D²-JSCC: Digital Deep Joint Source-Channel Coding for Semantic Communications Jianhao Huang, Kai Yuan, Chuan Huang, Member, IEEE, and Kaibin Huang, Fellow, IEEE Abstract—Semantic communications (SemCom) have emerged as a new paradigm for supporting sixth-generation (6G) applications, where semantic features of raw data are extracted and transmitted using artificial intelligence (AI) algorithms to attain high communication efficiencies. Most existing SemCom techniques rely on deep neural networks (DNNs) to implement analog (or semi-analog) source-channel mappings. These operations, however, are not compatible with existing digital communication architectures. To address this issue, we propose in this paper a novel framework of digital deep joint source-channel coding (D²-JSCC) targeting image transmission in SemCom. The framework features digital source and channel codings that are jointly optimized to reduce the end-to-end (E2E) distortion. First, deep source coding with an adaptive density model is designed to efficiently extract and encode semantic features according to their different distributions. Second, channel block coding is employed to protect encoded features against channel distortion. To facilitate their joint design, the E2E distortion is characterized as a function of the source and channel rates via the analysis of the Bayesian model of the D²-JSCC system and validated Lipschitz assumption on the DNNs. Then to minimize the E2E distortion, we propose an efficient two-step algorithm to find the optimal trade-off between the source and channel rates for a given channel signal-to-noise ratio (SNR). In the first step, the source encoder is initially optimized by selecting a DNN model with a suitable source rate from a designed look-up table consisting of a set of trained models. In the second step, the preceding DNNs (source encoder) are retrained to adapt to the channel SNR so as to achieve the optimal E2E performance. Via experiments on simulating the D²-JSCC with different channel codes and real datasets, the proposed framework is observed to outperform the classic deep JSCC. Furthermore, due to the source-channel integrated design, D²-JSCC is found to be free from the undesirable cliff effect and leveling-off effect, which commonly exists for digital systems designed based on the separation approach. Index Terms—Semantic communications, digital deep joint source-channel coding, deep learning, deep source coding, and joint source-channel rate control.D²-JSCC: Digital Deep Joint Source-Channel Coding for Semantic Communications Jianhao Huang, Kai Yuan, Chuan Huang, Member, IEEE, and Kaibin Huang, Fellow, IEEE Abstract—Semantic communications (SemCom) have emerged as a new paradigm for supporting sixth-generation (6G) applications, where semantic features of raw data are extracted and transmitted using artificial intelligence (AI) algorithms to attain high communication efficiencies. Most existing SemCom techniques rely on deep neural networks (DNNs) to implement analog (or semi-analog) source-channel mappings. These operations, however, are not compatible with existing digital communication architectures. To address this issue, we propose in this paper a novel framework of digital deep joint source-channel coding (D²-JSCC) targeting image transmission in SemCom. The framework features digital source and channel codings that are jointly optimized to reduce the end-to-end (E2E) distortion. First, deep source coding with an adaptive density model is designed to efficiently extract and encode semantic features according to their different distributions. Second, channel block coding is employed to protect encoded features against channel distortion. To facilitate their joint design, the E2E distortion is characterized as a function of the source and channel rates via the analysis of the Bayesian model of the D²-JSCC system and validated Lipschitz assumption on the DNNs. Then to minimize the E2E distortion, we propose an efficient two-step algorithm to find the optimal trade-off between the source and channel rates for a given channel signal-to-noise ratio (SNR). In the first step, the source encoder is initially optimized by selecting a DNN model with a suitable source rate from a designed look-up table consisting of a set of trained models. In the second step, the preceding DNNs (source encoder) are retrained to adapt to the channel SNR so as to achieve the optimal E2E performance. Via experiments on simulating the D²-JSCC with different channel codes and real datasets, the proposed framework is observed to outperform the classic deep JSCC. Furthermore, due to the source-channel integrated design, D²-JSCC is found to be free from the undesirable cliff effect and leveling-off effect, which commonly exists for digital systems designed based on the separation approach. Index Terms—Semantic communications, digital deep joint source-channel coding, deep learning, deep source coding, and joint source-channel rate control.