We consider a transmitter that encodes data packets using network coding and broadcasts coded packets. A receiver employing network decoding recovers the data packets if a sufficient number of error-free coded packets are gathered. The receiver does not abandon its efforts to recover the data packets if network decoding is unsuccessful; instead, it employs syndrome decoding (SD) in an effort to repair erroneously received coded packets, and then reattempts network decoding. Most decoding techniques, including SD, assume that errors are independently and identically distributed within received coded packets. Motivated by the guessing random additive noise decoding (GRAND) framework, we propose transversal GRAND (T-GRAND): an algorithm that exploits statistical dependence in the occurrence of errors, complements network decoding and recovers all data packets with a higher probability than SD. T-GRAND examines error vectors in order of their likelihood of occurring and altering the transmitted packets. Calculation and sorting of the likelihood values of all error vectors is a simple but computationally expensive process. To reduce the complexity of T-GRAND, we take advantage of the properties of the likelihood function and develop an efficient method, which identifies the most likely error vectors without computing and ordering their likelihoods.
翻译:我们考虑的是使用网络编码和广播编码包编码数据包的发件人。如果收集到足够数量的无误编码包,使用网络解码的接收人就会收回数据包。如果网络解码失败,接收人不会放弃恢复数据包的努力;相反,它使用综合解码(SD)来修复错误接收的编码包,然后重试网络解码。大多数解码技术,包括SD,都假定错误是独立和同样地分布于收到的编码包中。根据随机添加噪音解码(GRAND)框架,我们提议转基因GRAND(T-GRAND):一种在错误发生时利用统计依赖性的算法,补充网络解码和收回所有数据包,其概率高于SD。T-GRAND检查错误矢量的错误矢量,以了解其发生和改变传输包的可能性。所有错误矢量的可能值的计算和排序是一个简单但计算但成本高昂的过程。为了降低其可能性,我们选择了TGRAND计算方法的概率。