In this paper, we propose a rate-compatible partially-coupled staircase low density parity check (PS-LDPC) coding scheme for high speed inter-satellite communications. First, we introduce the encoding process and sliding window decoding (SWD) algorithm of PS-LDPC codes, and we investigate the error floor of component codes, which validate that the PS-LDPC codes with short block-length component code can maintain the reliability, and significantly reduce the decoding latency. Then, we analyze the density evolution (DE) of PS-LDPC codes based on the multi-edge type (MET)- LDPC framework under the Gaussian approximation, and derive its decoding thresholds of SWD. Further, we propose an optimized coupling pattern (OCP) encoding algorithm that achieves the optimal coupling patterns with the minimized threshold by introducing two-stage column permutations, and modify the message exchanges in SWD algorithm according to this encoding algorithm. Moreover, we design a new decoding algorithm, named cascaded SWD (C-SWD) algorithm, which reduces the error floor and enhances decoding performance by pre-decoding, reliability enhancement, and cascading belief propagation (BP) decoder or ordered likelihood decoder (OLD) due to the error floor. Simulation results demonstrate that our PS-LDPC coding scheme outperforms the existing rate-compatible spatially coupled LDPC (SC-LDPC) coding schemes in terms of bit error rate and complexity.

To assist the design and optimization of low-density parity-check (LDPC) codes via density evolution (DE) on binary input additive white Gaussian noise (BIAWGN) channels, we propose a novel mixed Gamma approximation (MGA) scheme to obtain more accurate distribution of messages updated and output by the check nodes during DE iterations. Firstly, we highlight the inaccuracy of existing Gaussian approximation (GA) methods in approximating the distribution of check node output messages, especially when the messages from variable nodes are small with high probability (i.e. low signal-to-noise ratio), and the check nodes have a large degree, which leads to inexact results in GA methods. Then, we establish the MGA scheme by utilizing the statistical properties of Gamma distribution and combine it with GA, which outperforms the existing GA methods in the metrics of error of output mean and Kullback-Leibler (KL) divergence of output distribution for a wide range of parameters. Simulation and analysis validate that our MGA scheme has the potential for the design and optimization of LDPC codes, which can provide adequately accurate estimation of check node outputs with moderate complexity for a variety of approximation methods, such as Gaussian capacity approximation, and significantly reduce the computational complexity by sacrificing minor accuracy.

Large Language Models (LLMs) specialized in code have shown exceptional proficiency across various programming-related tasks, particularly code generation. Nonetheless, due to its nature of pretraining on massive uncritically filtered data, prior studies have shown that code LLMs are prone to generate code with potential vulnerabilities. Existing approaches to mitigate this risk involve crafting data without vulnerability and subsequently retraining or fine-tuning the model. As the number of parameters exceeds a billion, the computation and data demands of the above approaches will be enormous. Moreover, an increasing number of code LLMs tend to be distributed as services, where the internal representation is not accessible, and the API is the only way to reach the LLM, making the prior mitigation strategies non-applicable. To cope with this, we propose CoSec, an on-the-fly Security hardening method of code LLMs based on security model-guided Co-decoding, to reduce the likelihood of code LLMs to generate code containing vulnerabilities. Our key idea is to train a separate but much smaller security model to co-decode with a target code LLM. Since the trained secure model has higher confidence for secure tokens, it guides the generation of the target base model towards more secure code generation. By adjusting the probability distributions of tokens during each step of the decoding process, our approach effectively influences the tendencies of generation without accessing the internal parameters of the target code LLM. We have conducted extensive experiments across various parameters in multiple code LLMs (i.e., CodeGen, StarCoder, and DeepSeek-Coder), and the results show that our approach is effective in security hardening. Specifically, our approach improves the average security ratio of six base models by 5.02%-37.14%, while maintaining the functional correctness of the target model.