 Research Article
 Open Access
 Published:
Combined Distributed Turbo Coding and Space Frequency Block Coding Techniques
EURASIP Journal on Wireless Communications and Networking volume 2010, Article number: 327041 (2010)
Abstract
The distributed spacetime (frequency) coding and distributed channel turbo coding used independently represent two cooperative techniques that can provide increased throughput and spectral efficiency at an imposed maximum Bit Error Rate (BER) and delay required from the new generation of cellular networks. This paper proposes two cooperative algorithms that employ jointly the two types of techniques, analyzes their BER and spectral efficiency performances versus the qualities of the channels involved, and presents some conclusions regarding the adaptive employment of these algorithms.
1. Introduction
Most of the services that should be provided by future wireless networks require low or very low and delay values and high data rates. The cooperative transmission techniques represent one of the most promising solutions in wireless networks for provisioning the increased capacity, extended coverage, and improved fairness [1–3] required by such services. They could ensure low , while still inserting limited transmission delays, and also significantly improve the spectral efficiency of wireless systems.
Another technique that could fulfill the above requirements is the Multiple Input Multiple OutputOrthogonal Frequency Division Multiplexing (MIMOOFDM) [4, 5], which has already been adopted in high rate wireless communications standards, such as WiMAX and LTE. However, considering a conventional cellular architecture with colocated antennas, there is significant correlation between channels in some environments; moreover, the use of an antenna array at the user terminals (UTs) may not be feasible due to size, cost, and hardware limitations. The OFDMMIMO could be also implemented through cooperation of users, which share their antennas and thereby create a Virtual Antenna Array (VAA) or a Virtual MIMO (VMIMO) system. In this context, the concept of Distributed SpaceTime Coding (DSTC) was introduced in [6, 7]. This approach allows singleantenna devices to gain some benefits from spatial diversity without the need for physical antenna arrays. Several recent works [8, 9] have considered either the design of DSTC or Distributed SpaceFrequency Coding (DSFC) or the application of the existing spacetime/frequency codes in a distributed manner for the wireless relaybased systems. The use of SpaceTime Block Coding (STBC) based on Alamouti schemes [10] implemented in a distributed manner in OFDMbased cooperative schemes has been discussed in [11, 12], while a fullrate and fulldiversity quasiorthogonal STBC scheme to be applied in virtual antenna arrays was proposed in [13]. In [14], Distributed SpaceFrequency Block Coding (DSFBC) schemes for OFDMbased cellular systems which use an antenna array at the BS and a single antenna at both the UT and RN have been proposed.
Another cooperative approach that aims at exploiting diversity is the Distributed Forward Error Correction Coding (DFEC). Such a cooperation scheme, proposed in [15], was intended initially to create transmit diversity in the uplink of a wireless system. Using standard FEC, partitioning of code words and transmitting these parts by the cooperating partners, together with error detection at each partner, could overcome the drawbacks of a simple cooperation based on repetition coding. The performances of FECbased cooperation schemes were investigated under various channel conditions and power allocation modes in [16, 17], while some algorithms are provided in [18] and throughput maximization methods are provided in [19]. Niu and Lu [20] have combined the OFDM flexible subcarrier allocation with distributed coding, extending the cooperative communication strategy from the time domain to the timefrequency domain, by incorporating the Orthogonal FrequencyDivision Multiple Access (OFDMA) concept. Practical distributed coding protocols that use RateCompatible Punctured Convolutional Codes (RCPCC) were proposed and investigated in [21]. This approach ensures high performances both for Amplify & Forward (AF) and Decode & Forward (DF) relaying schemes, while maintaining a low complexity.
One step further is the joint use of cooperative techniques, such as DST(F)BC or DFEC, with Network Coding (NC), which combines the advantages provided by each of the involved techniques and diminishes their shortcomings. Recent papers, such as [22–25], propose various versions of combining these techniques which provide results that are more than promising. Nevertheless, the employment of NCbased techniques involves more elaborate clusterselection techniques which seem to be difficult to implement in the present mobile cellular systems.
Therefore, this paper proposes two cooperation algorithms, serving one UT, that employ in a joint manner the distributed space frequency coding and distributed FEC, analyzes their performances and compares these performances with those of DSFC and DFEC cooperation algorithms used independently. The paper is structured as follows: Section 2 explains briefly the motivation of this study, while Section 3 presents the cooperation protocol and topologies used and briefly arguments their selection. Section 4 describes the DSFC and DFEC cooperative algorithms and the proposed combined DSFC+DFEC cooperation algorithms, while Section 5 briefly discusses the evaluation of their spectral efficiency. Section 6 describes the performance metrics employed and the test scenarios used for performance evaluation; it presents the simulation results obtained and analyzes these results. Finally, Section 7 presents some conclusions regarding the selection of the cooperative algorithm according to the given topology, scenario, and type of service that has to be provided.
2. Motivation and Objectives
The performances of the cooperative algorithms, , Bloc Error Rate (BLER), and spectral efficiency, are strongly affected by the combining method of the signals received on the source—destination and on the relay (relays)—destination links. Two main categories of messagecombining methods could be used:

(i)
symbollevel combining, which is specific to spacetime/spacefrequency coding and to maximum ratio combining. These message combining techniques provide diversity gain,

(ii)
bitlevel combining, that is, bitLLRs addition and/or concatenation, which is characteristic to distributed FEC. These message combining techniques provide less diversity gain, but they provide coding gain.
These combining methods exhibit different degrees of flexibility, when employed in different cooperative transmission scenarios. Symbollevel combining requires the same constellation on each transmission link, regardless of the significantly different qualities of the channels employed by each cooperation phase. Bitlevel combining has a greater flexibility, allowing the use of different constellations on different transmission links, according to each channel state, fact that has significant impact upon the spectral efficiency.
The joint use of the two types of message combining could ensure both improved and flexibility, thus providing greater spectral efficiency. One way to achieve this mix of message combining in cooperative networks would be to employ in a joint manner distributed FEC and distributed diversity techniques, thus providing both coding and diversity gains.
The main objective of the paper is to analyze the performances of some particular cooperation algorithms combining DSFC and DFEC within a topology containing a virtual MIMO scheme that uses the antennae of one or two relay nodes (RNs), to compare their and spectral efficiency performances to those of cooperation schemes using independently either the DSFC or DFEC techniques, and to identify scenarios within which these combined distributed coding schemes provide greater spectral efficiencies at an imposed . The applicability of these algorithms to several types of services, according to the and spectral efficiency requirements, will also be briefly considered.
3. Cooperation Protocol and Topologies
This paper considers a test topology, with singleantenna equipments, where two dedicated relay nodes (RN_{1}, RN_{2}), fixed or nomadic, assist the communication between the Base Station (BS) and the UT. The access scheme is OFDMA, the constellations used are QPSK, 16, and 64 QAM and all pointtopoint transmissions are Single Input Single Output (SISO) ones.
The cooperative algorithms studied employ the classical twophase cooperation protocol, which are supposed to occur successively in time, but might not use the same signal constellation.

(1)
In the "broadcast phase", the source node (BS or UT) sends its message to the RN and to the destination node (UT or BS, resp.). The content of the broadcast message is specific to the cooperation algorithm employed.

(2)
In the "relaying phase", the RNs decode the received message, perform the processing specific to the cooperation algorithm employed and send their messages to destination (UT or BS).
The destination jointly decodes the information received from the RNs or both from the source and RNs, according to the cooperation algorithm.
The two phases of the cooperation protocol applied to this topology are illustrated in Figure 1 for the downlink (DL) connection; that is, the broadcast message is transmitted to the RNs and UT, while the relay message, which depends on the DFEC algorithm employed, is transmitted jointly by the two RNs using a cooperative diversity scheme, like DSTC or DSFC. The message sent during the broadcast phase might be employed or not by the destination's receiver.
Since the number of RNs is limited by relay assignment, resource allocation and signaling issues, the test topology can be simplified by imposing the source to act as one of the RNs and transmit both during the broadcast phase, as source, and during the relaying phase, as one of the RNs, as shown in Figure 1.
The asymmetrical twoRN topology, with different ratios received from the two RNs, could be transformed into a symmetrical topology for easier analysis and simulation, by considering an equivalent value that is received from each RN on the RNdestination links, as shown in Figure 2.
4. Cooperative Distributed Coding Algorithms
This section gives a short overview of the cooperation algorithms employing Alamoutibased DSFC and Turbo Coding (TC)based DFEC techniques and describes the proposed combined DSFCDFEC cooperation algorithms.
4.1. Distributed SpaceFrequency Coding (DSFC)
The topology with two RNs contains five links; namely, the direct BSUT link, defined by the channel, the BSRN_{ i } links , defined by the channels, and the RN_{i}UT links, defined by channels , as shown in Figure 1. Within the topology with one RN, the BSRN_{2} link is an ideal one, while the RN_{2}UT link is represented by another realization of the channel.
The operations performed by this DSFC algorithm during cooperation are briefly described below.

(1)
In the broadcast phase, the source node transmits the coded block ( information bits and check bits) towards the RNs and destination, using a modulation adapted to the channels involved.

(2)
In the relaying phase, the RNs decode and reencode the message with the same FEC code, apply a DSFCAlamouti scheme [10] and transmit their perfectly synchronized messages on the RN_{ i }destination channels using the same signal constellation (not necessarily the same as in the first phase).

(3)
At the destination end, the DSFCdecoded symbols and the ones received from the source during the broadcast phase are MRCcombined to provide the symbols that are fed to the FEC decoder. Because this algorithm uses at destination signals received both from RNs and the source, it will be denoted as the composed DSFC, cDSFC. Since the messages received during the cooperation phases are combined at QAMsymbol level, all links should use the same modulation.
To point out the effects of the direct link transmission upon the performance of the DSFC scheme, an alternative version, called simple DSFC (sDSFC), which does not use the direct link at the receiver's end, is also considered. Hence, different signal constellations might be used during the two cooperation phases.
In the subsequent sections, we consider that all channels involved are complex flat Rayleighfaded channels, and the noise samples have zeromean and variance equaling . We also consider that the OFDM subcarrier separation is significantly lower than the channel's coherence bandwidth, and so, the fading over two adjacent subcarriers can be considered flat.
Considering the cDSFC algorithm, the instantaneous on subcarrier obtained after the MRCcombining performed at destination between the symbols received on the direct link and those provided by the Alamouti decoding of the DSFC signals on the RN_{i}destination links is [14, 26]
where represents the complex coefficient of the flat Rayleigh faded BSUT channel, during the broadcast phase, for the th subcarrier with an average power , denotes the RN_{i}UT channel during relaying phase, for the th subcarrier with an average power of , in the assumption that the fading over two adjacent subcarriers can be considered flat; that is, is equal to . We also assume that the noise variance of the signals received at the UT during the two phases to be equal, that is, .
If the topology with one RN is considered, see Figure 1, then the BS acts as the second RN (in the DL), and therefore, in relation (1), should be replaced by , the complex flat Rayleigh BSUT channel's realization for the th subcarrier during the relaying phase.
If the direct link is not used in the decoding process at the receiving end (the sDSFC algorithm) the instantaneous on subcarrier is expressed in a similar manner by (2) [14, 26] and is smaller that the one ensured by the cDSFC algorithm, see(1)
If the channels are correctly equalized, we may assume that the LLRs of all bits of the FEC codeword are extracted from the same equivalent channel, with SNRs expressed by (1) for the algorithm which employ the sourcedestination link, respectively, by (2) for topologies which do not employ this link.
4.2. Distributed FEC Cooperation Algorithms
Distributed FEC algorithms use the classical twophase cooperation protocol [16, 17], applied within a topology with one RN, for example, RN_{1}, which is particularized in Figure 3. Most of distributed FEC algorithms use the same encoder both at source and at RN, some of them employing different puncturing patterns for the two transmissions. Usually, Convolutional Turbo Codes (CTCs) or Low Density Parity Check (LDPC) codes are employed to implement the distributed FEC.
4.2.1. Distributed FEC with Incremental Redundancy
The Incremental Redundancy DFEC (IRDFEC) algorithm that uses CTCs is briefly described below and represented in Figure 3.

(i)
Broadcast Phase
The UT (or the BS) encodes the information bits using a CTC code with a coding rate (the mother code rate). The resulted check bits are appropriately punctured according to a rate matching algorithm [27], to obtain a desired coding rate . The resulted coded blocks of length are then sent by the source (UT or BS) over the sourcedestination and sourceRN links.

(ii)
Relaying Phase
The RN decodes the received block, using a turbo decoder, and it reencodes these bits using the same CTC encoder. Then, it selects a number of additional check bits , by using a different puncturing pattern corresponding to a coding rate , and these bits are transmitted over the RNdestination link. The two coding rates and are chosen so that the global coding rate, , which is expressed by (3), would equal the rate of the mother code

(iii)
Decoding
At destination, before turbodecoding, the blocks received both from source and RN are assembled and completed according to the employed puncturing rules. The information and the check bits generated by the source are received at smaller equivalent values, , than the check bits generated by the relay, , as shown by (4), fact that represents the main disadvantage of IRDFEC
The advantage of the IRDFEC scheme consists of the relatively small amount of timefrequency resources required by the relaying phase, which increase the spectral efficiency, and the possibility to build distributed Hybrid Automatic Repeat Request (HARQ) schemes based on this cooperation scheme.
4.2.2. Hybrid Distributed FEC with Incremental Redundancy
The effects of small SNRs on the direct link might be overcome by a Hybrid IRDFEC (HIRDFEC) algorithm based both on repetition and incremental redundancy encoding. The HIRDFEC algorithm is similar to the IRDFEC one, see Figure 3, but in the relaying phase the RN sends, besides the check bits, the decoded information bits . The coding rate obtained in the relaying phase is .
The decoding performed at the destination node is schematically represented in Figure 4. The destination node combines the LLRs corresponding to the information bits received over the direct and relay links, then it reorders the check bits received on the two links and concatenates them in order to restore the LLRflow of the complete rate codeword, which is fed into the turbo decoder.
The global coding rate is the same as the one of the IRDFEC algorithm, (3), but this algorithm involves the transmission of two sets of information bits, and therefore, in the computation of the payload bit rate and spectral efficiency, a transmission rate, , given by (5) should be considered
The spectral efficiency of this algorithm is smaller, but the information bits are better protected, since they are transmitted both on the direct and on the relay links, and therefore, they are received under an equivalent , , expressed by (6), which is greater than the one ensured by the IRDFEC for these bits. As for the and check bits, they are received on similar conditions as in the IRDFEC algorithm
4.2.3. Combined DSFC+DFEC Cooperation Algorithms
Distributed turbo coding algorithms (IRDFEC or HIRDFEC) are able to provide increased spectral efficiency, system flexibility but also significant coding gains if the sourceRN and RNdestination links have good qualities. These conditions cannot be ensured only by positioning the relay, while the employment of powerful channel codes decreases the spectral efficiency and increases the complexity.
The quality of the transmission between the RN and destination can be significantly improved by using one or two RNs to implement a DSFC (or DSTC) algorithm, due to the diversity provided on the uncorrelated RN_{i}destination links. In the same time, a small could be ensured in the broadcast phase by placing the RNs closer to the source. Therefore, the combined use of DFEC and DSFC algorithms could provide improved performances and allow the use of simplified relay selection algorithms.
The combined sDSFC+DFEC algorithms proposed are schematically represented in Figure 1 for the DL connection in the particular case when only 2 relays are used to implement the sDSFC in the relaying phase. A brief description of the operations performed is presented below.

(i)
Broadcast phase. The source (BS) broadcasts the information bits encoded with a CTC of rate ( check bits) over the BSUT and BSRN_{i} links.

(ii)
Relaying phase. The RNs performs the DFEC decoding, followed by the HIRDFEC or IRDFEC encoding. Then, the two RNs perform the DSFC encoding, that is, Alamouti scheme, described in Section 4.1, using the same QAM constellation, which might be different from the one employed during the broadcast phase.

(iii)
Decoding at destination. The destination performs the following operations:

(1)
demodulates and extracts the LLRs of the bits transmitted during the broadcast phase,

(2)
extracts the symbols transmitted during relay phase by SFCdecoding and extracts the LLRs of the (for HIRDFEC) or (for IRFEC) received bits; note that the message received on the direct link, during the broadcast phase, is not used in this operation,

(3)
combines the LLRs of the bits received on both broadcast and relay phase (only for HIRDFEC),

(4)
reorders the LLRs of the received bits and performs the DFEC decoding.

(1)
4.3. Some Considerations Regarding the Effects of the Errors on the SourceRelays Links
The qualities of the sourcerelay links have a significant effect upon the global provided by the cooperative algorithms. In order to evaluate their effects upon the performance of the proposed algorithms, we assume that if the block received by the one of the RNs is decoded with errors, the RN reencodes the decoded bits and apply the corresponding cooperation algorithm. Another option would be to make the RN stop transmitting any message and to signalize this fact to destination. But this second approach would require additional signaling and adaptive use of the cooperation algorithm at destination.
Denoting by the block error probability at destination provided by the algorithm , if the messages transmitted by RNs are correct, and by and the block error probabilities after the RN_{i} decoding, the global block error probability of the whole cooperative algorithm, , can be expressed using the probability of a correct decoding at destination , by
The values of and differ for the two ways of transmission. For the DL connection, due to the higher BS antenna and to the possibility to employ RNs that have Line Of Sight (LOS) channels to the BS, the two , and the corresponding , can be considered negligible and the global is established by the provided by the cooperative algorithm at the UT. For the UL connection, the error probabilities of the UTRN_{i} links cannot be neglected and the global and are dictated by both the cooperative decoding in the BS (destination), that is, and , and by the error probabilities of the UTRN_{i} links, that is, and . Therefore, the and are expected to be greater on the UL than on the DL connection, in such a topology.
5. Computation of the Spectral Efficiency Provided by the Proposed Algorithms
The spectral efficiency is one of the main criteria used to select the appropriate cooperative transmission algorithm. The spectral efficiency provided by the cooperative algorithm is expressed by (8) in terms of the nominal bit rate , bit error probability , which define the throughput , and the employed bandwidth
The nominal bit rate and the bandwidth are dependent on the cooperation algorithm's structure and the parameters of the transmission scheme. The bit error probability is expressed in terms of an equivalent at the decoder's input, which includes the values of the on the sourcedestination and RNdestination channels. This equivalent depends on the cooperation algorithm and on the combining method employed.
5.1. Spectral Efficiency of the IRDFEC Algorithm
We consider that during the broadcast phase the number of bits/QAM symbol is , while during the relaying phase it is . Then, the number of QAM symbols required to transmit the messages during the two cooperation phases is computed using the considerations of Section 4.2.1 and is expressed by
We assume that the symbols are transmitted in an OFDM system that has subcarriers and OFDMsymbol periods per resource allocation unit, with an separation frequency between subcarriers and a guard interval of g% of the symbol period. Considering further that the nominal bit rate is obtained by dividing the number of information bits to the time required to transmit all coded bits and that the bandwidth occupied equals the spectral efficiency provided by this algorithm is given by, as shown in [28]
The factor expresses the fact that during the two phases different QAM constellations are used, while indicates that in the relaying phase only a fraction of the first message's length is transmitted.
5.2. Spectral Efficiency of the HIRDFEC Algorithm
Assuming again that during the broadcast phase, the number of bits/QAM symbol is , and during the relaying phase, it is , and using the considerations of Section 4.2.2, the number of QAM symbols required transmitting the messages during the two cooperation phases equals
Then, using a similar reasoning as above, the spectral efficiency of the transmission that employs HIRDFEC is expressed by
The nominal spectral efficiency of the IRDFEC is greater than the one of HIRDFEC due to the smaller number of additional bits transmitted during the relaying phase. Nevertheless, the spectral efficiency is also influenced by , which should be smaller for the HIRDFEC.
5.3. Spectral Efficiency of the DSFC Algorithms
The spectral efficiency of the sDSFC algorithm could be derived by using the same reasoning as for the HIRDFEC algorithm. The spectral efficiency has expressions similar to (12), in which the bit error rate should be the one provided by this algorithm, that is, BER_{sDSFC}.
For the cDSFC algorithm, since the combining is performed at QAM symbollevel, the two phases of cooperation should employ the same number of bits/QAM symbol. The spectral efficiency of this algorithm can be computed using (13), where denotes the coding rate of the FEC used
5.4. Spectral Efficiency of the Combined DSFC+DFEC Algorithms
Since the two combined DSFCDFEC algorithms are obtained superimposing the sDSFC over the IRDFEC or HIRDFEC algorithms, their spectral efficiencies should be computed using (10) for DSFC+IRDFEC and (12) for the DSFC+HIRDFEC. In these relations, the used should be the one provided by the respective combined algorithm.
6. Performance Evaluation of the DSFC and DFEC Cooperation Algorithms
This section presents a comparative performance evaluation of the coded cooperative algorithms described in the previous section. The performances are evaluated in the assumption that the RNs are perfectly synchronized and that perfect Channel State Information (CSI) is available in all network nodes.
6.1. Performance Metrics and Simulation Scenarios
The performance metrics employed are the and the spectral efficiency. The global of the studied algorithms is obtained by computer simulations, while the spectral efficiency is obtained by computation using the relations presented in Section 5. Both performance metrics provided by each algorithm are evaluated in terms of of the direct BSUT link, while the of the other links are equal to, or greater with a constant value than the current value of of the direct link.
The channel model employed on all links is briefly summarized below:

(i)
propagation loss with a path loss exponent of 2,

(ii)
multipath propagation power delay profile: ITUT pedestrian B,

(iii)
quasistatic Rayleigh small scale fading,

(iv)
the additive noise is complex Gaussian noise with zero mean value (AWGN).
The broadcast phase uses QPSK, while the relaying phase uses either QPSK or 16 QAM or 64 QAM. The channel codes employed by the DFEC algorithms are obtained by puncturing a mother turbo code of rate defined in [27], generated by the feedback polynomial 13_{8} and the feedforward polynomial 15_{8}. For the cDSFC algorithm, the FEC code employed has a rate . The coded block is 7200bit long, with 3600 information bits. The IRDFEC and HIRDFEC transmissions use additionally a group of 3600 check bits computed and transmitted by the RN (or RNs), the global coding rate being .
The scenarios selected for performance evaluation consider the cooperative topologies with two RNs and with one RN (see Figure 1) and are described below; they are meant to point out the differences between the performances provided in the DL and UL connections. The relations between the values of the component channels are presented in Table 1.

(1)
Scenario D1 is defined for the DL connection; it considers that the qualities of the RN_{i}UT links are comparable to the one of the direct BSUT link, while the BSRN_{i} links have better qualities due to the higher BS antenna and appropriate selection of the fixed and dedicated RNs.

(2)
Scenario D2 is also defined for the DL connection, but it is an asymmetrical one which considers that one of the RN_{i}UT links has better quality than the direct BSUT link. This scenario describes a situation when one of the relays could be better positioned relatively to the destination. The same scenario could be employed for the topology with one RN, as well.

(3)
Scenario U, is defined to point out the effects of potential shadowing that might affect the UTRN_{i} transmissions, upon the UL cooperative connection. Therefore, the values of both UTRN_{i} channels (Scenario U1), or the value of one of these channels (Scenario U2), were set to be smaller than that the one of the RN_{i}BS channels.
In all scenarios, the DFEC algorithms (using one RN) employ the UTRN_{i} link that has the highest .
6.2. Performances on the Downlink Connection
The provided by the studied algorithms in the DL connection within scenarios D1 and D2 are shown in Figures 5 and 6. These results, obtained from extensive computer simulations, lead to the following conclusions.

(1)
The cDSFC cooperative algorithm, using the signal received on the direct BSUT link in the combined MRC decoding, ensures a significantly smaller (see Figure 5). This can be explained by the greater equivalent , see (1), provided by the use of the BSUT signal in the combing process at destination.
The increase of the of the RN_{i}UT links, scenario D2, leads to a small influence of the direct link for low values of the reference , while for greater values of the reference the influence of the direct link increases, as results from comparing the cDSFC and sDSFC curves between (−4; 0) dB and above 2 dB, respectively, in Figure 6. This behavior is explained by (1).
There should also be noted the decrease of the provided by the sDSFC algorithm in scenario D2, compared to scenario D1, due to the increased equivalent , see (2).

(2)
The DFEC algorithms, when are not combined with DSFC, provide poorer performance than the cDSFC algorithm, and in some cases (see Figure 6) poorer performances than the simple DSFC. This is mainly explained by three facts:

(i)
DFEC algorithms employ only one RN, so there is no diversity for the and check bits (see Figures 3 and 4), while for the information bits only the HIRDFEC provides diversity,

(ii)
the turbodecoder "combines" the LLRs of all received bits, providing only a coding gain,

(iii)
the LLRs of the bits within a coded block have different levels of reliability since they are obtained from two different links, with different , and by different processing.
As expected, HIRDFEC ensures smaller than IRDFEC. A comparison between Figures 5 and 6 shows that the improvement of the RN_{i}UT links does not bring significant decrease of the provided by the DFEC algorithms.

(3)
The use of sDSFC algorithm in the relaying phase of the DFEC algorithms; that is, sDSFC+IRDFEC or HIRDFEC leads to a significant improvement of their performances. The sDSFC provides diversity for the bits transmitted during the relaying phase, that is, or , which is transformed by the bitlevel combining and by the turbodecoder into an additional coding gain. The improvement of the RN_{i}UT links in scenario D2 (see Figure 6) brings no significant variation of the provided by these algorithms compared to the ones of Figure 5. This could be explained by the fact that only a part of the coded bits are transmitted on the better RN_{i}UT channels, and their more reliable LLRs do not improve significantly the performance of the FEC turbo decoding process.
The performances of the combined algorithms are still poorer than the ones of cDSFC because the use of sDSFC improves only the quality of the (IR) or and (HIR) received LLRs. Still, due to the bitlevel combining and especially to the effects of the poorly received bits, the coding gain brought is smaller than the diversity gain provided by the cDSFBC algorithm, which uses the direct link.
6.3. Performances on the Uplink Connection
The performances provided by the studied cooperative algorithms within scenario U1 are presented in Figure 7 and lead to the following conclusions.

(1)
The cDSFC algorithm provides lower than sDSFC, due to the same reasons as for the DL connection. Nevertheless, the values of provided by the two algorithms for the same values of the component channels are significantly greater than the ones provided in the D1 scenario, see Figure 5. These poorer performances are due to the worse source (UT)RN_{i} links and could be explained by using relation (7), where probabilities and are no longer negligible and so the global and are not depending only on the (or ) provided by the DSFC decoder at destination. Another effect of the errors on the UTRN_{i} links is the decrease of the diversity gain, expressed by a smaller slope of the versus curves of these algorithms.

(2)
The DFEC algorithms provide values that are comparable to the ones of the sDSFC, but greater than the ones of the cDSFC. The differences in the performances are significantly smaller than in the downlink case.

(3)
The combination of the DFEC techniques with the sDSFC leads to lower values, due to the same reasons as in the DL case, but the performance improvement brought by this combination is significantly smaller than in the DL connection, due to the poorer source (UT)RN_{i} links. The improvement of the UTRN_{2} channel, scenario U2, leads to slightly smaller values for all algorithms than the ones provided in scenario U1, as results from the comparison between Figure 7 and Figure 8. The major characteristic of this scenario is that the DFEC algorithms provide better performances if they are not combined with sDSFC. This is because they need to use only the good UTRN_{2} link during the relaying phase, while the sDSFC employs both UTRN_{i} links, out of which one is of poor quality. The increase can be explained by using (7).
The main conclusion is that in the UL connection, the insertion of the sDSFC in the DFEC algorithms is beneficial only if the two UTRN_{i} links have about the same quality; otherwise, the DFEC algorithms used alone could provide smaller , because they could employ only the best UTRN_{i} link.
6.4. Spectral Efficiency Performances
The spectral efficiency performances of the studied algorithms were evaluated only for the DL connection, since according to (10), (12), and (13), the only factor differing for the two ways of transmission is the bit error rate, which was analyzed in the previous section. Figure 9 shows the spectral efficiencies computed for the studied algorithms in the D1 scenario when . The main conclusions drawn are the following.
(i)The two algorithms that use the IRDFEC (combined or not with sDSFC) provide the highest spectral efficiencies due to the small redundancy inserted, see (10). The HIRDFECbased algorithms provide smaller spectral efficiencies due to their greater redundancy during the relaying phase, which cannot be compensated by the smaller provided, see (12). The flat parts (zones) of the curves exhibited by DFEC algorithms are extended with approximately 2 dB by combining them with the sDSFC algorithm.
(ii)The cDFSC algorithm ensures about the same spectral efficiency as the HIRDFEC algorithm, because they both transmit about the same redundancy, see (13) and (12), while the differences in are not big enough to affect significantly the spectral efficiency. The sDSFC provides a narrower flat zone, due to the greater needed to ensure a negligible , for example, 10^{‒ 3}, as shown in Figure 5.
Concluding, the IRDFEC algorithm provides the greatest spectral efficiency and should be preferred for applications where the target is not set to small values, while the cDSFC should be used in applications which require small values.
The spectral efficiencies of all algorithms described above, except for the cDSFC, can be increased by using a higher modulation on the RN_{i}destination link(s) during the relaying phase, as results by increasing in (10) or (12). For a fair comparison, the increase of requires that the higher constellation should ensure the same on the RN_{i}UT links as the one ensured by QPSK. This would require an increased with 4 dB for 16 QAM and with 8.3 dB for 64 QAM . Such an improvement of the RNUT channels could be accomplished either by changing the positions of the two RNs or by increasing the RN's transmitted power or by both. The spectral efficiencies provided by the studied algorithms versus within the D1 scenario modified according to the above values, are presented in Figures 10 and 11. The figures also present the spectral efficiency provided by cDSFC algorithm for and , as reference.
The major difference between Figures 10 and 11 and the curves of Figure 9 lies in the greater values of the spectral efficiencies in the flat zones, due to the higher which ensures about the same . Compared to the spectral efficiency of cDSFC with , the spectral efficiency of IRDFECbased algorithms is increased in the flat zones by a factor expressed by (14a). The values of equal 1.6 for and 1.72 for . A similar factor for the algorithms that use the HIRDFEC, computed using (12) and (13) is expressed by (14b); it equals 1.33 for and 1.5 for
The spectral efficiencies provided by these cooperative algorithms in the D2 scenario are presented in Figure 12, for . The significant extension of the flat zone of the sDSFC algorithm, compared to Figure 9, can be explained by its significantly smaller (see Figure 6) though the maximum value of its spectral efficiency has not changed, see (12). The rest of the algorithms exhibit similar performances to the ones provided for poorer RN_{i}UT channels of scenario D1, Figure 9, but their flat zones are slightly extended due to the better RNUT channel available in this scenario.
Finally, Figures 13 and 14 show the spectral efficiencies provided in the modified D2 scenarios defined above, when higher order modulations, that is, and , are used in the relaying phase. Due to the employment of a larger constellation on the RN_{i}UT links with correspondingly increased , the values of the spectral efficiencies of all algorithms are greater than the ones of Figure 12, except for cDSFC algorithm which should use .
The spectral efficiencies provided by these algorithms in UL connections, scenarios U1 and U2, have similar behaviors in terms of the of the direct link, but their flat zones are narrower than the corresponding ones in the DL, due to the greater values occurring in the uplink, see Section 6.3.
7. Conclusions
This paper has studied the and spectral efficiency performances provided in some relevant DL and UL scenarios by two algorithms that employ in a joint manner the DSFC and DFEC cooperation algorithms. Their performances were compared to the ones provided by the constituent DSFC and, respectively, DFEC algorithms used independently. The combination of these two types of cooperation algorithms exploits both the flexibility of DFEC and the diversity provided by DSFC, while simplifying the relay assignment issue. The diversity provided by DSFC on the RNdestination links allows the placement of the RNs closer to the source and so the sourceRN transmissions would not require the high redundancy of smallrate channel codes. The use of DFEC algorithms involves the direct link that brings an extra coding gain to compensate the decrease of the RNdestination link's quality due to the positioning of the relay closer to the source.
The results obtained in scenarios with good sourceRN and relatively poor RNdestination channels, that is, scenario D1, show that combined sDSFC+DFEC algorithms could provide the best tradeoff between and spectral efficiency performances. This tradeoff could be "finetuned" by the amount of redundancy employed in the relaying phase of cooperation, by using either the HIRDFEC algorithm that provides lower values, or the IRDFEC one, which provides the greatest spectral efficiency. Even if the cDSFC algorithm, which uses the direct link at destination, provides the smallest out of all studied algorithms in all scenarios considered, its spectral efficiency and linkadaptation flexibility are small due to the combining at symbol level, which in its turn provides a greater diversity gain. If the RNdestination link's quality could be improved by relayassignment while still ensuring good sourceRN links, for example, scenario D2, the sDSFC algorithm is the best choice considering both and spectral efficiency performances, but the greatest spectral efficiency could be provided by IRDFEC algorithms.
For scenarios with poor sourceRN links, for example, scenarios U1 and U2, all DFEC algorithms analyzed present comparable performances to the ones of the cDSFC algorithm. In such scenarios, the sDSFC+DFEC or even only DFEC algorithms are the best choice if both and spectral efficiency performances and system flexibility are to be taken into account.
The results obtained also indicate how these cooperative algorithms should be used adaptively to match the performance requirements ( and spectral efficiency) of various services. For highly interactive applications which require low or very low values and not a great spectral efficiency, for example, video conferences, the best option would be the cDSFC, due to its symbollevel combining. For widely used applications requiring relatively low , for example, audio and video streaming, the sDSFC+HIRDFEC algorithm is one of the best options, since it ensures a relatively low and a high spectral efficiency. For popular applications that accept higher values, for example, telephony or messaging, the IRDFEC combined with sDSFC on the RN_{i}destination links would be advisable, since it ensures the highest spectral efficiency, which is an important factor for this type of services.
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Acknowledgment
The authors wish to acknowledge the support of the ICTFP7 European project "Enhanced Wireless Communication Systems Employing Cooperative Diversity—CODIV", FP7/ICT/2007/215477.
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Bota, V., Polgar, Z.A., Silva, A. et al. Combined Distributed Turbo Coding and Space Frequency Block Coding Techniques. J Wireless Com Network 2010, 327041 (2010). https://doi.org/10.1155/2010/327041
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Keywords
 Spectral Efficiency
 Code Rate
 Turbo Code
 Single Input Single Output
 Flat Zone