Optimized Distributed Generalized Reed-Solomon Coding with Space-Time Block Coded Spatial Modulation
Abstract
:1. Introduction
- The DGRSC-STBC-SM scheme is first proposed, where the source and relay nodes use different GRS codes. In the DGRSC-STBC-SM scheme, the relay selects partial symbols from the decoded source information symbols for further encoding. For each selection at the relay, the destination then generates a codeword set through the mutual cooperation between the source and relay.
- To construct an optimal codeword set at the destination with the best weight distribution, we propose an optimal symbol selection algorithm at the relay to determine the best selection pattern by which partial symbols are chosen from the decoded source information symbols for further encoding.
- However, for a longer block length code, the complexity of the algorithm is very high. Thus, it is not realistic from a practical perspective. To reduce the computational complexity of the optimal symbol selection algorithm, the low-complexity symbol selection algorithm is then proposed. In the low-complexity symbol selection algorithm, partial source information symbol sequences are considered to determine the optimized selection pattern from the local selection patterns at the relay.
2. Related Work
3. Generalized Distributed Channel Coding Combined with STBC-SM Based on Subset Method
3.1. Distributed Channel Coding Based on the Subset Method
3.2. Incorporation of STBC-SM into Distributed Channel Coding
4. Distributed GRS-Coded STBC-SM Scheme for Wireless Communications
5. Proposed Efficient Symbol Selection Algorithms
5.1. Algorithm 1: Optimal Symbol Selection Algorithm
5.1.1. General Description of the Optimal Symbol Selection Algorithm
- (1)
- If and , , and return back to step 4.
- (2)
- Else, i.e., or , the searching algorithm halts.
5.1.2. Example 1
5.2. Algorithm 2: Low-Complexity Symbol Selection Algorithm
5.2.1. General Description of the Low-Complexity Symbol Selection Algorithm
- (1)
- Split into two parts, where all the elements of form the first part, and the other elements in but not in form the second part.
- (2)
- elements are reasonably selected from as all roots of . On the one hand, n elements of elements are randomly chosen in the first part, and the remaining elements are fixedly selected in the second part, which generates cases. On the other hand, the roles of random and fixed selection are reversed, i.e., we randomly choose elements from the second part, and fixedly choose the elements from the first part, which yields cases.
- (3)
- Based on the above process, information symbol sequences are obtained.
- (1)
- First partition information symbols at the source into two parts. Scenario (i): the first symbols and the last symbols form the first and second parts, respectively, where is the smallest integer larger than or equal to . Scenario (ii): the first symbols and the last symbols form the first and second parts, respectively. The symmetric structures of symbols are shown in Figure 3.
- (2)
- The relay selects symbols from symbols. In scenario (i), we select more symbols in the first part. Specifically, symbols are randomly chosen in the first part and symbols are fixedly chosen in the second part, which generates cases. In scenario (ii), more symbols are chosen in the second part. Specifically, randomly choose symbols in the second part and fixedly choose symbols in the first part, which also generates cases.
- (3)
- Obtain the set of P selection patterns by the above process.
5.2.2. Example 2
- (1)
- Firstly divide 16 elements of into two parts, where all the 10 elements of constitute the first part and the six elements in but not in constitute the second part.
- (2)
- Select ( elements from as all roots of . (i) elements of elements are randomly selected from the first part and the remaining elements are fixedly selected from the second part. (ii) elements of elements are randomly selected from the second part and the remaining elements are fixedly selected from the first part. The process of choosing elements is listed in Table 4.
- (3)
- Obtain information symbol sequences based on (1) and (2).
- (1)
- Divide information symbols at the source into two parts. Scenario (i): the first three symbols and the last two symbols form the first and second parts, respectively. Scenario (ii): the first two symbols and the last three symbols form the first and second parts, respectively.
- (2)
- The relay selects symbols from symbols. In scenario (i), we randomly select two symbols in the first part and fixedly select one symbol in the second part. In scenario (ii), we randomly select two symbols in the second part and fixedly select one symbol in the first part.
- (3)
- The set of selection patterns is determined as
5.3. Complexity Comparisons between Two Algorithms
6. Decoding Algorithm at the Destination
7. Simulation Results
7.1. Performance Comparisons of DGRSC-STBC-SM Scheme under Various Symbol Selection Algorithms
7.2. Error Performance of DGRSC-STBC-SM and Non-Cooperative Counterpart
7.3. Performance Comparisons between DGRSC-STBC-SM Scheme and Existing Scheme
7.4. Comparisons of DGRSC-STBC-SM Scheme with Different Numbers of Receiving Antennas
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Field Elements | Binary Vectors | Nt = 4, BPSK | |
---|---|---|---|
Active TACs | Modulated Symbols | ||
0 | [0, 0, 0, 0] | (1, 2) | (, 1) |
1 | [1, 0, 0, 0] | (2, 3) | (1, 1) |
[0, 1, 0, 0] | (3, 4) | (1, 1) | |
[0, 0, 1, 0] | (1, 2) | (1, 1) | |
[0, 0, 0, 1] | (1, 2) | (1, 1) | |
[1, 1, 0, 0] | (4, 1) | (1, 1) | |
[0, 1, 1, 0] | (3, 4) | (1, 1) | |
[0, 0, 1, 1] | (1, 2) | (1, 1) | |
[1, 1, 0, 1] | (4, 1) | (1, 1) | |
[1, 0, 1, 0] | (2, 3) | (1, 1) | |
[0, 1, 0, 1] | (3, 4) | (1, 1) | |
[1, 1, 1, 0] | (4, 1) | (1, 1) | |
[0, 1, 1, 1] | (3, 4) | (. 1, 1) | |
[1, 1, 1, 1] | (4, 1) | (1, 1) | |
[1, 0, 1, 1] | (2, 3) | (1, 1) | |
[1, 0, 0, 1] | (2, 3) | (1, 1) |
3 | (3, 0) |
4 | (4, 0) |
5 | (5, 0) |
7 | (3, 4) |
8 | (3, 5), (4, 4) |
9 | (4, 5), (5, 4) |
10 | (5, 5) |
0 | 0 | 7 | 56 | |
0 | 0 | 7 | 49 | |
0 | 0 | 7 | 56 |
wt(c) = i | J | 1st Part: 10 − i | 2nd Part: J − (10 − i) |
---|---|---|---|
6 | 4 | 4 | 0 |
7 | 3 | 3 | 0 |
4 | 3 | 1 | |
8 | 2 | 2 | 0 |
3 | 2 | 1 | |
4 | 2 | 2 | |
9 | 1 | 1 | 0 |
2 | 1 | 1 | |
3 | 1 | 2 | |
4 | 1 | 3 | |
10 | 0 | 0 | 0 |
1 | 0 | 1 | |
2 | 0 | 2 | |
3 | 0 | 3 | |
4 | 0 | 4 |
wt(|c|cj|) | (wt(c), wt(cj)) |
---|---|
6 | (6, 0) |
7 | (7, 0) |
8 | (8, 0) |
9 | (9, 0) |
10 | (10,0) |
14 | (6, 8) |
15 | (6,9), (7,8) |
16 | (6,10), (7,9), (8,8) |
17 | (6,11), (7,10), (8,9), (9,8) |
18 | (6,12), (7,11), (8,10), (9,9),(10,8) |
19 | (6,13), (7,12), (8,11), (9,10), (10,9), (11,8) |
20 | (6,14), (7,13), (8,12), (9,11), (10,10), (11,9), (12,8) |
0 | 0 | 0 | 90 | |
0 | 0 | 15 | — | |
0 | 0 | 0 | 90 | |
0 | 0 | 0 | 90 | |
0 | 0 | 0 | 60 | |
0 | 0 | 0 | 9 | |
0 | 0 | 0 | 10 |
Parameters | Algorithm 1 | Algorithm 2 | Percentage Reduction, % |
---|---|---|---|
104,960 | 46,400 | 56 | |
1,667,235,840 | 704,161,440 | 58 |
Cases | Parameter Vectors | |
---|---|---|
1 | ||
2 | ||
3 |
Parameters | Specification |
---|---|
Source coding | |
Relay coding | |
Effective code rate of destination | 1/4, 19/50, 51/126 |
Channel model | Slow Rayleigh fading channel |
MIMO configuration | STBC-SM: , 4, 5, 6 , 4-QAM, , 4-QAM, , 6 , 16-QAM, , 6 |
MIMO detection | Maximum likelihood (ML) detection |
GRS decoding algorithm | Euclidean decoding algorithm |
Cases | ||
---|---|---|
1 | [2, 3, 4] | [1, 3, 4] |
2 | —— | [5, 8, 9, 10, 12, 13, 14, 15, 17, 18] |
3 | —— | [0, 1, 2, 3, 4, 5, 6, 11, 12, 13, 16, 18, 19, 22, 24, 25, 26, 27, 29, 31, 33, 34, 35, 40, 42, 44, 45, 47, 48, 49, 50] |
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Zhao, C.; Yang, F.; Waweru, D.K.; Chen, C.; Xu, H. Optimized Distributed Generalized Reed-Solomon Coding with Space-Time Block Coded Spatial Modulation. Sensors 2022, 22, 6305. https://doi.org/10.3390/s22166305
Zhao C, Yang F, Waweru DK, Chen C, Xu H. Optimized Distributed Generalized Reed-Solomon Coding with Space-Time Block Coded Spatial Modulation. Sensors. 2022; 22(16):6305. https://doi.org/10.3390/s22166305
Chicago/Turabian StyleZhao, Chunli, Fengfan Yang, Daniel Kariuki Waweru, Chen Chen, and Hongjun Xu. 2022. "Optimized Distributed Generalized Reed-Solomon Coding with Space-Time Block Coded Spatial Modulation" Sensors 22, no. 16: 6305. https://doi.org/10.3390/s22166305
APA StyleZhao, C., Yang, F., Waweru, D. K., Chen, C., & Xu, H. (2022). Optimized Distributed Generalized Reed-Solomon Coding with Space-Time Block Coded Spatial Modulation. Sensors, 22(16), 6305. https://doi.org/10.3390/s22166305