A New Decoding Algorithm Based on the JN Algorithm
4.3 Simulation Results
In this section, simulation results of the proposed algorithm and the comparison between different algorithms are presented. We use “JN” to represent the JN algorithm in [11],
“OSD(1)” to represent the OSD algorithm with order-1 in [4], “JNOSD” to represent the
algorithm introduced in [15] and “M-JNOSD”(Modified-JNOSD) to represent the algorithm in [16]. We first show the simulation results of (15,7) RS code in Fig. 4.2. In this simulation,
3 3.5 4 4.5 5 5.5
10-6 10-5 10-4 10-3 10-2
SNR(dB)
BER
(15,7)RS code; AWGN channel; BPSK
JN OSD(1) JNOSD M-JNOSD Proposed
Figure 4.2: Performance comparison of RS (15,7)
𝛼 = 0.1, 𝑙𝑚𝑎𝑥 = 20 for the JN algorithm and 𝐴 = 3.0 for the modified JNOSD algorithm.
At bit error rate = 10−5, JNOSD provides about a 0.5dB gain over JN and OSD algorithm.
The modified JNOSD algorithm has a 0.45dB gain compare with JNOSD. The proposed algorithm, is 0.25dB better than the modified JNOSD algorithm and the performance is very close to the ML decoding.
Next we consider (15,9) RS code as shown in Fig. 4.3 The coefficients of simulation are set as follows: 𝛼 = 0.1, 𝑙𝑚𝑎𝑥 = 20 and 𝐴 = 3.0. At bit error rate = 10−5, OSD(1) is 0.4dB better than the JN algorithm. JNOSD is 0.25dB better than OSD(1).The modified JNOSD is about 0.1dB better than the original JNOSD. The performance of the proposed algorithm is almost the same sa the modified JNOSD algorithm in this case. The reason is
3 3.5 4 4.5 5 5.5 10-6
10-5 10-4 10-3 10-2
SNR(dB)
BER
(15,9)RS code; AWGN channel; BPSK
JN OSD(1) JNOSD M-JNOSD Proposed
Figure 4.3: Performance comparison of RS (15,9)
The simulation results for the (31,23) RS code are shown in Fig. 4.4. At bit error rate
= 10−5, JNOSD provides a 0.25dB gain over JN and OSD algorithm. The modified JNOSD algorithm is 0.4dB better than JNOSD algorithm. The proposed algorithm performs 0.3dB better than the modified JNOSD algorithm.
Fig. 4.5 shows the simulation results for the (31,25) RS code. At bit error rate = 10−5, JNOSD is about 0.2dB better than OSD(1) and 0.3dB better than the JN algorithm. The modified JNOSD is 0.4dB better than the original JNOSD algorithm. In this case, our algorithm has only a 0.06dB gain compared with the modified JNOSD algorithm.
3 3.5 4 4.5 5 5.5 10-6
10-5 10-4 10-3 10-2 10-1
SNR(dB)
BER
(31,23)RS code; AWGN channel; BPSK
JN OSD JNOSD M-JNOSD Proposed
Figure 4.4: Performance comparison of RS (31,23)
3 3.5 4 4.5 5 5.5 10-6
10-5 10-4 10-3 10-2 10-1
SNR(dB)
BER
(31,25)RS code; AWGN channel; BPSK
JN OSD(1) JNOSD M-JNOSD Proposed
Figure 4.5: Performance comparison of RS (31,25)
Chapter 5 Conclusions
In this thesis, we first introduce how to map RS codes into it’s binary representations. By doing so, we can transform the decoding problem of RS codes into the decoding of binary linear block codes. Many decoding algorithms designed for binary linear block codes can therefore be used. Then we briefly review the previous works of decoding RS codes. They are the OSD and the JN algorithm. After reviewing these two algorithms, we analyse the advantages and the drawbacks of the JN algorithm. We discover that the main reason of decoding failure in the JN algorithm is the errors in MRPs. In order to deal with this problem, we propose a new algorithm, which uses the concept in the OSD algorithm before doing the JN algorithm.
From the simulation results, the proposed algorithm has very good performance com-pared with the previous work such as JN and OSD(1). It also outperforms JNOSD and the modified JNOSD algorithm. Although many decoders are needed in the proposed al-gorithm, they can run in parallel. The same concept of our algorithm can also be applied to the modified JNOSD algorithm. It means that we modify the received vector before doing the modified JNOSD algorithm. The simulation results show that after doing so, the performance is better than the original modified JNOSD algorithm and is also better than the original proposed algorithm. To sum up, in this thesis, we propose a new soft input soft output decoding algorithm based on JN and OSD algorithm. The idea of the proposed
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