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## Improving error correcting performance by increasing code memory

By considering the TBICM scheme of 1.3.5.2, a straightforward solution to improve the diversity order of the coded modulation involves increasing the component code memory. As the Hamming distance of the code increases with the component code memory , TBICM achieves higher orders of diversity for higher values of . Quoting [41] when increases from 3 to 4, or equivalently the number of states rises from 8 to 16, a 30 to 50 % improvement in the minimum Hamming distance of double binary turbo codes is observed. In order to estimate the induced improvement in error correcting performance when high order modulations are considered, we have studied the 16-state double binary turbo codes in TBICM scenarios with the systematic allocation.In g. 2.1, g. 2.2 and g. 2.3, we have plotted the BER simulation results of the DVB-RCS code compared to its extension to 16-state constituent codes in TBCIM schemes for the transmission of 16,000-information bit frames and for spectral e ciencies ranging from 1.0 to 6.0 bpcu. For the 16-state code, the following ARP parameters (P = 396, Q1 = 6; Q2 = 1; Q3 = 2) have been used. Excluding the case of 256-QAM TBICM with R = 3=4 (spectral e ciency 6.0 bpcu), the error oor is lowered by at least two orders of magnitude when the 16-state turbo code replaces the 8-state DVB-RCS code. This leads to lower gaps to capacity for low BERs. For the highest e ciency value, the error oor is lowered only by half an order of magnitude. This can be explained by the signi cant decay of the Hamming distance with increasing code rate even for the 16-state code. No convergence threshold penalty has to be paid when increasing the code memory. A slight gain can even be obtained in some cases such as 256-QAM TBICM with R = 1=2. In order to attain each of the two spectral e ciencies of 3.0 and 4.0 bpcu, two coding and modulation solutions were simulated. The BER results tend to favor the association of a high order modulation scheme and a lower code rate than the other competing case. The selection of a winning coding and modulation scheme could have been be predicted by the computation of the asymptotical gain as proposed in [22].

As a conclusion, despite the additional improvement in error correcting performance in-troduced by increasing the code memory, when we consider high order modulation schemes coupled with high code rates, the gain in the oor region is limited. Moreover, the increase of the code memory from 3 to 4 leads to doubling the decoding complexity. This is the reason why we have investigated another technique allowing the same decoder complexity to be kept while doubling the diversity order by introducing modi cations to the modula-tor/demodulator couple. This technique is detailed in the following section.

### Doubling the diversity order of TBICM schemes

In this section, we propose a low complexity solution intended to double the diversity order of TBICM schemes. This solution relies on two indispensable parts: correlating the in-phase I and quadrature Q components of the transmitted signal making these two components fade independently. We start with a description of the proposed solution through detailing the founding tiers followed by a mathematical justi cation of doubling the diversity order. Then, we provide a comprehensive description of the proposed system before showing some Monte Carlo simula-tion results.

#### Correlating the in-phase and quadrature components

For QAM schemes, as Gray mapping is used for TBICM, the I and Q channels are mapped separatly as two independent PAMs. In the example of g. 2.4, bits S1 and S2 are mapped on the I channel independently of bits S3 and S4 which are mapped on the Q channel. All constellation points cannot be uniquely identi ed in the I channel or the Q channel separately. In order to circumvent this natural independence and hope for any improvement in the diversity order, we should correlate the I and Q channels of every constellation point. This correlation has as purpose to uniquely identify every constellation point from any component axis.

Several means of correlating I and Q components could be imagined such as precoding or changing the constellation mapping. Since Gray mapping is mandatory due to the use of a turbo code (see section 1.3.5.3), a simple answer to the correlation procedure to be performed involves applying a simple rotation to the constellation as shown in g. 2.5. This approach is a particular case of the multidimensional modulation schemes designed to optimize diversity order over fading channels and detailed in [45, 46, 47, 48]. The value of the rotation angle is based on a lattice study of the spatial distribution of constellations in a Rayleigh fading environment. It is chosen intentionally to achieve an optimal distribution in terms of spatial separation of the constellation points in signal space. A rotation angle of =8 is shown to be optimal in the case of QAMs [48] since it maximizes the minimum Euclidean distance of the constellation in every component axis.

**Ensuring independent fading for in-phase and quadrature components**

When a transmitted constellation point is subject to a fading event, its I and Q coordinates fade identically. When subject to a destructive fading, the information transmitted on I and Q channels su ers from an irreversible loss leading to an erroneous detection of the symbol at the receiver side. If I and Q fade independently, in most cases it is highly unlikely to have both subject to severe fading. Consequently, when combined with the constellation rotation proposed in the previous section, this feature is expected to help the demodulator recover the whole transmitted information. One way to allow both component axes to fade independently is to introduce coordinate interleaving. This solution known as Signal Space Diversity (SSD) was rst proposed as means of increasing diversity for TCM in [49]. The main drawback of coordinate interleaving is the need to quantize and store the modulator signal to be transmitted, operation which requires allocating large amounts of rapid access memory. Simpli ed component interleaving can be introduced depending on the fading channel model. In [36], the authors proposed the replacement of I and Q component interleaving by a simple time delay for one of the two component axes over uncorrelated at Rayleigh fading channels. In fact, since any two modulation symbols of a frame are subject to an independent fading in the case of uncorrelated at fading, a simple delay of the I component with respect to the Q component of only one symbol period is su cient for having these two subject to di erent fading amplitudes. We can imagine extending this concept to other types of widely used fading channels:

For correlated fading channels [7, 50], the delay should be superior to the correlation length in number of symbol periods.

For block fading channels [7, 50], a number of di erent delay values, equal to the size of the faded blocks, should be introduced. Then a suitable switching operation should be performed for the delayed component of the transmitted signal so that successive components in a given faded block are not a ected by the same fading event. I and Q channels being a ected by independent Gaussian noise components, the I or Q delay becomes transparent over Gaussian channel. Consequently, the proposed solution o ers identical performance to the pragmatic approach over this type of channels and close to the optimum performance attained by a TTCM. From the implementation point of view, an additional latency consisting of a delay identi-cal to the one introduced at the transmitter is needed in order to match the I and Q channels for accurate detection of the transmitted signal.

**Table of contents :**

Table of contents

Introduction

**I Turbo coded modulations and fading channels **

**1 Coded modulations and fading channels **

1.1 The fading channel model

1.1.1 General description of fading channels

1.1.2 Mathematical model for at fading channels

1.2 Theoretical limits for transmissions over fading channels

1.2.1 Capacity computation

1.2.2 Achievable optimal coded performance

1.3 Coded modulations over at fading channels

1.3.1 A brief review of previous studies

1.3.2 Factors acting on the error correcting performance of coded modulations over fading channels

1.3.3 The Bit-Interleaved Coded Modulation (BICM)

1.3.3.1 System description

1.3.3.2 Reasons behind the improvement in performance with respect to TCM

1.3.4 The Bit-Interleaved Coded Modulation with Iterative Demodulation Bit-Interleaved Coded Modulation with Iterative Demodulation (BICM-ID) i

1.3.4.1 System description

1.3.4.2 Reasons behind the performance improvement with respect to BICM

1.3.5 Turbo coded modulation schemes

1.3.5.1 Brief review of previous work

1.3.5.2 Turbo Bit-Interleaved Coded Modulation (TBICM)

1.3.5.3 Turbo Bit-Interleaved Coded Modulation with Iterative Demodulation Turbo Bit-Interleaved Coded Modulation with Iterative Demodulation (TBICM-ID)

1.4 Conclusion

**2 Improving error rates of TBICM schemes over Rayleigh fading channel **

2.1 Improving error correcting performance by increasing code memory

2.2 Doubling the diversity order of TBICM schemes

2.2.1 Correlating the in-phase and quadrature components

2.2.2 Ensuring independent fading for in-phase and quadrature components

2.2.3 Eect on the diversity order of the TBICM scheme

2.2.4 Overall system description of a Turbo Bit-Interleaved Coded Modulation with Signal Space Diversity (TBICM-SSD)

2.2.5 Performance comparison of TBICM and TBICM-SSD schemes over at fading channels

2.3 Improving error correcting performance of TBICM-SSD schemes

2.3.1 Uncoded modulator analysis

2.3.1.1 EXIT chart analysis

2.3.1.2 Uncoded genie-aided performance

2.3.2 Turbo Bit-Interleaved Coded Modulation with Iterative Demodulation and Signal Space Diversity (TBICM-ID-SSD)

2.3.2.1 TBICM-ID-SSD system description

2.3.2.2 EXIT chart analysis of the decoder in a TBICM-ID-SSD scheme

2.3.3 Expected in uence of code rate, frame length and code memory on performance of TBICM-ID-SSD schemes

2.4 Monte Carlo simulation results of TBICM-ID-SSD schemes

2.4.1 Simulation results for the transmission of long data blocks over at fading Rayleigh channel

2.4.2 Comparison with TBICM-ID schemes

2.4.3 Simulation results for the transmission of shorter data blocks over at fading Rayleigh channel

2.4.4 Performance of TBICM-ID-SSD schemes over Rician fading channels

2.5 Conclusion

**II Coded continuous phase modulation schemes for satellite transmis- sions **

**3 Continuous Phase Modulation **

3.1 The CPM general description

3.2 The Rimoldi decomposition of CPM

3.3 CPM schemes under consideration

3.4 Computation of the spectral eciency of CPM

3.5 Capacity and information rate of CPM schemes

3.6 CPM error events and normalized squared Euclidean distance

3.6.1 CPM error events

3.6.2 Normalized squared Euclidean distance of CPM

3.7 Conclusion

**4 Study of coded continuous phase modulation schemes for satellite transmissions**

4.1 General description of a coded CPM

4.2 Study objectives and parameters

4.2.1 Error correcting performance of SCCPM

4.2.2 Study scenario

4.3 The choice of CPM parameters

4.3.1 Introduction

4.3.2 Methodology based on convergence property of SCCPM

4.3.3 Convergence study and illustration example

4.3.3.1 Illustration example

4.3.4 Conclusion: design guidelines for the selection of CPM parameters

4.4 Study of the eect of CPM precoding on coded systems

4.5 Outer FEC selection for SCCPM

4.5.1 Review of the previous work on coded CPM systems

4.5.2 Description of the SCCPM solutions covered in our study

4.5.3 Design methodology and tools for SCCPM outer FEC selection

4.5.3.1 Design methodology

4.5.3.2 Bound derivation for bit-interleaved systems:

4.5.3.3 Bound derivation for symbol-interleaved systems

4.5.4 Symbol-interleaved SCCPM

4.5.4.1 Introduction

4.5.4.2 Signal mapping

4.5.4.3 Symbol-interleaved SCCPM with codes over rings

4.5.4.4 Symbol-interleaved SCCPM with log2Mbinary convolutional codes

4.5.4.5 Frame error rate Monte Carlo simulation results

4.5.4.6 Symbol-interleaved SCCPM with turbo codes

4.5.4.7 Conclusions on symbol-based SCCPM

4.5.5 Bit-interleaved SCCPM

4.5.5.1 Introduction

4.5.5.2 Signal mapping

4.5.5.3 Bit-interleaved SCCPM with convolutional codes

4.5.5.4 Bit-interleaved SCCPM with turbo-like outer codes

4.5.5.5 Bit-interleaved Flexi-like SCCPM structure

4.5.5.6 Bit-interleaved SCCPM with extended BCH codes

4.6 Conclusion

**5 Final selection of the SCCPM parameters for 0:75 to 2:25 bps/Hz spectral eciencies **

5.1 Steps for selecting CPM parameters and code rate

5.2 Set of CPM parameters and code rates used for the search process

5.3 Example of CPM parameters and code rate selection for a target spectral eciency of 1.5 bps/Hz

5.4 Selected SCCPM schemes

5.4.1 General remarks about the selection procedure

5.4.2 CPM selection for spectral eciencies ranging from 0.75 to 2.25 bps/Hz

5.4.3 Code selection validation using FER Monte Carlo simulations

5.4.3.1 Simulation results for the 0.75 and 2.25 bps/Hz cases

5.4.3.2 Eect of the frame length

5.5 Conclusion

Conclusion

List of gures

List of tables

List of acronyms

List of publications

**Bibliography**