# Design and Analysis of Joint Source-Channel Code System with Fixed-Length Code
## 1 Introduction  
With the escalation in the number of cellular mobile phones and the popularity of wireless networks, high data rate transmission is required. However, the wireless channel is restricted by transmission power and limited available bandwidth, so challenges still exist in designing reliable and efficient communication systems. In classical communication systems, the source encoder and the channel encoder are designed separately. The source encoder removes redundancy from the source to improve the transmission rate and the channel encoder re-inserts controlled redundancy to resist the channel noise. According to [PERSON]'s source and channel separation theorem, the system can achieve a near-capacity performance if the source and channel coding are both optimal [1]. However, due to the severe delay and computational complexity restrictions in practical applications, the theorem does not hold, and the separate source and channel code (SSCC) system usually inflicts a loss of optimality. This motivates the studies of joint source-channel code (JSCC) systems to narrow the gap to the global optimum. JSCC systems can exploit the residual redundancy in source-coded parameters to realize a better transmission performance. In [2], the authors proposed a soft-bit source decoder (SBSD), which uses the a priori knowledge of source statistics to calculate the reliability of source-coded bits. Then, the SBSD was applied in an iterative source-channel decoding (ISCD) structure, improving the error-correction capability of the channel decoder [3]. Moreover, the source encoder and the bit-interleaved coded modulation wereserially concatenated [4] to further improve the bandwidth and power efficiency of the system by exchanging extrinsic information between the source decoder, the channel decoder, and the demodulator. These previous studies on ISCD systems usually used near-entropy codes for source compression. Because very limited redundancy is left in the source-coded bits after the compression encoding, the iteration gain of ISCD is limited [5]. It has been found that the application of source codes with introduced redundancy as an alternative to classical entropy codes can achieve significant performance improvement. Several redundant source codes were proposed, including the variable-length codes (VLCs) [6; 7; 8; 9] and the fixed-length codes (FLCs). VLCs were designed to increase the free distance to improve the error-correction performance. [6]. Recently, several efficient algorithms were proposed to construct near-optimal VLCs that have the minimum average codeword length with low search complexity [7; 8; 9]. The VLCs are sensitive to error propagation and suffer from a high decoding complexity, while the FLCs have the advantages of inherent synchronization and low-complexity because the symbol positions in the coded bitstream are fixed. Thus, the FLCs have been investigated by many studies. The non-redundant index assignment for quantized source symbols proposed in [10] is the first joint source-channel code scheme based on FLCs. However, this JSCC scheme has a limited error correction capability, since the index has nonredundant bits. To solve this problem, the authors in [11] utilized a linear block code (LBC) to realize a redundancy index assignment for source symbols. The introduced redundancy of source code was exploited by SBSD at the receiving side, and the convergence performance of ISCD was improved. Additionally, the generator metrics of LBCs were further optimized to maximize the minimum Hamming distance of codewords [12]. This optimization of source codes reduced the error floor of ISCD. Similarly, the authors in [13] proposed simple algorithms to generate a class of short block codes that have diverse minimum Hamming distance (\(d_{\text{min}}\)) values. In multimedia communication, these block codes are used to deliberately impose additional redundancy in the source coded video bit-stream [14]. In [15], the effects of Hamming distance were investigated for an FLC-based JSCC system.