BS except that encoding is replaced with decoding, the method  500  will be briefly discussed as follows. 
     In some embodiments, the method  500  starts with operation  502  in which downlink control information (DCI) is received. According to some embodiments, the DCI includes various information such as, for example, a modulation and coding scheme (MCS) index (hereinafter “I MCS ”), a new data indicator (hereinafter “NDI”), a redundancy version (hereinafter “RV”), a number of physical resource blocks (hereinafter “PRB”), etc. Next, the method  500  proceeds to determination operation  504  in which the UE determines whether a first or second predefined condition is satisfied. In some embodiments, the first predefined condition includes at least one of the following: whether the RV is equal to RV0, whether a current logic state of the NDI is equal to a logic “0,” and whether the NDI presents a transition to a different logic state (e.g., whether the NDI has been toggled to a value different from a previously received value, which indicates a first transmission); and the second predefined condition includes at least one of the following: whether the RV is equal to RV1, RV2, or RV3, whether a current logic state of the NDI is equal to a logic “1,” and whether the NDI lacks a transition to a different logic state (e.g., whether the NDI has been toggled to a value different from a previously received value, which indicates a retransmission). When the first predefined condition is satisfied, the method  500  proceeds to operation  506 ; and when the second predefined condition is satisfied, the method  500  proceeds to operation  508 . In some embodiments, in operation  506 , the UE is configured to process the various information contained in the DCI to select one from the above-mentioned BG1 and BG2 that are predefined by the QC-LDPC code; and on the other hand, in operation  508 , the UE is configured to use the various information contained in the DCI to directly select one from the above-mentioned BG1 and BG2 (i.e., no further processing on the various information). It is noted that the above-described techniques performed by the BS in operation  306  can also be performed by the UE in operation  506  to select a BG, and the above-described techniques performed by the BS in operation  308  can also be performed by the UE in operation  508  to select a BG while remaining within the scope of the present disclosure. After the BG is selected either at operation  506  or  508 , the method  500  continues to operation  510  in which the UE uses the selected BG to retrieve information bits from a signal encoded by the QC-LDPC code. In some embodiments, in operation  510 , in addition to at least one decoding process using the selected BG being performed, one or more further steps (e.g., a symbol de-modulation step, a step to estimate a corresponding parity check matrix as mentioned above, a de-interleaving step, a de-rate matching step, etc.) may be performed before the information bits are decoded. 
     While various embodiments of the invention have been described above, it should be understood that they have been presented by way of example only, and not by way of limitation. Likewise, the various diagrams may depict an example architectural or configuration, which are provided to enable persons of ordinary skill in the art to understand exemplary features and functions of the invention. Such persons would understand, however, that the invention is not restricted to the illustrated example architectures or configurations, but can be implemented using a variety of alternative architectures and configurations. Additionally, as would be understood by persons of ordinary skill in the art, one or more features of one embodiment can be combined with one or more features of another embodiment described herein. Thus, the breadth and scope of the present disclosure should not be limited by any of the above-described exemplary embodiments. 
     It is also understood that any reference to an element herein using a designation such as “first,” “second,” and so forth does not generally limit the quantity or order of those elements. Rather, these designations can be used herein as a convenient means of distinguishing between two or more elements or instances of an element. Thus, a reference to first and second elements does not mean that only two elements can be employed, or that the first element must precede the second element in some manner. 
     Additionally, a person having ordinary skill in the art would understand that information and signals can be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits and symbols, for example, which may be referenced in the above description can be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof. 
     A person of ordinary skill in the art would further appreciate that any of the various illustrative logical blocks, modules, processors, means, circuits, methods and functions described in connection with the aspects disclosed herein can be implemented by electronic hardware (e.g., a digital implementation, an analog implementation, or a combination of the two), firmware, various forms of program or design code incorporating instructions (which can be referred to herein, for convenience, as “software” or a “software module), or any combination of these techniques. To clearly illustrate this interchangeability of hardware, firmware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware, firmware or software, or a combination of these techniques, depends upon the particular application and design constraints imposed on the overall system. Skilled artisans can implement the described functionality in various ways for each particular application, but such implementation decisions do not cause a departure from the scope of the present disclosure. 
     Furthermore, a person of ordinary skill in the art would understand that various illustrative logical blocks, modules, devices, components and circuits described herein can be implemented within or performed by an integrated circuit (IC) that can include a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, or any combination thereof. The logical blocks, modules, and circuits can further include antennas and/or transceivers to communicate with various components within the network or within the device. A general purpose processor can be a microprocessor, but in the alternative, the processor can be any conventional processor, controller, or state machine. A processor can also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other suitable configuration to perform the functions described herein. 
     If implemented in software, the functions can be stored as one or more instructions or code on a computer-readable medium. Thus, the steps of a method or algorithm disclosed herein can be implemented as software stored on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that can be enabled to transfer a computer program or code from one place to another. A storage media can be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store desired program code in the form of instructions or data structures and that can be accessed by a computer. 
     In this document, the term “module” as used herein, refers to software, firmware, hardware, and any combination of these elements for performing the associated functions described herein. Additionally, for purpose of discussion, the various modules are described as discrete modules; however, as would be apparent to one of ordinary skill in the art, two or more modules may be combined to form a single module that performs the associated functions according embodiments of the invention. 
     Additionally, memory or other storage, as well as communication components, may be employed in embodiments of the invention. It will be appreciated that, for clarity purposes, the above description has described embodiments of the invention with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functionality between different functional units, processing logic elements or domains may be used without detracting from the invention. For example, functionality illustrated to be performed by separate processing logic elements, or controllers, may be performed by the same processing logic element, or controller. Hence, references to specific functional units are only references to a suitable means for providing the described functionality, rather than indicative of a strict logical or physical structure or organization. 
     Various modifications to the implementations described in this disclosure will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other implementations without departing from the scope of this disclosure. Thus, the disclosure is not intended to be limited to the implementations shown herein, but is to be accorded the widest scope consistent with the novel features and principles disclosed herein, as recited in the claims below.