# Transmitter Diversity Gain Technique Aided Irregular Channel Coding for Mobile Video Transmission
## 5 IRCCs Channel Code Design  
IRCC comprising of \(I_{n}\) constituent subcodes that are constructed by selecting the basic main code having code-rate--\(r_{1}\) and the rest of the subcodes \((I_{n}-1)\) are designed in correspondence with that main code [24; 46]. The convergence behavior of iterative decoding is improved by designing irregular codes that are based on a simplified efficient optimization algorithm. Convergence is sometimes possible through specific code-rates on scanning the proper code through many possible subcodes. The search procedure can be reduced by defining a family of subcodes and it is generally referred to as the irregular code [24]. The subcodes \(([I_{n}-1])\) in which the codewords having \(rate-r_{i}>r_{1}\) (higher rates than the main code), where \(i=1,2,3\ldots I_{n}\) is achieved by puncturing and the codewords of rate--\(r_{i}<r_{1}\) (lower rates than the main code) is obtained by addingmore generator polynomials. The encoder of IRCC codes encodes \(k\) information bits into \(n\) coded bits, and each subcode encodes a fraction \((\alpha_{i}r_{i}n)\) of information bits and generated \((\alpha_{i}n)\) coded bits. Furthermore, the weighting coefficient \((\alpha_{i})\) represents the relative size of a fraction or weighting coefficient with \(i=1,2,3\ldots\mathrm{I}_{n}\), while the target code-rate \(R\ \varepsilon[0\quad 1]\) should satisfy the following condition. \(\sum_{i=1}^{n}\alpha_{i}=1\) and  
\[\sum_{i=1}^{I_{n}}\alpha_{i}r_{i}=R,\quad\text{ where }\alpha_{i}\in[0\quad 1]\]  
As a design example, the iterative paradigm of the inner and outer codes operates at a constant overall bit budget rate of \(3/4\) and, logically, the redundancy is incorporated by the outer IRCC code and the inner code is operated at the unity rate. IRCC uni-code is used as a reference scheme, which employs the rate \(3/4\) single constituent code for regular channel coding of the H. 264 partitions, while a subset of the 17 constituent subcodes of the considered IRCC is utilized using the optimization procedure that was defined in [24], in order to perform irregular error protection of the H.264/AVC coded video. The mutual information \((I_{A1})\) for outer IRCC decoder is the information sharing between the A-priori information \((L_{IRCC}^{\mathrm{APF}}(x_{i}^{\prime}))\) and the transmitted information \((L_{D,p}(\hat{x}_{i}))\), as given below. \[I_{A1}=I(L_{D,p}(\hat{x}_{i});L_{IRCC}^{apr}(x_{i}^{\prime})) \tag{26}\]  
Mutual information \((I_{E1})\) is the information transfer between the extrinsic information \((L_{IRCC}^{\mathrm{extr}}(x_{i}^{\prime}))\) and transmitted information \((L_{D,p})\) i.e.,  
\[I_{E1}=I(L_{D,p}(\hat{x}_{i});L_{IRCC}^{\mathrm{extr}}(x_{i}^{\prime}))) \tag{27}\]  
The outer IRCC convergence characteristic transfer function can also be obtained, as given below:  
\[I_{E1}=T_{IRCC-\mathrm{code}}(I_{A1}) \tag{28}\]  
Similarly, the mutual information \((I_{A2})\) for URC decoder is the information sharing between the A-priori information \((L_{URC}^{apr}(\hat{x}_{i}))\) and the transmitted information \((L_{M,\mu}(\hat{y}))\) i.e.,  
\[I_{A2}=I(L_{D,p}(\hat{x}_{i});L_{URC}^{apr}(\hat{x}_{i})) \tag{29}\]  
While  
\[I_{E2}=I(L_{D,p}(\hat{x}_{i});L_{URC}^{etr}(\hat{x}_{i})) \tag{30}\]  
and the transfer characteristic function \((I_{E2})\) for Rate- 1 precoder is dependent on the \(E_{b}/N_{0}\) received from the channel and as well in the mapping between \(I_{A2}\) and \(I_{E2}\), as denoted by the following equation. \[I_{E2}=T_{URC-Code}(I_{A2},E_{b}/N_{0}) \tag{31}\]  
The resultant output information after \(k\) iterations at the outer decoder can be obtained from the following equation [46]. \[\Omega_{k}=T_{IRCC}(T_{URC}(\Omega_{k-1},E_{b}/N_{0})) \tag{32}\]  
In our considered irregular error protection mechanism, we utilized IRCC having subcode-rates \(r_{i}=[0.10,\ 0.15,\ 0.20,\ 0.25,\ 0.30,\ 0.35,\ 0.40,\ \ldots 0.90]\).