Goal-oriented Luby transform (LT) codes are required in different scenarios. Based on the random walk model, analysis of ripple size evolution provides an effective method to design LT codes. However, the ripple addition in each step depends on both the number of symbols released in the current step and the ripple size in the last step, leading to distortion. Therefore, the authors propose a random walk algorithm with barrier (RWA-B) to model the ripple addition directly. To evaluate the performance of ripple size evolution, they utilise generalised degree distribution algorithm to generate corresponding degree distribution. Through analysing the relationship between the performance of generated ripple size evolution and the parameters of RWA-B, they design an iterator greedy algorithm to search the optimal ripple size evolution for desired goals. As a result, they compare three goal-oriented degree distributions with others through numerical simulations. In binary erasure channel, both the memory usage oriented and block error rate (BER) oriented degree distributions outperform others with lowest average overhead, and the overhead oriented degree distribution outperforms others in terms of average overhead and average degree. In additive white Gaussian noise channel, the BER-oriented degree distribution outperforms others in terms of BER and average overhead.

中文翻译：

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LT代码最佳度分布的面向目标设计

在不同情况下都需要面向目标的Luby变换（LT）代码。基于随机游动模型，分析纹波大小演变为设计LT码提供了一种有效的方法。但是，每个步骤中的纹波增加取决于当前步骤中释放的符号数量和最后一步中的纹波大小，从而导致失真。因此，作者提出了一种带有势垒的随机游走算法（RWA-B），以直接对纹波加法建模。为了评估波纹大小演化的性能，他们利用广义度分布算法生成相应的度分布。通过分析产生的纹波大小演变的性能与RWA-B参数之间的关系，他们设计了一种迭代器贪婪算法，以搜索所需目标的最佳纹波大小演变。结果，他们通过数值模拟比较了三种面向目标的学位分布。在二进制擦除通道中，面向内存使用率和面向块错误率（BER）的程度分布均以最低的平均开销胜过其他，而面向开销的程度分布在平均开销和平均程度方面均优于其他开销。在加性高斯白噪声信道中，面向BER的度分布在BER和平均开销方面优于其他。在平均间接费用和平均程度方面，间接费用取向度分布优于其他方面。在加性高斯白噪声信道中，面向BER的度分布在BER和平均开销方面优于其他。在平均间接费用和平均程度方面，间接费用取向度分布优于其他方面。在加性高斯白噪声通道中，面向BER的度分布在BER和平均开销方面优于其他类型。