Patent Publication Number: US-8526454-B2

Title: Apparatus and method for bit remapping in a relay enhanced communication system

Description:
TECHNICAL FIELD 
     The present invention is directed, in general, to communication systems and, in particular, to an apparatus and method for bit remapping at a relay node in a communication system. 
     BACKGROUND 
     Long term evolution (“LTE”) of the Third Generation Partnership Project (“3GPP”), also referred to as 3GPP LTE, refers to research and development involving the 3GPP Release 8 and beyond, which is the name generally used to describe an ongoing effort across the industry aimed at identifying technologies and capabilities that can improve systems such as the universal mobile telecommunication system (“UMTS”). The goals of this broadly based project include improving communication efficiency, lowering costs, improving services, making use of new spectrum opportunities, and achieving better integration with other open standards. The 3GPP LTE project is not itself a standard-generating effort, but will result in new recommendations for standards for the UMTS. 
     The Evolved Universal Terrestrial Radio Access Network (“E-UTRAN”) in 3GPP includes base stations providing user plane (including packet data convergence protocol/radio link control/medium access control/physical (“PDCP/RLC/MAC/PHY”) sublayers) and control plane (including radio resource control (“RRC”) sublayer) protocol terminations towards wireless communication devices such as cellular telephones. A wireless communication device or terminal is generally known as user equipment (“UE”). A base station (“BS”) is an entity of a communication network often referred to as a Node B or an NB. Particularly in the E-UTRAN, an “evolved” base station is referred to as an eNodeB. For details about the overall architecture of the E-UTRAN, see 3GPP Technical Specification (“TS”) 36.300 v8.5.0 (2008-05), which is incorporated herein by reference. 
     As wireless communication systems such as cellular telephone, satellite, and microwave communication systems become widely deployed and continue to attract a growing number of users, there is a pressing need to accommodate a large and variable number of communication devices transmitting a growing range of communication applications with fixed resources. Traditional communication system designs employing a fixed communication resource have become challenged to accommodate the rapidly growing customer base and the expanding levels of service. One area that has challenged the need to expand communication links over longer distances is the use of a communication node such as an intermediate relay node between user equipment and a base station. Relaying by an intermediate node between a user equipment and a base station can be employed in wireless communication systems to increase system radio coverage area, enhance channel reliability, provide cooperative diversity, offer inter-user cooperation, etc. 
     In relay-enhanced wireless communication systems, an access communication link or access link (a source-to-relay node link) and a relay communication link or relay link (a relay-to-destination node link) may provide less than desirable performance and different levels of communication channel quality in different radio environments, particularly in the presence of various levels of noise in a communication link. To improve the overall throughput of a wireless communication system, an adaptive modulation and coding (“AMC”) strategy may be applied separately to the access link and the relay link. For example, for the uplink case from user equipment to a base station through a relay node, the access link is from the user equipment to the relay node, which may be the less reliable link. The relay link refers to the link from a relay node to a base station, and this link may be the more reliable link. In this case, the modulation order of the relay link may be higher than that of the access link. 
     To include more general, practical communication systems, the access and relay links may be referred to as a “first hop” and a “second hop.” In the uplink case, the first hop refers to a link from the user equipment to a relay node, and the second hop refers to the link from the relay node to a base station or to a relay node to another relay node. In this general description, in a downlink case of a one relay-enhanced wireless communication system, the first hop may refer to the link from a base station to a relay node, and the second hop may refer to a link from a relay node to a user equipment. 
     To provide reliable and efficient communication from user equipment through a relay node to a base station, it is necessary to re-modulate and forward received signals at a relay node operating under a demodulate and forward (“DmF”) mode, as described in IEEE Standard C802, 16j-07/052r13, entitled “Demodulation and Forwarding Method in Relay Stations,” Jul. 19, 2007, which is incorporated herein by reference. A demodulate and forward relay node demodulates and makes hard detection decisions on its received signals to form an estimated codeword, and then forwards the estimated codeword to the destination node. 
     In a conventional wireless communication system employing a relay node, the bits of a received signal are sequentially mapped into the bits of a transmitted signal. In view of the growing deployment of communication systems such as cellular communication systems and market expectations for reliable communication between a base station and the user equipment, it would be beneficial to incorporate improvements for mapping the bits of a received signal at a relay node on to a transmitted signal when the transmitted signal is transmitted with a modulation scheme different from the modulation scheme of the received signal. Therefore, what is needed in the art is a system and method that avoids deficiencies of bit mapping schemes at a relay node employed in present communication systems. 
     SUMMARY OF THE INVENTION 
     These and other problems are generally solved or circumvented, and technical advantages are generally achieved, by embodiments of the present invention, which include an apparatus and method for bit remapping at a relay node in a communication system. In one embodiment, an apparatus (e.g., a relay node) includes a processor configured to remap an order of bits of a received signal from a source node to a different order of bits for a transmitted signal to a destination node when the transmitted signal is constructed with a modulation scheme different from the received signal. 
     The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter, which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures or processes for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIGS. 1 ,  2 , and  3  illustrate system level diagrams of embodiments of communication systems including a base station and wireless communication devices that provide an environment for application of the principles of the present invention; 
         FIGS. 4 and 5  illustrate system level diagrams of embodiments of communication systems including a wireless communication systems that provide an environment for application of the principles of the present invention; 
         FIG. 6  illustrates a system level diagram of an embodiment of a communication element of a communication system for application of the principles of the present invention; 
         FIG. 7  illustrates a flowchart of a transport channel signal process for an uplink-shared channel; 
         FIG. 8  illustrates a flowchart demonstrating signal processing in a demodulate and forward mode at a relay node; 
         FIG. 9  illustrates a flowchart demonstrating a bit mapping process in a demodulate and forward relay node when a different modulation scheme is employed for two hops; 
         FIGS. 10 and 11 , illustrated are flowcharts demonstrating embodiments of a bit remapping processes when modulation schemes of two hops for a received signal and a transmitted signal at a relay node are different according to the principles of the present invention; 
         FIGS. 12 and 13 , illustrated are graphical representations demonstrating exemplary performance parameters of remapping processes according to the principles of the present invention; 
         FIG. 14  illustrates a flowchart demonstrating an embodiment of a bit interleaving process when modulation schemes of two hops for a received signal and a transmitted signal at a relay node are different according to the principles of the present invention; and 
         FIGS. 15 to 19  illustrate graphical representations demonstrating exemplary performance parameters of remapping processes according to the principles of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The making and using of the presently preferred embodiments are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention. In view of the foregoing, the present invention will be described with respect to exemplary embodiments in a specific context of a system and method for mapping bits of a received signal at a relay node on to a transmitted signal, particularly when the transmitted signal is transmitted with a modulation scheme different from the modulation scheme of the received signal. 
     Turning now to  FIG. 1 , illustrated is a system level diagram of an embodiment of a communication system including a base station (“BS”)  115  and a wireless communication device that provides an environment for application of the principles of the present invention. In the illustrated embodiment, a relay node  105  communicates with the base station  115  (a destination node) and the wireless communication device  145  (e.g. user equipment (“UE”), a source node). The relay node  105  may be another base station or another user equipment. In the exemplary scenario illustrated in  FIG. 1 , a lower order modulation scheme is used for a first hop and a higher order modulation scheme is used for a second hop. 
     Thus, the communication system is employed with a communication link in a relay-enhanced communication network that includes two hops employing the relay node  105 . The relay node  105  employs a demodulate and forward (“DmF”) mode and the modulation scheme is chosen independently for each hop. While the modulation order might be same for each hop, in the instant case, the second hop is more reliable then the first hop such that a lower order modulation is used for the first hop, and a higher order modulation is used for the second hop. Contrary to the modulation scheme mentioned above, current wireless communication systems typically do not use a mode of operation wherein a different order demodulator and/or modulator are employed at a relay node  105 . 
     Turning now to  FIG. 2 , illustrated is a system level diagram of an embodiment of a communication system including a base station (“BS”)  215  and wireless communication devices  235 ,  240 ,  245  (e.g., mobile station such as user equipment) that provides an environment for application of the principles of the present invention. The base station  215  is coupled to a public switched telephone network (not shown). The base station  215  is configured with a plurality of antennas to transmit and receive signals in a plurality of sectors including a first sector  220 , a second sector  225 , and a third sector  230 , each of which typically spans 120 degrees. The sectors are formed by focusing and phasing the radiated and received signals from the base station antennas. The plurality of sectors increases the number of the wireless communication devices  235 ,  240 ,  245  that can simultaneously communicate with the base station  215  without the need to increase the utilized bandwidth by reduction of interference that results from focusing and phasing base station antennas. The radiated and received frequencies utilized by the communication system illustrated in  FIG. 2  would typically be two gigahertz to provide non-line-of-sight communication. 
     Turning now to  FIG. 3 , illustrated is a system level diagram of an embodiment of a communication system including wireless communication devices that provides an environment for application of the principles of the present invention. The communication system includes a base station (“BS”)  310  coupled by communication link or path  320  (e.g., by a fiber-optic communication path) to a core telecommunications network such as public switched telephone network (“PSTN”)  330 . The base station  310  is coupled by wireless communication links or paths  340 ,  350  to wireless communication devices  360 ,  370 , respectively that lie within its cellular area  390 . 
     In operation of the communication system illustrated in  FIG. 3 , the base station  310  communicates with each wireless communication device  360 ,  370  through control and data communication resources allocated by the base station  310  over the communication paths  340 ,  350 , respectively. The control and data communication resources may include frequency and time-slot communication resources in frequency division duplex (“FDD”) and/or time division duplex (“TDD”) communication modes. 
     Turning now to  FIG. 4 , illustrated is a system level diagram of an embodiment of a communication system including a wireless communication system that provides an environment for the application of the principles of the present invention. The wireless communication system may be configured to provide evolved UMTS terrestrial radio access network (“E-UTRAN”) universal mobile telecommunications services. A mobile management entity/system architecture evolution gateway (“MME/SAE GW,” one of which is designated  410 ) provides control functionality for an E-UTRAN node B (designated “eNB,” an “evolved node B,” also referred to as a “base station,” one of which is designated  420 ) via an S1 communication link (ones of which are designated “S1 link”). The base stations  420  communicate via X2 communication links (designated “X2 link”). The various communication links are typically fiber, microwave, or other high-frequency metallic communication paths such as coaxial links, or combinations thereof. 
     The base stations  420  communicate with user equipment (“UE,” ones of which are designated  430 ), which is typically a mobile transceiver carried by a user. Thus, communication links (designated “Uu” communication links, ones of which are designated “Uu link”) coupling the base stations  420  to the user equipment  430  are air links employing a wireless communication signal such as, for example, an orthogonal frequency division multiplex (“OFDM”) signal. 
     Turning now to  FIG. 5 , illustrated is a system level diagram of an embodiment of a communication system including a wireless communication system that provides an environment for the application of the principles of the present invention. The wireless communication system provides an E-UTRAN architecture including base stations (one of which is designated  510 ) providing E-UTRAN user plane (packet data convergence protocol/radio link control/media access control/physical) and control plane (radio resource control) protocol terminations towards user equipment  520 . The base stations  510  are interconnected with X2 interfaces or communication links (designated “X2”). The base stations  510  are also connected by S I interfaces or communication links (designated “S1”) to an evolved packet core (“EPC”) including a mobile management entity/system architecture evolution gateway (“MME/SAE GW,” one of which is designated  530 ). The S1 interface supports a multiple entity relationship between the mobile management entity/system architecture evolution gateway  530  and the base stations  510 . For applications supporting inter-public land mobile handover, inter-eNB active mode mobility is supported by the mobile management entity/system architecture evolution gateway  530  relocation via the S1 interface. 
     The base stations  510  may host functions such as radio resource management. For instance, the base stations  510  may perform functions such as internet protocol (“IP”) header compression and encryption of user data streams, ciphering of user data streams, radio bearer control, radio admission control, connection mobility control, dynamic allocation of resources to user equipment in both the uplink and the downlink, selection of a mobility management entity at the user equipment attachment, routing of user plane data towards the user plane entity, scheduling and transmission of paging messages (originated from the mobility management entity), scheduling and transmission of broadcast information (originated from the mobility management entity or operations and maintenance), and measurement and reporting configuration for mobility and scheduling. The mobile management entity/system architecture evolution gateway  530  may host functions such as distribution of paging messages to the base stations  510 , security control, termination of U-plane packets for paging reasons, switching of U-plane for support of the user equipment mobility, idle state mobility control, and system architecture evolution bearer control. The user equipment  520  receives an allocation of a group of information blocks from the base stations  510 . 
     Turning now to  FIG. 6 , illustrated is a system level diagram of an embodiment of a communication element  610  of a communication system for application of the principles of the present invention. The communication element or device  610  may represent, without limitation, a base station, user equipment (e.g., a subscriber station, terminal, mobile station, a wireless communication device), a network control element, a communication node, or the like. The communication element  610  includes, at least, a processor  620 , memory  650  that stores programs and data of a temporary or more permanent nature, an antenna  660 , and a radio frequency transceiver  670  coupled to the antenna  660  and the processor  620  for bidirectional wireless communication. The communication element  610  may provide point-to-point and/or point-to-multipoint communication services. 
     The communication element  610 , such as a base station in a cellular network, may be coupled to a communication network element, such as a network control element  680  of a public switched telecommunication network (“PSTN”). The network control element  680  may, in turn, be formed with a processor, memory, and other electronic elements (not shown). The network control element  680  generally provides access to a telecommunication network such as a PSTN. Access may be provided using fiber optic, coaxial, twisted pair, microwave communication, or similar link coupled to an appropriate link-terminating element. A communication element  610  formed as user equipment is generally a self-contained device intended to be carried by an end user. 
     The processor  620  in the communication element  610 , which may be implemented with one or a plurality of processing devices, performs functions associated with its operation including, without limitation, encoding and decoding (encoder/decoder  623 ) of individual bits forming a communication message, formatting of information, and overall control (controller  625 ) of the communication element  610 , including processes related to management of resources (resource manager  628 ). Exemplary functions related to management of resources include, without limitation, hardware installation, traffic management, performance data analysis, tracking of end users and equipment, configuration management, end user administration, management of user equipment, management of tariffs, subscriptions, and billing, and the like. For instance, in accordance with the memory  650 , the resource manager  628  is configured to allocate time and frequency communication resources for transmission of data to/from the communication element  610  and format messages including the communication resources therefor. The processor  620  (via, for instance, a remapper  624 ) further includes processes to perform bit remapping processes in accordance with a communication node (e.g., a relay node such as a base station or user equipment) as described herein. It should be understood that the term encoder/decoder  623  is applied generically to a module that can perform ones of selected functions such as, without limitation, encoding, decoding, interleaving and/or de-interleaving. 
     The execution of all or portions of particular functions or processes related to management of resources may be performed in equipment separate from and/or coupled to the communication element  610 , with the results of such functions or processes communicated for execution to the communication element  610 . The processor  620  of the communication element  610  may be of any type suitable to the local application environment, and may include one or more of general-purpose computers, special purpose computers, microprocessors, digital signal processors (“DSPs”), and processors based on a multi-core processor architecture, as non-limiting examples. 
     The transceiver  670  of the communication element  610  modulates information on to a carrier waveform for transmission by the communication element  610  via the antenna  660  to another communication element. The transceiver  670  demodulates information received via the antenna  660  for further processing by other communication elements. 
     The memory  650  of the communication element  610 , as introduced above, may be of any type suitable to the local application environment, and may be implemented using any suitable volatile or nonvolatile data storage technology such as a semiconductor-based memory device, a magnetic memory device and system, an optical memory device and system, fixed memory, and removable memory. The programs stored in the memory  650  may include program instructions that, when executed by an associated processor, enable the communication element to perform tasks as described herein. Of course, the memory  650  may form a data buffer for data transmitted to and from the communication element  610 . Exemplary embodiments of the system, subsystems, and modules as described herein may be implemented, at least in part, by computer software executable by processors of, for instance, the user equipment and the base station, or by hardware, or by combinations thereof As will become more apparent, systems, subsystems and modules may be embodied in the communication element as illustrated and described herein. 
     A conventional bit mapping solution for a relay node when a different order of demodulator and modulator are employed at the relay node would just sequentially map received bits into transmitted bits, as could be interpreted from 3GPP TS 36.212 v8.2.0 (2008-3), which is incorporated herein by reference, and which will be described further hereinbelow. In a conventional bit mapping solution, a demodulated codeword from a low order constellation is directly re-modulated onto a higher order constellation without reordering of the received bits. 
     A demodulate and forward (“DmF”) mode represents a tradeoff between amplify and forward (“AF”) and decode and forward (“DcF”) modes or strategies. An amplify and forward relay node only amplifies and forwards the received signal, whereas a decode and forward relay node demodulates, decodes, and then re-encodes and forwards the received signal. A demodulate and forward relay node demodulates and makes hard detection decisions on received signals to form an estimated codeword before forwarding. Thus, error performance at a destination node with an intervening demodulate and forward relay node would be expected to perform better than one with an amplify and forward relay node. Processing delay at a relay node operating in the demodulate and forward mode would be less than that of a node operating in decode and forward mode due to the absence of a decoder in the demodulate and forward relay node. Therefore, demodulate and forward mode is a potentially advantageous solution for relay-enhanced wireless communication systems, especially for systems with a tight delay requirement. 
     Turning now to  FIG. 7 , illustrated is a flowchart of a transport channel signal process for an uplink-shared channel (“UL-SCH”) that may be inferred from the 3GPP TS 36.212. It is assumed that a demodulate and forward relay node is inserted in a communication link between a source node, such as a user equipment, and a destination node, such as a base station. In a module  710 , a cyclic redundancy check (“CRC”) code is attached to a data word to be transmitted. In a module  720 , a code block is segmented, and a cyclic redundancy check code is attached to the code block. In a module  730 , the code block with the attached cyclic redundancy check code is encoded. In a module  740 , the data are rate matched to the channel to provide a necessary level of redundancy in the transmitted signal. In a module  750  the code block is concatenated. In a module  760 , data and control information for the channel are multiplexed. In a module  770 , the multiplexed data are interleaved for transmission across a wireless communication channel. Thus, after multiplexing with encoded control signals, encoded data and control signals are interleaved together at a symbol level for protection against burst errors. Then the interleaved symbols are modulated according to a certain constellation format, and up-converted for transmission. 
     Turning now to  FIG. 8 , illustrated is a flowchart demonstrating signal processing in a demodulate and forward mode at a relay node. It is assumed here that the same modulation order (i.e., the number of bits in a modulation symbol of a constellation) is selected for both hops when a relay node is inserted in a communication link between a source node such as user equipment and a destination node such as a base station. At the source node, channel encoding is performed in a module  810 , followed by symbol interleaving in a module  820  and signal modulation in a module  830 . At the relay node, the signal is demodulated and hard detection decisions are made in a module  840 , followed by signal re-modulation in a module  850 . Since the same modulation order is used for reception and transmission at the relay node (i.e., for the two hops), no bit reordering is required for re-transmission of the signal. At the destination node, the signal is demodulated in a module  860 , followed by symbol de-interleaving in a module  870 , and channel decoding in a module  880 . The modules or steps indicated in  FIG. 8  individually perform signal processing steps well understood in the art, and will not be described in further detail. 
     Turning now to  FIG. 9 , illustrated is a flowchart demonstrating a bit mapping process in a demodulate and forward relay node when a different modulation scheme is employed for two hops that may be inferred from the 3GPP TS 36.212. When a lower order demodulation and a higher order modulation are respectively employed for the two hops, a conventional demodulation and re-modulation procedure at a relay node is employed wherein the received bits are sequentially mapped into the transmitted bits without reordering. At the source node, the signal is encoded in a module  910 , followed by a symbol interleaving in a module  920 , and signal modulation in a module  930 . The relay node first demodulates received symbols in a module  940  according to a modulation format Mod 1 , and makes hard detection decisions to form an estimated interleaved codeword. The modulation format or scheme refers to the complex-plane constellation describing the received or transmitted signals. Then, the estimated interleaved codeword is de-interleaved in a module  950  according to the lower order modulation format Mod 1  to recover the original codeword sequence. Following procedures as described in the 3GPP TS 36.212, the next module is to re-interleave the codeword in a module  960  according to the higher order modulation format Mod 2  for transmission by the relay node. Finally, the re-interleaved codeword is re-modulated at the relay node in a module  970  according to higher order modulation format Mod 2 . Here, Mod 1  and Mod 2  denote, respectively, the modulation format or schemes of the first hop (the source node to the relay node) and the second hop (the relay node to the destination node), respectively. Correspondingly, the terms M 1  and M 2  denote their respective modulation orders. At the destination node, the signal is demodulated in a module  980 , followed by symbol de-interleaving in a module  990 , and channel decoding in a module  995 . The symbol interleaving and de-interleaving can be viewed as a subgroup-wise bit-interleaver and de-interleaver, respectively, based on a modulation-based alphabet. 
     Returning to the relay node, when the modulation order M 1  is not the same as the modulation order M 2 , especially when the modulation order M 2  is not an integer multiple of the modulation order M 1 , some of the coded bits in the modulation format Mod 1  would be separated into different modulation format Mod 2  symbols. An example is now described to explain this separation phenomenon. In this example, a 16 quadrature amplitude modulation (“QAM”) is selected for the first hop (i.e., one modulation symbol in a constellation of 16 symbols represents four bits), and 64 QAM is selected for the second hop (i.e., one modulation symbol in a constellation of 64 symbols represents six bits). Thus, Mod 1 =16 QAM, M 1 =4, Mod 2 =64 QAM and M 2 =6. For the sake of simplicity of explanation, only the in-phase signal component is considered. In this example, three in-phase 16 QAM components, each consisting of two bits, are mapped on to two in-phase 64 QAM components, each consisting of three bits. Following a conventional process as inferred from 3GPP TS 36.212, codes bits in each 16/64 QAM component would be sequentially mapped without reordering according to the following process. 
     
       
         
           
             
               
                 
                   
                     
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     In the expression (1) above, the symbol I i  represents an information bit to be communicated. It is observed in the expression (1) that the bits from the second 16 QAM signal are distributed across two 64 QAM signals, thereby disturbing their “integrality.” Mapping the bits of one modulation symbol into another modulation symbol without distributing the bits across different modulation symbols is referred to herein as maintaining integrality. A number of issues are raised regarding a conventional solution from 3GPP TS 36.212. 
     The first issue raised regarding a conventional solution is maintaining integrality of transmitted symbols. Considering the first hop, bits distilled from the same modulation format Mod 1  components generally experience the same channel fading and noise, whereas bits distilled from a different modulation format components may experience noise and fading in uncorrelated channels. When remapping from the modulation format Mod 1  symbols to the modulation format Mod 2  symbols, a question to be addressed for reliable communication is how bits distilled from the modulation format Mod 1  components should be mapped into another modulation format Mod 2  component(s). Recall that detection of a symbol after transmission through a noisy channel includes statistical processing that assesses admissible and inadmissible bit sequences for a code word that contains deliberately inserted redundant data. Thus, an issue for reliable communication is whether the integrality of a modulation format Mod 1  component should be preserved as much as possible after remapping, and whether preserving the integrality of a modulation format Mod 1  component after remapping would bring improvement to system performance. 
     A second consideration is protecting the integrality of symbols. The integrality of constellation components is involuntarily preserved in the process illustrated in  FIG. 9  to some degree, particularly for the same received and transmitted modulation level at a relay node. But there is often opportunity, conventionally ignored, to preserve integrality of the modulation format Mod 1  components when the modulation level is different. 
     Another consideration is treatment of differing reception reliabilities within each symbol. When the modulation order M is more than three (i.e., when a constellation symbol represents more than three bits), bits in one modulation component may have different decoding reliability. For example, when Gray code mapping (as illustrated in Table 1, wherein successive symbols are mapped into a binary code with the fewest overall number of bit changes between adjacent symbols) is adopted for 16 QAM, I 1 /Q 1  bits would be more reliable than I 2 /Q 2  bits, wherein the “I” bits represents the in-phase component and the “Q” represents the quadrature phase component. This is also true for Gray code mapping 64 QAM (as illustrated in Table 2). In other words, the reliability is in a regressive order from I 1 /Q 1  to I 2 /Q 2 , in which I 1 I 2 /Q 1 Q 2  are the two most reliable bits (including the most significant bit and the middle significant bit) in each component. Computation of the reliability of correctly receiving a transmitted bit in a constellation symbol transmitted across a noisy communication channel is well understood in the art, and will not be further described herein in the interest of brevity. 
     It can be seen that in a conventional bit mapping scheme in accordance with expression (1), an integral 16 QAM component is not mapped on to the two most reliable positions in a 64 QAM component (e.g., bits I 5 I 6  are conventionally mapped on to the two least reliable positions (middle significant bit and the least significant bit) in a 64 QAM component). Notice that in 64 QAM as illustrated in Table 2, the most significant bit when it is “0” is mapped entirely into the left-half signal constellation plane, and the most significant bit when it is “1” is mapped entirely into the right-half signal constellation plane, which provides the most reliable signal detection opportunity. Such wide separation of bits in the constellation does not occur for the middle significant bit or the least significant bit. This mapping rule would thus weaken the final equivalent reliability of the integral 16 QAM components at the destination. This phenomenon will be addressed and will be improved on as described further hereinbelow. 
                     TABLE 1                  Gray Code Mapping for 16 QAM                             I 1 I 2  (Q 1 Q 2 )   Constellation Point                       00   −3/{square root over (10)}(j)           01   −1/{square root over (10)}(j)           11     1/{square root over (10)}(j)           10     3/{square root over (10)}(j)                        
In Table 1 above and in Table 2 below, the in-phase data are mapped onto the real axis, and quadrature data are mapped onto the imaginary axis as represented by entries in parentheses.
 
     Another issue for reliable communication is how to treat different symbols. To be reliably decoded at a destination node, each symbol from the first hop should be treated equally at the relay node. In addition to the factors described above, a balance between the modulation format Mod 1  symbols should be taken into account. 
                     TABLE 2                  Gray Code Mapping for 64 QAM                             I 1 I 2 I 3  (Q 1 Q 2 Q 3 )   Constellation Point                       000   −7/{square root over (42)}(j)           001   −5/{square root over (42)}(j)           011   −3/{square root over (42)}(j)           010   −1/{square root over (42)}(j)           110     1/{square root over (42)}(j)           111     3/{square root over (42)}(j)           101     5/{square root over (42)}(j)           100     7/{square root over (42)}(j)                        
As introduced herein, a remapping process at a relay node is described when modulation modes of two hops for a communication link or path are different.
 
     Turning now to  FIGS. 10 and 11 , illustrated are flowcharts demonstrating embodiments of a bit remapping process when modulation schemes of two hops for a received signal and a transmitted signal at a relay node are different according to the principles of the present invention. In addition to the modules or steps mentioned above at a relay node, a bit remapping module  1050  is now inserted between a symbol de-interleaving module  1045  and a symbol interleaving module  1055 , and is described further hereinbelow. Additionally, a bit demapping module  1090  is inserted at a destination node. 
     Regarding  FIG. 11 , illustrated is a simplified process of a remapping process according to the principles of the present invention. As illustrated in  FIG. 11 , the source node now contains a symbol interleaving module  1120 . While the relay node includes a remapping module  1150 , the relay node does not include the interleaving and a de-interleaving modules. Omission of these modules or steps in the relay node may provide a reduction of latency delay associated with signal processing. Additionally, the order of demapping module  1180  and de-interleaving module  1190  at the destination node has now been interchanged in comparison to the remapping process illustrated with respect to  FIG. 10 . Additionally, Mod 1  and Mod 2  denote, respectively, the modulation format or schemes of a first hop (the source node to the relay node) and a second hop (the relay node to the destination node), respectively. Correspondingly, the terms M 1  and M 2  denote their respective modulation orders. 
     The remapping process as introduced herein includes three considerations or factors, which are considered and taken as a whole. When two or more factors conflict with each other, they may be considered in priority order, beginning with the first rule recited below having highest priority. 
     The first rule is to protect the most significant bit of the modulation format Mod 1  symbols. This means that if bit I i  is in a more reliable position than bit I j  in the modulation format Mod 1  symbols, then after remapping on to the modulation format Mod 2  symbols, bit I i  is mapped into a more reliable position than bit I j . Stated more generally, bit I i  is not mapped into a less reliable position than bit I j . The second rule is to preserve integrality of the bits in a modulation symbol. Preserve the integrality of bits in the modulation format Mod 1  symbols, and then protect the integrality of bits in modulation format Mod 1  symbols at a more reliable position, if possible, in the modulation format Mod 2  symbols. 
     The third rule is to maintain equilibrium for the bits in modulation format Mod 1  symbols. This means that based on the above two rules, each modulation format Mod 1  symbol is treated equally. For example, when Mod 1 =64 QAM and Mod 2 =256 QAM, although the first remapping process illustrated below is strictly in accordance with rule 1 and rule 2, the performance of the second remapping process illustrated below is better than that of the first. If each 64 QAM symbol has the same reliability, in the second remapping process, equivalent performance of S 64QAM  at the destination is not maintained as a result of the splitting. The split bits should be mapped on to more reliable positions in 256 QAM symbols. Thus, equilibrium among each modulation format Mod 1  symbol is important. 
                 (         I   1     ⁢           ⁢     I   2     ⁢           ⁢     I   3         S       64   ⁢   QAM     ,   1         )     ⁢     (         I   4     ⁢           ⁢     I   5     ⁢           ⁢     I   6         S       64   ⁢   QAM     ,   2         )     ⁢     (         I   7     ⁢           ⁢     I   8     ⁢           ⁢     I   9         S       64   ⁢   QAM     ,   3         )     ⁢     (         I   10     ⁢           ⁢     I     11   ⁢               ⁢           ⁢     I   12         S       64   ⁢   QAM     ,   4         )       →       (         I   1     ⁢           ⁢     I   2     ⁢           ⁢     I     3   ⁢               ⁢           ⁢     I   10         S       256   ⁢   QAM     ,   1         )     ⁢     (         I   4     ⁢           ⁢     I   5     ⁢           ⁢     I   6     ⁢           ⁢     I   11         S       256   ⁢   QAM     ,   2         )     ⁢     (         I   7     ⁢           ⁢     I   8     ⁢           ⁢     I   9     ⁢           ⁢     I   12         S       256   ⁢   QAM     ,   2         )                       (         I   1     ⁢           ⁢     I   2     ⁢           ⁢     I   3         S       64   ⁢   QAM     ,   1         )     ⁢     (         I   4     ⁢           ⁢     I   5     ⁢           ⁢     I   6         S       64   ⁢   QAM     ,   2         )     ⁢     (         I   7     ⁢           ⁢     I   8     ⁢           ⁢     I   9         S       64   ⁢   QAM     ,   3         )     ⁢     (         I   10     ⁢           ⁢     I     11   ⁢               ⁢           ⁢     I   12         S       64   ⁢   QAM     ,   4         )       →       (         I   10     ⁢           ⁢     I   1     ⁢           ⁢     I     2   ⁢               ⁢           ⁢     I   3         S       256   ⁢   QAM     ,   1         )     ⁢     (         I   11     ⁢           ⁢     I   4     ⁢           ⁢     I   5     ⁢           ⁢     I   6         S       256   ⁢   QAM     ,   2         )     ⁢     (         I   7     ⁢           ⁢     I   8     ⁢           ⁢     I   9     ⁢           ⁢     I   12         S       256   ⁢   QAM     ,   2         )             
Bit remapping schemes for Mod 1 =64 QAM and Mod 2 =256 QAM are illustrated in Table 3 below.
 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Bit Remapping Processes for Mod 1  = 64 QAM and Mod 2  = 256 QAM 
               
            
           
           
               
               
            
               
                 Modulations 
                 Mod 1  = 64 QAM, Mod 2  = 256 QAM 
               
               
                   
               
               
                 Optimum remapping 
                 (10 1 2 3) (11 4 5 6) (7 8 9 12); 
               
               
                 schemes 
                 (10 1 2 3) (4 5 6 11) (7 8 9 12); 
               
               
                   
                 their equivalents. 
               
               
                 Other potential promising 
                 (1 2 3 10) (4 5 6 11) (7 8 9 12); 
               
               
                 schemes 
                 (1 2 10 3) (4 5 11 6) (7 8 9 12); 
               
               
                   
                 (1 2 10 3) (4 5 6 11) (7 8 9 12); 
               
               
                   
                 (10 1 2 3) (11 4 5 6) (12 7 8 9); 
               
               
                   
                 (1 2 3 9) (4 5 6 12) (7 10 11 8); 
               
               
                   
                 (1 2 3 9) (4 5 6 12) (7 8 10 11); 
               
               
                   
                 (7 1 2 3) (10 4 5 6) (8 11 12 9); 
               
               
                   
                 their equivalents; 
               
               
                   
                 other schemes which take the three remapping 
               
               
                   
                 rules into account as a whole. 
               
               
                   
               
            
           
         
       
     
     If the communication channel for each modulation format Mod 1  symbol is different (i.e., if each modulation format Mod 1  symbol has different reliability), communication channel effects such as an increased noise level should be taken into account. For example, in an OFDM system, the modulation format Mod 1  symbols in deeply faded subcarriers should be split on to different modulation format Mod 2  symbols. Implementation of these rules will now be described for the exemplary case of Mod 1 =16 QAM, and Mod 2 =64 QAM, and a comparison among several remapping processes as introduced herein will be made. 
     Turning now to  FIGS. 12 and 13 , illustrated are graphical representations demonstrating exemplary performance parameters of remapping processes according to the principles of the present invention. Beginning with  FIG. 12 , illustrated is a graphical representation of a frame error rate (“FER”) of several bit remapping processes when Mod 1 =16 QAM, Mod 2 =64 QAM, and the signal to noise ratio (“SNR”) of the second hop is 10 decibels (“dB”). The expression (1 2 3) (4 5 6) in  FIGS. 12 and 13  represents the bit mapping between the modulation symbols as illustrated by the conventional bit mapping expression (2) below. 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             1 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             3 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             4 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             6 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             3 
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             1 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             3 
                           
                         
                         
                           S 
                           
                             
                               64 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             4 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             6 
                           
                         
                         
                           S 
                           
                             
                               64 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The sign “=” in  FIGS. 12 and 13  indicates that the two operations on both sides of the sign “=” have the same performance or equivalent effect. Selected parameters are listed below in Table 4. The corresponding curves when the signal to noise ratio of the second hop is 18 dB are illustrated in  FIG. 13 . As illustrated in  FIGS. 12 and 13 , a bit remapping process as introduced herein provides a significant level of frame error rate improvement over a substantial range of signal to noise ratio. 
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Selected Parameters 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Modulation of the 1 st  hop 
                 Mod 1  = 16 QAM, M 1  = 4 
               
               
                   
                 Modulation of the 2 nd  hop 
                 Mod 2  = 64 QAM, M 2  = 6 
               
               
                   
                 Channel model 
                 AWGN for both the 1 st  and 2 nd  hop 
               
               
                   
                 Channel code parameters 
                 ⅓ Turbo code, [11 13] oct   
               
               
                   
                 Channel code length 
                 k = 320, n = 972 
               
               
                   
                 SNR (Es/No) of 2 nd  hop 
                 10 dB, 18 dB 
               
               
                   
                   
               
            
           
         
       
     
     Referring to  FIG. 12 , an optimum bit remapping process is (1 2 5) (3 4 6)=(1 2 6) (3 4 5). This remapping process outperforms a conventional solution inferred from the 3GPP TS 36.212 by about 1.5 dB when the bit error rate is 0.1. In this remapping process, integrality of S 16QAM,1  and S 16QAM,2  are preserved and mapped onto the two most reliable positions of 64 QAM symbols. Bits of the split symbol I 5 I 6  are allocated to the least significant bits of the 64 QAM symbols. Two other bit remapping processes, (1 2 6) (5 3 4) and (1 2 6) (3 5 4), also produce a favorable level of performance. These other processes substantially conform to the three rules introduced hereinabove. 
     Turning now to  FIG. 14 , illustrated is a flowchart demonstrating an embodiment of a bit interleaving process when modulation schemes of two hops for a received signal and a transmitted signal at a relay node are different according to the principles of the present invention. The bit interleaving process provides a benchmark for performance comparison employable with a bit remapping process in accordance with the principles of the present invention. A characteristic of the bit interleaving process illustrated in  FIG. 14  is that a bit interleaver module  1450  is inserted in the relay node between a symbol de-interleaving-1 module  1445  and a symbol interleaving-2 module  1460 . As illustrated in  FIG. 14 , the relay node now contains a demodulation and hard-decision module  1440  and the bit interleaver module  1450 . The destination node now contains a bit de-interleaving module  1490  inserted between a symbol de-interleaving-2 module  1485  and a channel-decoding module  1495 . A function of the bit interleaving module  1450  is to rearrange bits randomly. Other bit interleaving processes can be similarly constructed. 
     An optimum and several alternative bit remapping processes, constructed in accordance with embodiments of the present invention, are listed below in Table 5. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Bit Remapping Processes for Mod 1  = 16 QAM and Mod 2  = 64 QAM 
               
            
           
           
               
               
            
               
                 Modulation 
                 Mod 1  = 16 QAM, Mod 2  = 64 QAM 
               
               
                   
               
               
                 Optimum remapping 
                 (1 2 6) (3 4 5) = (1 2 5) (3 4 6) and its 
               
               
                 scheme 
                 equivalent 
               
               
                 Other promising schemes 
                 (1 2 6) (5 3 4) = (1 2 5) (6 3 4); 
               
               
                   
                 (1 2 6) (3 5 4) = (1 2 5) (3 6 4); 
               
               
                   
                 their equivalents; 
               
               
                   
                 other schemes that take the three remapping 
               
               
                   
                 rules into account as a whole. 
               
               
                   
               
            
           
         
       
     
     Implementation of the optimum bit remapping process (1 2 6) (3 4 5) is now described as an exemplary embodiment. The implementation includes four important elements and steps. The first step includes preserving the integrality of the largest number of 16 QAM symbols. If the number of 16 QAM symbols is N 1 , the number of 64 QAM symbols is N 2 =(⅔)N 1 , recalling that a 16 QAM symbol represents four bits and a 64 QAM symbol represents six bits. Only 2N 2  16 QAM bits (including N 2  in-phase bits and N 2  quadrature bits) can be kept integral, while the remaining 2N 2 ′=(⅔)N 1  16 QAM bits should be split. 
     The second step includes mapping the 2N 2  integral 16 QAM bits on to the most significant bit and the middle significant bit of each 64 QAM component. According to the third step, when remapping the integral 16 QAM bits, rule 1 should be followed. In other words, if bit I 1  and bit I 2  are the most significant bit and the least significant bit of a 16 QAM component, then bit I 1  should be mapped as the most significant bit of the 64 QAM component and bit I 2  should be mapped as the middle significant bit of this component. The fourth step includes mapping the other 2N 2 ′ split 16 QAM bits onto the least significant bit of each 64 QAM component. 
     A simplified process, constructed according to an embodiment, to reduce latency delay by the proposed remapping processes has been introduced herein. Recognizing that latency delay at a relay node is generally a consequence of bit processing, a simplified process to simplify processing at a relay node is to omit the symbol de-interleaver  1  module and the symbol interleaver  2  module as illustrated in  FIG. 11 . The symbol de-interleaver module  1190  at the destination node is designed according to the modulation format Mod 1  and the demapping module  1180  is inserted therein. To execute symbol de-interleaver  1  at the destination node accurately, a relay node forwards information about the structure of modulation format Mod 1  to the destination node, which requires additional signals to carry this further information. In this simplified arrangement, bits can be remapped and re-modulated as soon as modulation order M 2  bits are received without receiving the whole codeword. This may further reduce processing delay at a relay node. Performance of the optimum remapping scheme (1 2 3) (4 5 6)→(1 2 6) (3 4 5) under other coding rates and other coding modes can be demonstrated by numerical calculation. 
     Thus, with reference to  FIG. 6  introduced above, an apparatus (e.g., relay node such as a base station or user equipment)  610  includes a processor  620  (via, for instance, a remapper  624 ) configured to remap an order of bits of a received signal from a source node (e.g., user equipment) to a different order of bits for a transmitted signal to a destination node (e.g., a base station) when the transmitted signal is constructed with a modulation scheme different from the received signal. The processor  620  (via, for instance, the remapper  624 ) may maintain integrality of bits between the received and transmitted signals in accordance with remapping the order of bits of the received signal to the different order of bits for the transmitted signal. Additionally, the processor  620  (via, for instance, the remapper  624 ) is configured to remap bits of a constellation associated with the received signal having a highest reliability into bits of a constellation associated with the transmitted signal having a highest reliability. As an example, if the received signal is constructed with a 16 QAM scheme and the transmitted signal is constructed with a 256 QAM scheme, the order of bits of the received signal is (1 2 3) (4 5 6) (7 8 9) (10 11 12) and the different order of bits for the transmitted signal is one of (10 1 2 3) (11 4 5 6) (7 8 9 12) and (10 1 2 3) (4 5 6 11) (7 8 9 12). As another example, if the received signal is constructed with a 16 QAM scheme and the transmitted signal is constructed with a 64 QAM scheme, the order of bits of the received signal is (1 2) (3 4) (5 6) and the different order of bits for the transmitted signal is one of (1 2 6) (3 4 5) and (1 2 5) (3 4 6). 
     The processor  620  (via, for instance, an encoder/decoder  623 ) is also configured to de-interleave symbols formed by bits of the received signal prior to remapping the order of bits of the received signal and interleave symbols formed by bits of the transmitted signal after remapping the order of bits of the received signal to the different order of bits for the transmitted signal. The relay node  610  also includes a transceiver  670  configured to demodulate the received signal prior to remapping the order of bits of the received signal and modulate the transmitted signal after remapping the order of bits of the received signal to the different order of bits for the transmitted signal. 
     Turning now to  FIGS. 15 to 19 , illustrated are graphical representations demonstrating exemplary performance parameters of remapping processes according to the principles of the present invention. More specifically,  FIG. 15  provides exemplary results of a frame error rate performance according to a remapping process with Mod 1 =16 QAM, Mod 2 =64 QAM, for a rate 1/2 turbo code when the signal to noise ratio of the second hop is 15 dB, and  FIG. 16  provides exemplary results of a frame error rate performance according to a remapping process with Mod 1 =16 QAM, Mod 2 =64 QAM, for a 2/3 turbo code when the signal to noise ratio of the second hop is 18 dB. Other selected parameters can be found in Table 4.  FIG. 17  provides exemplary results of a frame error rate performance according to a remapping process with Mod 1 =16 QAM, Mod 2 =64 QAM, for a 1/2 rate conventional code when the signal to noise ratio of the second hop is 18 dB. These curves illustrate that an optimum remapping process outperforms other processes in the illustrated cases. 
     Following the three bit remapping rules introduced hereinabove, some promising alternative remapping schemes are compared for the case of Mod 1 =16 QAM and Mod 2 =256 QAM. In this case, two 16 QAM symbols are mapped to one 256 QAM symbol, recognizing that one 16 QAM symbol represents four bits, and one 256 QAM symbol represents precisely twice as many bits. A conventional solution for an in-phase or quadrature component based on the 3GPP TS 36.212 is represented by expression (3) below. 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             
                               1 
                               ⁢ 
                               
                                   
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             3 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             4 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     ( 
                     
                       
                         
                           I 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           2 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           3 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           4 
                         
                       
                       
                         S 
                         
                           
                             256 
                             ⁢ 
                             QAM 
                           
                           , 
                           1 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Two schemes shown in expressions (4a) and (4b) below are compared with a conventional solution based on the 3GPP TS 36.212. A frame error rate performance according to a remapping process with Mod 1 =16 QAM, Mod 2 =256 QAM, for a 1/3 rate turbo code when the signal to noise ratio of the second hop is 25 dB is shown in  FIG. 18 . Results describing comparison of the bit remapping processes are presented in Table 6 below. 
     Among these bit remapping processes, the optimum is (1 2) (3 4)→(1 3 4 2), which best combines the three rules. The conventional solution (1 2) (3 4)→(1 2 3 4) that preserves integrality of all the 16 QAM symbols and protects half the number of integral 16 QAM symbols, also provides reasonably good performance. 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             1 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             3 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             4 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     ( 
                     
                       
                         
                           I 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           3 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           2 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           4 
                         
                       
                       
                         S 
                         
                           
                             256 
                             ⁢ 
                             QAM 
                           
                           , 
                           1 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             1 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             3 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             4 
                           
                         
                         
                           S 
                           
                             
                               16 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     ( 
                     
                       
                         
                           I 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           3 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           4 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           2 
                         
                       
                       
                         S 
                         
                           
                             256 
                             ⁢ 
                             QAM 
                           
                           , 
                           1 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Bit Remapping Processes for Mod 1  = 16 QAM and Mod 2  = 256 QAM 
               
            
           
           
               
               
            
               
                 Modulation 
                 Mod 1  = 16 QAM, Mod 2  = 256 QAM 
               
               
                   
               
               
                 Optimum remapping scheme 
                 (1 3 4 2) = (3 1 2 4) and its equivalent 
               
               
                 Other potential promising 
                 (1 2 3 4) = (3 4 1 2); 
               
               
                 schemes 
                 its equivalents; 
               
               
                   
                 other schemes which take the 3 remapping 
               
               
                   
                 rules into account as a whole. 
               
               
                   
               
            
           
         
       
     
     Several remapping processes are now compared for the exemplary case of Mod 1 =64 QAM, and Mod 2 =256 QAM constructed according to an embodiment of the present invention. In this case, four 64 QAM symbols are mapped onto three 256 QAM symbols. The 3GPP TS 36.212 conventional solution is (1 2 3 4) (5 6 7 8) (9 10 11 12), which is represented below by expression (5). 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             1 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             3 
                           
                         
                         
                           S 
                           
                             
                               64 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             4 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             6 
                           
                         
                         
                           S 
                           
                             
                               64 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             7 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             8 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             9 
                           
                         
                         
                           S 
                           
                             
                               64 
                               ⁢ 
                               QAM 
                             
                             , 
                             3 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             10 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             
                               11 
                               ⁢ 
                               
                                   
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             12 
                           
                         
                         
                           S 
                           
                             
                               64 
                               ⁢ 
                               QAM 
                             
                             , 
                             4 
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     
                       ( 
                       
                         
                           
                             I 
                             1 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             
                               3 
                               ⁢ 
                               
                                   
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             4 
                           
                         
                         
                           S 
                           
                             
                               256 
                               ⁢ 
                               QAM 
                             
                             , 
                             1 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             6 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             7 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             8 
                           
                         
                         
                           S 
                           
                             
                               256 
                               ⁢ 
                               QAM 
                             
                             , 
                             2 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             I 
                             9 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             10 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             11 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             12 
                           
                         
                         
                           S 
                           
                             
                               256 
                               ⁢ 
                               QAM 
                             
                             , 
                             3 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Several bit remapping processes are now compared with the conventional scheme. The frame error rate performance according to a remapping process with Mod 1 =16 QAM, Mod 2 =256 QAM, for a 1/3 rate turbo code when the signal to noise ratio of the second hop is 25 dB is shown in  FIG. 19 . 
     Two optimum bit remapping processes are (1 2 3) (4 5 6) (7 8 9) (10 11 12)→(10 12 3) (11 4 5 6) (7 8 9 12) and (1 2 3) (4 5 6) (7 8 9) (10 11 12) (10 12 3) (4 5 6 11) (7 8 9 12). Both of these processes preserve a maximum number of integral 64 QAM symbols (three integral symbols in every four 64 QAM symbols). Besides protecting the integral 64 QAM symbols, the two processes account for equilibrium. The optimum bit remapping processes and other promising processes are listed in Table 7. Without exception, all the processes constructed according to embodiments of the present invention preserve and protect two or three integral symbols in every four 64 QAM symbols, and then treat fairly every 64 QAM symbol. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Bit Remapping Processes for Mod 1  = 64 QAM and Mod 2  = 256 QAM 
               
            
           
           
               
               
            
               
                 Modulations 
                 Mod 1  = 64 QAM, Mod 2  = 256 QAM 
               
               
                   
               
               
                 Optimum remapping 
                 (10 1 2 3) (11 4 5 6) (7 8 9 12); 
               
               
                 scheme 
                 (10 1 2 3) (4 5 6 11) (7 8 9 12); 
               
               
                   
                 their equivalent. 
               
               
                 Other potential promising 
                 (1 2 3 10) (4 5 6 11) (7 8 9 12); 
               
               
                 schemes 
                 (1 2 10 3) (4 5 11 6) (7 8 9 12); 
               
               
                   
                 (1 2 10 3) (4 5 6 11) (7 8 9 12); 
               
               
                   
                 (10 1 2 3) (11 4 5 6) (12 7 8 9); 
               
               
                   
                 (1 2 3 9) (4 5 6 12) (7 10 11 8); 
               
               
                   
                 (1 2 3 9) (4 5 6 12) (7 8 10 11); 
               
               
                   
                 (7 1 2 3) (10 4 5 6) (8 11 12 9); 
               
               
                   
                 their equivalents; 
               
               
                   
                 other schemes which take the three remapping 
               
               
                   
                 rules into account as a whole. 
               
               
                   
               
            
           
         
       
     
     The bit remapping processes introduced herein may improve frame error rate performance significantly without introducing implementation complexity, and may be executed with less processing delay. These bit remapping processes may introduce insubstantial additional hardware or additional control signaling, etc., on a remapping function at a relay node, and may be implemented in software. It should be understood that selected steps of the method of operating the communication system may be reordered or omitted, or other steps may be added thereto, and still fall within the broad scope of the present invention. 
     In addition, program or code segments making up the various embodiments of the present invention may be stored in a computer readable medium or transmitted by a computer data signal embodied in a carrier wave, or a signal modulated by a carrier, over a transmission medium. The “computer readable medium” may include any medium that can store or transfer information. Examples of the computer readable medium include an electronic circuit, a semiconductor memory device, a ROM, a flash memory, an erasable ROM (“EROM”), a floppy diskette, a compact disk CD-ROM, an optical disk, a hard disk, a fiber optic medium, a radio frequency (“RF”) link, and the like. The computer data signal may include any signal that can propagate over a transmission medium such as electronic communication network channels, optical fibers, air, electromagnetic links, RF links, and the like. The code segments may be downloaded via computer networks such as the Internet, Intranet, and the like. 
     As described above, the exemplary embodiment provides both a method and corresponding apparatus consisting of various modules providing functionality for performing the steps of the method. The modules may be implemented as hardware (embodied in one or more chips including an integrated circuit such as an application specific integrated circuit), or may be implemented as software or firmware for execution by a computer processor. In particular, in the case of firmware or software, the exemplary embodiment can be provided as a computer program product including a computer readable storage structure embodying computer program code (i.e., software or firmware) thereon for execution by the computer processor. 
     Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. For example, many of the features and functions discussed above can be implemented in software, hardware, or firmware, or a combination thereof. Also, many of the features, functions and steps of operating the same may be reordered, omitted, added, etc., and still fall within the broad scope of the present invention. 
     Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present invention, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.