A New Hybrid Prime Code for OCDMA Network Multimedia Applications
Abstract
:1. Introduction
- (1)
- Maximum number of code sequences for maximum number of users, leading to an increase in the network capacity for data and multimedia applications.
- (2)
- Minimum code length to increase the user bit rate.
- (3)
- Optimal code weight for good network bit error rate (BER) performance.
- (4)
- Minimum cross-correlation values to prevent multiple access interference (MAI).
- (5)
- Reliable code parameter variation while keeping the same cross-correlation value.
- (6)
- Simplicity of code generation.
- (7)
- Minimum cost with respect to the line coding techniques in optical domain.
- (1)
- High signal integrity in the midst of interference at the receiving end.
- (2)
- Broader network capacity.
2. Literature Review
3. Code Construction
3.1. Code Construction Procedure
- (a)
- Arrange the code sequences in the first tree, row by row in one column, as shown in Table 3, column 1.
- (b)
- (c)
- Rotate the final code sequences in column 2 horizontally from right to left until the first code word in this sequence becomes the last one, as shown in Table 3, column 3.
Column 1 | Column 2 | Column 3 | |||
---|---|---|---|---|---|
Code Index m | First Tree Code Sequences | Merged Code Sequences | Resultant Code Sequences | ||
0 | C0 | C00 | = 100001000000010000100000 | ||
C01 | = 010000010000100000001000 | ||||
C02 | = 010000100000100001000000 | ||||
C03 | = 100000001000010000010000 | ||||
1 | C1 | C10 | = 100000100000001000010000 | ||
C11 | = 001000010000010000000100 | ||||
C12 | = 001000010000100000100000 | ||||
C13 | = 010000000100001000010000 | ||||
2 | C2 | C20 | = 100000010000000100001000 | ||
C21 | = 000100010000001000000010 | ||||
C22 | = 000100001000100000010000 | ||||
C23 | = 001000000010000100010000 | ||||
3 | C3 | C30 | = 100000001000000010000100 | ||
C31 | = 000010010000000100000001 | ||||
C32 | = 000010000100100000001000 | ||||
C33 | = 000100000001000010010000 | ||||
4 | C4 | C40 | = 010000000100001000000010 | ||
C41 | = 000001001000000010000100 | ||||
C42 | = 001000000010010000000100 | ||||
C43 | = 000010000100000001001000 | ||||
5 | C5 | C50 | = 010000000010000100000001 | ||
C51 | = 000000101000000001000010 | ||||
C52 | = 000100000001010000000010 | ||||
C53 | = 000001000010000000101000 | ||||
6 | C6 | C60 | = 010001000000000010010000 | ||
C61 | = 001000001000100000000001 | ||||
C62 | = 000010010000010001000000 | ||||
C63 | = 100000000001001000001000 | ||||
7 | C7 | C70 | = 001000100000000100001000 | ||
C71 | = 000100000100010000000010 | ||||
C72 | = 000100001000001000100000 | ||||
C73 | = 010000000010000100000100 | ||||
8 | C8 | C80 | = 001000010000000010000100 | ||
C81 | = 000010000100001000000001 | ||||
C82 | = 000010000100001000010000 | ||||
C83 | = 001000000001000010000100 | ||||
9 | C9 | C90 | = 000100001000000010000010 | ||
C91 | = 000001000010000100000001 | ||||
C92 | = 000010000010000100001000 | ||||
C93 | = 000100000001000001000010 | ||||
10 | C10 | C100 | = 010000000100100000000001 | ||
C101 | = 000000101000000010010000 | ||||
C102 | = 100000000001010000000100 | ||||
C103 | = 000010010000000000101000 | ||||
11 | C11 | C110 | = 001001000000100000001000 | ||
C111 | = 000100000100100000010000 | ||||
C112 | = 100000001000001001000000 | ||||
C113 | = 100000010000000100000100 | ||||
12 | C12 | C120 | = 000100100000100000000100 | ||
C121 | = 000010000010010000010000 | ||||
C122 | = 100000000100000100100000 | ||||
C123 | = 010000010000000010000010 | ||||
13 | C13 | C130 | = 000010010000100000000010 | ||
C131 | = 000001000001001000010000 | ||||
C132 | = 100000000010000010010000 | ||||
C133 | = 001000010000000001000001 | ||||
14 | C14 | C140 | = 001000001000010000000001 | ||
C141 | = 000000100100000100001000 | ||||
C142 | = 010000000001001000001000 | ||||
C143 | = 000100001000000000100100 | ||||
15 | C15 | C150 | = 000101000000010000000100 | ||
C151 | = 000010000010100000001000 | ||||
C152 | = 010000000100000101000000 | ||||
C153 | = 100000001000000010000010 | ||||
16 | C16 | C160 | = 000010100000010000000010 | ||
C161 | = 000001000001010000001000 | ||||
C162 | = 010000000010000010100000 | ||||
C163 | = 010000001000000001000001 | ||||
17 | C17 | C170 | = 000100010000001000000001 | ||
C171 | = 000000100010001000000100 | ||||
C172 | = 001000000001000100010000 | ||||
C173 | = 001000000100000000100010 | ||||
18 | C18 | C180 | = 000011000000001000000010 | ||
C181 | = 000001000001100000000100 | ||||
C182 | = 001000000010000011000000 | ||||
C183 | = 100000000100000001000001 | ||||
19 | C19 | C190 | = 000010100000000100000001 | ||
C191 | = 000000100001010000000010 | ||||
C192 | = 000100000001000010100000 | ||||
C193 | = 010000000010000000100001 |
- Limited cross-correlation “0” or “1”;
- Very large number of code sequences can provide a large number of simultaneous users without sacrificing performance;
- Shorter code length for the same higher bit rate transmission.
3.2. Correlation Properties
- (a)
- The peak value of the auto-correlation property is 2n, where n is an integer number equal to the number of code words used to construct the code sequence in each tree.
- (b)
- The value of the cross-correlation property is “0” or “1” between any two different code sequences in the coding of Table 3 and is independent of whether these two codes share the same code index or not.
- (c)
- and
4. Correlation Results
5. The Proposed OCDMA System Model
6. BER Performance Analysis
- Code length equal to , where is the prime number and n is the number of the different prime numbers used for the code construction.
7. Throughput Analysis
8. EVM Analysis
9. Simulation Results
10. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Folded Code Sequences | Code Sequences | ||||||
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Folded Code Sequences | Code Sequences | ||||||||||
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X62X02 | X02X62 | ||||||||||
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Morsy, M.A.; Aly, M.H. A New Hybrid Prime Code for OCDMA Network Multimedia Applications. Electronics 2021, 10, 2705. https://doi.org/10.3390/electronics10212705
Morsy MA, Aly MH. A New Hybrid Prime Code for OCDMA Network Multimedia Applications. Electronics. 2021; 10(21):2705. https://doi.org/10.3390/electronics10212705
Chicago/Turabian StyleMorsy, Morsy A., and Moustafa H. Aly. 2021. "A New Hybrid Prime Code for OCDMA Network Multimedia Applications" Electronics 10, no. 21: 2705. https://doi.org/10.3390/electronics10212705