# Design and Analysis of Joint Source-Channel Code System with Fixed-Length Code
## 1 Introduction
An improvement in the SER performance was observed with the increase in the minimum Hamming distance. The authors in [16] compared the performance of three different types of JSCC schemes using FLCs and convolutional codes, namely, nonconvergent serial-concatenated coding, self-concatenated coding, and convergent serial concatenated coding. In [17], the author proposed a three-stage, serially concatenated JSCC scheme, which was constituted by the source block code, the unity-rate convolutional code and the space-time code. The bit error rate (BER) floor is averted due to the employment of a recursive unity-rate code. In addition, due to the outstanding error-correction performance of low-density parity-check (LDPC) codes and the polar codes, JSCC schemes where double low-density parity-check (D-LDPC) codes [18] and double polar codes [19] are used as source code and channel code for binary independent and identically distributed sources are proposed. Source statistics, which greatly affect the performance of the JSCC system, were subsequently raised in [20] and discussed in-depth in [21]. In the noisy communication with nonuniform sources, the source codeword assignment can greatly affect how well the JSCC decoder exploits the residual source redundancy, and the symbol error rate performance gap between the optimized codeword assignments and bad codeword assignments could be significant [22]. Moreover, the extrinsic information transfer (EXIT) chart can effectively analyze the convergence performance of JSCC. With the aid of an EXIT chart, near-capacity performance can be obtained by optimizing all components of the system. One optimization method is irregular codes, such as irregular convolutional codes (IrCCs) [23; 24; 25], irregular VLCs (IrVLCs) [26; 27], irregular redundant index assignments [11], and irregular unity-rate codes (IrURCs) [28]. These irregular codes were employed in the JSCC system, making the EXIT curves of the source decoder and channel decoder accurately matched. In this paper, we propose a novel joint source-channel code system based on fixed-length source code and irregular channel code in order to both improve symbol error rate performance and reduce calculation complexity. The main novelties and contributions are summarized as follows. First, we derive the close-form expression of the source symbol error rate (SER) performance of a joint source-channel code system based on soft-bit source decoder. Second, we propose a source coding scheme based on the fixed-length source code. By optimizing the fixed-length codeword assignment with the aid of a binary switch algorithm (BSA), the proposed scheme achieves nearly the same decoding complexity as the linear block code in [13], while the symbol error rate and convergence performance are much better than the traditional schemes. Third, based on EXIT chart analysis, we innovatively design the joint source-channel code system by introducing a low-complexity, irregular recursive nonsystematic convolutional code (RNSC). The subcodes were chosen from unity-rate RNSCs with small constraint lengths, such that the overall decoding complexity of the channel decoder was reduced. Last, via simulation results, we show that the proposed joint source-channel code system realizes a near-capacity iterative decoding performance with a relatively low calculation complexity as compared to benchmark schemes. The rest of this paper is organized as follows: Section 2 introduces the model of our JSCC system. Section 3 discusses the design guidelines of source block codes and provides the algorithms for generating the fixed-length codewords. Section 4 presents the optimization of the irregular channel code based on EXIT chart analysis. Then, Section 5 discusses the simulations results. Finally, Section 6 concludes the study.