)1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiaoiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiaoiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiaoiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiaoiao University, Xiamen 361021, China; [EMAIL_ADDRESS] (C.C. );[EMAIL_ADDRESS] (Q.C. )1 Xiamen Key Laboratory of Mobile Multimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China; chen_chen_chen@hqu. including constellation mappings [15] and optimized protograph low-density parity-check (LDPC) codes with unequal power allocation [16]. For the residual source redundancy after source coding, in [17], a novel PAS strategy was proposed for a joint source and channel coded modulation (JSCCM) system. By using source encoders to transform the non-uniform source bit sequence directly into bitstreams with the desired distribution, the PAS strategy for JSCCM systems avoids the rate loss and the high latency of traditional PAS schemes. Additionally, it is important to match source codes with source probabilities in JSCCM systems to effectively use the residual redundancy. Considering some communication applications with dynamically changing source statistics, rate-compatible source codes in JSCCM systems are essential for adaptive coding. Substantial efforts have been invested in the source code design for JSCC. In [18], a source protograph extrinsic information transfer (PEXIT) algorithm was proposed, which utilizes the source decoding threshold to evaluate the error-floor level. Further, a rate-compatible family of source codes with good source decoding thresholds was proposed for JSCC systems in [19]. Moreover, several optimized source-linking matrices have been suggested to further improve the error-floor performance [20]. However, the source code designs above only focus on improving the source decoding threshold for the JSCC system, which would yield a loss in the shaping gap for the JSCCM system due to the mismatch between the source probabilities and the source codes. In [17], the source codes in JSCCM systems were optimized for a specific source probability, but they may fail to ensure the PAS performance for source probabilities with slight variations. Consequently, these source codes may not be suitable for adaptive coding in JSCCM systems with dynamically changing source probabilities. In this paper, we present a study on the construction of a family of rate-compatible source codes for JSCCM systems.