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## SoftCast: A joint source-channel coding scheme

Source-channel separation theorem tells us that in point-to-point communication we can perform source coding and channel coding separately. However, in the broadcast scenario, a joint source-channel coding scheme can be better than separate coding in some cases [GRV03]. In Section 2.1.2 SoftCast [JK10a] an analog coding based joint source-channel video coding and video transmission scheme is presented.

### Information-theoretic foundations of SoftCast

In this section, we will present the information-theoretic ideas which support SoftCast. At rst the source-channel separation theorem is recalled. The denitions of rate R, channel capacity C and rate distortion function R(D) are given as in [CT06]. Denition 1. Let X be a nite set of input channel symbols, Y be a nite set of output channel symbols and p (yjx) the channel transition probability, where x 2 X and y 2 Y. An (M; n) code for the channel (X; p (yjx) ; Y) consists of

1) an index set f1; 2; : : : ;Mg :

2) an encoding function Xn: f1; 2; : : : ;Mg ! Xn, yielding codewords xn (1) ; xn (2) ; : : : ; xn (M) : The set of codwords is called codebook.

3) a decoding function.

**Improvements of SoftCast**

Even though SoftCast oers a graceful video performance in broadcast scenario. However there is still a much room to improve SoftCast. For example, combines with digital coding scheme, e.g. quantization and motion estimation, to increase the performance; chunk size computation under power constraint and bandwidth constraint; the adaptation of SoftCast under more complex channel model and etc. In this section, we will present some important improvements of SoftCast.

#### Energy distribution Modeling

In SoftCast [JK10a], after a GoP has been transformed by 3D-DCT, the resulting DCT coef- cients are grouped into chunks. It is generally assumed that the coecients within a chunk follow the same distribution and have the same variance. In this way, we only need to compute the scaling factor for each chunk rather than for each DCT coecient. Moreover, only the variances of each chunk are transmitted as meta-data to receiver. Therefore the computation cost and overhead rate are reduced. However, the drawback is a reduced accuracy of the estimated variance of DCT components within each chunk, which can aect the overall performance [XZW+17a]. To improve this estimation, in [XWF+13, XZW+17b], it has been proposed an adaptive chunk division scheme and a piecewise log linear model of energy distribution instead of using rectangular equal size chunk (See Figure 2.9). In this way, the exprimental result shows that it improves SoftCast by 3 5dB and reduces the meta-data at the same time.

**Table of contents :**

**1 Introduction **

1.1 Context and motivation

1.2 Contributions

1.3 Organization of thesis

**2 Related work and prior results **

2.1 SoftCast: A joint source-channel coding scheme

2.1.1 Information-theoretic foundations of SoftCast

2.1.2 SoftCast

2.2 Improvements of SoftCast

2.2.1 Dcast

2.2.2 WaveCast

2.2.3 WSVC

2.2.4 Energy distribution Modeling

2.2.5 ParCast+

2.2.6 Application of Shannon-Kotel’nikov Mapping In LVC

2.2.7 Conclusion

**3 Optimal Power Allocation **

3.1 Introduction

3.2 Precoding and decoding matrices

3.3 Total Power Constraint

3.3.1 Optimal decoding matrix

3.3.2 Optimal precoding matrix

3.3.3 A toy example

3.4 Per Subchannel Power Constraints

3.4.1 Evaluation of em

3.4.2 When the conditions of Theorem 2 are satised

3.4.3 When the conditions of Theorem 2 are not satised

3.5 Precoding Matrix Design in multicast scenarii

3.5.1 Multicast scenario with linearly degraded multicast channels

3.5.1.1 Total Power Constraint

3.5.1.2 Per-subchannel power constraint

3.5.2 General multicast channels

3.5.2.1 Eigenvalues of

3.5.2.2 Eigenvalues of

3.6 Simulations

3.6.1 Simulation conditions

3.6.2 Metadata

3.6.3 Total Power Constraint

3.6.4 Per Subchannel Power Constraints

3.6.5 Mismatch

3.6.5.1 Total Power Constraint

3.6.5.2 Per-subchannel Power Constraint

3.7 Conclusions

**4 Sub-Optimal Power Allocation **

4.1 Simple Chunk Scaling

4.2 Power Allocation with Inferred Split Position (PAISP)

4.3 PAISP with Dichotomy

4.4 Power Allocation with Local Power Adjustment

4.5 Limits of PAISP and PALPA

4.6 Simulation results

4.6.1 Comparison of the power allocation methods

4.6.2 Complexity comparison

4.6.3 Mismatch

4.7 Conclusions

**5 Impulse error mitigation for LVC schemes **

5.1 Introduction and main contributions

5.2 Related work

5.3 Linear Video Coding and OFDM Transmission Scheme

5.3.1 Joint source-channel coding

5.3.2 Transmission

5.3.3 Channel model

5.3.4 Baseline receiver

5.3.5 Power allocation and chunk selection

5.4 Impulse Noise Correction

5.5 Sub-channel provisioning for impulse noise mitigation

5.5.1 Residual noise after impulse noise mitigation

5.5.2 Estimation of 2

5.5.3 Optimization of sub-channel provisioning

5.6 Simulation

5.6.1 Compared LVC schemes

5.6.2 Simulation parameters

5.6.3 Simulation results

5.6.3.1 Impact of rd on the eciency of impulse noise correction

5.6.3.2 Optimal subchannel provisioning

5.6.3.3 Analysis of the eect of mismatched channel conditions

5.7 Conclusion

**6 Conclusions and Perspectives **

6.1 Conclusions

6.2 Perspectives

6.2.1 Precoding matrix design for multicast

6.2.2 Optimization of the amount of Metadata

6.2.3 Application of Deep Learning to SoftCast schemes . .