# Hybrid Window Decoding for Joint Source Channel Anytime Coding System
## 1 Introduction  
The separate source-channel coding technique is based on the Shannon separation coding theorem, which assumes that the source entropy is less than the channel capacity under the conditions of unrestricted delay, complexity and code length. That is, the separation coding is asymptotically optimal. Joint source channel coding (JSCC) is a kind of coding technology that designs source/channel encoding and decoding in an interdependent way, so as to achieve the overall optimal communication system [1]. JSCC technology can be used in any system that violates the condition of the separation coding theorem and needs to consider both the source side and the channel side, such as communication systems with limitations of power, bandwidth, complexity or delay, multi-user system with shared channel, and different types of communication environments composed of heterogeneous sources or channels, etc. In recent years, the increasingly mature deep learning technology has brought new design ideas for JSCC technology, and set off a new wave of research [2, 3, 4]. The benefits of JSCC are reflected in the following aspects: (a) Improve the transmission efficiency: with comprehensive consideration of the characteristics of the source and channel, JSCC can optimize the coding scheme, reduce the size of the transmitted data, so as to improve the transmission efficiency. This means that more information can be transmitted with the same bandwidth, or less transmission time with the same amount of information. (b) Reduce the error rate: JSCC can adjust the coding mode according to the specific situation of the channel to reduce the bit error rate during transmission. This means that data are less error-prone during transmission, improving the reliability and accuracy of data. (c) Improve the system robustness: JSCC is designed with channel variation and interference in mind, making the system more stable and reliable in the face of different channel conditions. This allows the system to adapt to a wider range of environments, reducing transmission failures due to channel changes. In terms of JSCC technologies that are not based on deep learning, there are several typical schemes. At the sending side, the channel encoder can provide the channel state information (CSI) to the source encoder for the bit allocation [5; 6] and the source code optimization [7]. On the other hand, the source encoder can also provide the source significance information (SSI) for the unequal error protection (UEP) during the channel coding or modulation [8; 9]. At the receiving side, the source _a prior_ information and _a posterior_ information can be used for iterative decoding between the source and channel decoders, which is one of the most popular JSCC solutions and also the focus of this paper. Fresia first proposed a JSCC system that completes the source compression and error correction using two block LDPC codes (D-LDPC), then implements the joint belief propagation (BP) decoding within a global factor graph model framework, including both source and channel coding structures [10]. After that, various codes were introduced into the JSCC system, such as the block double protograph LDPC (DP-LDPC) code [11; 12], the block double Polar (D-Polar) code [13], the spatially coupled LDPC (SC-LDPC) code [14; 15; 16], and the spatially coupled repeat-accumulate (SC-RA) code [17; 18], etc. Among the above solutions, we focus on the scheme termed SC-RA based joint source channel anytime coding (JSCAC). It is a specific JSCC scheme combined with anytime coding techniques, i.e., causal spatially coupled coding and expanding window decoding [19; 20]. The anytime properties of the JSCAC scheme account for both delay and reliability, making it particularly suitable for transmission scenarios demanding both low delay and high reliability. However, the prior-art expanding window decoding strategies have noticeable decoding complexities and memory space requirements [17; 18], which affect the practical applications of JSCAC systems.