2.5 Proposed interleaver design method
2.6.3 Simulated TC error rate performance
The performance of TCs using different interleaver configurations was simulated over the AWGN channel with a BPSK modulation and a maximum of sixteen decoding iterations, using the MAP algorithm described in Section 1.1.1.2. The estimated distance spectra listed in Tables 2.6 and B.8 for K= 1504 and in Tables B.2 and B.11 forK= 6144 are used to compute the FER and BER union bounds truncated
2.6. APPLICATION EXAMPLES 61 to the third distance spectrum element for performance comparison, as introduced in Section 1.1.1.5. Furthermore, error rate simulation results for the LTE [3] TC are included for comparison in a similar simulation scenario.
Figs. 2.12 and 2.13 show the FER and BER performance of the 8-state CRSC(13, 15)8 TC for R= 2/3 andR= 4/5, and of the CRSC(13,15,17)8 TC for R= 1/3 and K= 1504. The interleaver parameters for the different puncturing constraints are listed in Tables 2.5, B.7, and 2.9. We observe that DPC and DPPC interleavers achieve a good asymptotic performance gain compared to the NDP interleaver, even with a convergence improvement for R = 2/3 and R= 4/5. The gain in the TC error floor region obtained by the DPC interleaver compared to the NDP interleaver is lower for the low code rates than for the higher ones. The proposed DPPC interleaver achieves a higher asymptotic performance gain than the DPC interleaver for all considered code rates. In addition, the proposed DPPC ARP interleaver provides a gain of about 0.5 and 0.7 dB in convergence threshold for R= 2/3 and R= 4/5, respectively and almost 4 decades in error floor in both cases, compared to the puncturing pattern and the interleaver adopted in LTE (see Fig. 2.12). In the R= 1/3 case, a gain of “only” 2 decades in error floor is achieved by the proposed DPPC ARP interleaver, compared to the interleaver adopted in LTE (see Fig. 2.12).
In fact, for R= 1/3 no puncturing is included in the LTE system and therefore, no bad interactions between interleaver and puncturing pattern may occur, which is not the case for higher code rates.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Figure 2.12: Frame error rate performance comparison between the different ARP interleaver configurations over the AWGN channel forR= 2/3 andR= 4/5,K= 1504, and CRSC constituent codes with generator polynomials (13,15)8.
62 CHAPTER 2. EFFICIENT PUNCTURE-CONSTRAINED INTERLEAVER
Figure 2.13: Bit error rate performance comparison between the different ARP interleaver configurations over the AWGN channel forR= 2/3 andR= 4/5 ,K= 1504, and CRSC constituent codes with generator polynomials (13,15)8.
Figs. 2.14 and 2.15 show the FER and BER performance of the 8-state CRSC(13, 15)8 TC for K= 6144 and for the interleaver parameters listed in Tables B.1 and B.10 for the different puncturing constraints. A similar behavior as for K = 1504 is found, only the proposed DPPC interleaver achieves the same gain in error floor performance for both code rates compared to the NDP interleaver. Furthermore, the DPPC interleaver provides a gain of about 0.2 and 0.25 dB in convergence threshold for R= 2/3 and R= 4/5, respectively and of about 3 decades in error floor in both cases, compared to the puncturing pattern and the interleaver adopted in LTE (see Fig. 2.14).
As we can observe in all presented application examples, the best TC error floor performance is provided by the proposed DPPC ARP interleaver as predicted by the evaluated Hamming distance spectra. Furthermore, improvements in TC error floor performance are obtained by introducing data puncturing into the TC structure, which was already identified in the respective puncturing mask selection process.
Thus, the TC minimum distance appears to be more related to parity positions than to data positions. It is noteworthy that a considerable asymptotic gain is obtained by the proposed DPPC interleaver compared to the puncturing pattern and interleaver adopted in LTE. Actually, the rate matching process and the QPP interleaver of LTE are not suited to the low error rates required in future generation of wireless communication systems.
2.6. APPLICATION EXAMPLES 63
Figure 2.14: Frame error rate performance comparison between the different ARP interleaver configurations over the AWGN channel forR= 2/3 andR= 4/5,K= 6144, and CRSC constituent codes with generator polynomials (13,15)8.
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Figure 2.15: Bit error rate performance comparison between the different ARP interleaver configurations over the AWGN channel forR= 2/3 andR= 4/5 ,K= 6144, and CRSC constituent codes with generator polynomials (13,15)8.
64 CHAPTER 2. EFFICIENT PUNCTURE-CONSTRAINED INTERLEAVER
2.7 Conclusion
In this chapter, a new method to design puncture-constrained ARP interleavers for TCs is proposed. It calls for a joint optimization of puncturing patterns and interleaver function. Catastrophic puncturing masks for the constituent codes of the TC are early identified in the selection process by evaluating their respective distance spectrum. A modified EXIT chart analysis is also proposed to identify a suitable puncturing mask for TC convergence performance improvement, with data puncturing.
It was shown that significant improvements in convergence threshold and error floor can be achieved by including puncturing constraints into the interleaver design.
In addition to a noticeable increase in the percentage of ARP candidates found gen-erating high minimum Hamming distance values, the proposed parity puncturing constraint reduces the average time to find such interleavers. Finally, the presented method allows an easy introduction of puncturing constraints as well as the val-idation of other design criteria such as span properties and correlation girth into the interleaver design. The generation of ARP interleavers validating the differ-ent design criteria is greatly simplified in comparison to previous methods, since the proposed graphical approach suitably limits the search space for the different interleaver parameters.
Chapter 3
Exploring precoding techniques for turbo codes
A
mong the various techniques to improve TC performance, it was shown that the prefixing of a rate-1 accumulator to a turbo encoder allows improving its error correction performance without altering its coding rate [23]. In this chapter, we study the application of this precoding technique to improve the performance of the 8-state TC of the LTE standard [3]. Furthermore, a new precoding structure is proposed allowing asymptotic TC performance improvements.This chapter is organized as follows: in Section 3.1, the reference Precoded Turbo Code (PTC), introduced in Section 1.1.2, is analyzed. A suitable optimization tool for the selection of the precoding ratio is then proposed, based on the extrinsic information exchange between the constituent codes of the TC. Next, two new pre-coding structures, hybrid and composite, are introduced and optimized, leading to the final selection of a suitable precoding structure for TCs. Afterwards, Section 3.2 explores possible improvements for the selected precoding structure: the effects of the precoding pattern and of the constituent code of the precoder on the error rate performance are studied. Then, some design criteria for PTC interleavers are identified in Section 3.3. A performance example of the proposed precoding struc-ture is given and compared to LTE performance in Section 3.4. Finally, Section 3.5 concludes the chapter.
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66 CHAPTER 3. PRECODING TECHNIQUES FOR TURBO CODES
3.1 Selection of a suitable precoding structure
In this section, different precoding structures are studied for the 8-state CRSC(13,15)8 TC, for code rate R= 4/5 and data sequence size K= 1504. The used puncturing pattern corresponds to the parity-only punctured version of the code (DPR = 0) from Table B.5. The different precoding structures and parameters are compared assuming uniform interleaving to average its effect on the error rate performance of the code. First, an optimization of the precoding ratio ρ of the reference pre-coding structure, shown in Fig. 1.7, is performed. Then, some modified prepre-coding structures are proposed and analyzed. Finally, a conclusion on the choice of the precoding structure is given.