Optimal Memory Order of Memory-Based LT Encoders for Finite Block-Length Codes Over Binary Erasure Channels
Optimal Memory Order of Memory-Based LT Encoders for Finite Block-Length Codes Over Binary Erasure Channels
复制标题
二进制擦除通道上有限块长度代码的基于内存的 LT 编码器的最佳内存顺序
DOI：
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发表时间：
2019
影响因子：
8.3
通讯作者：
E. Perrins
中科院分区：
文献类型：
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作者：
Luyao Shang;E. Perrins
基于存储器的LT编码器（MBLTE）已被证明在误比特率（BER）和解码收敛速度方面比常规LT编码器具有更好的性能。在本文中，我们探讨了整个家庭的MBLTE有限块长度码的二进制擦除信道（BEC）。我们提出了一种算法来扩展的第一和第二阶MBLTE的方法，以任意$i$阶MBLTE。我们分析了这样的编码器的性能数学特征的预期累积数量的恢复变量节点在每个解码轮。我们定义了基于内存的编码方法（MBEM）的阈值，并表明MBLTEs的性能随着内存顺序的增加而增加，达到这个阈值。超过这一点，我们表明，MBLTE的性能饱和，如果信道擦除概率为零，否则会降低。我们制定了一个优化问题，以解决最佳的内存顺序的基础上是否达到MBEM阈值。我们提出了一套广泛的数值结果。这些表明我们的分析和计算机模拟之间的协议。他们还表明，我们的优化问题是有效的，在解码收敛速度，BER/帧错误率和错误地板方面确定最佳的存储器顺序的MBLTE。
Memory-based LT encoders (MBLTEs) have been shown to have better performance than the regular LT encoder in terms of bit error rate (BER) and decoding convergence speed. In this paper, we explore the entire family of MBLTEs for finite block-length codes over the binary erasure channel (BEC). We propose an algorithm to extend the first and second order MBLTE approach to an arbitrary $i$ -th order MBLTE. We analyze the performance of such encoders mathematically by characterizing the expected accumulated number of recovered variable nodes at each decoding round. We define the threshold of the memory-based encoding method (MBEM) and show that the performance of MBLTEs increases as the memory order increases up to the point where this threshold is achieved. Beyond this point, we show that the performance of MBLTEs saturates if the channel erasure probability is zero and degrades otherwise. We formulate an optimization problem to solve for the optimal memory order based on whether or not the MBEM threshold is achieved. We present an extensive set of numerical results. These show agreement between our analysis and computer simulations. They also show that our optimization problem is efficient in determining the optimal memory order of MBLTEs in terms of decoding convergence speed, BER/frame-error-rate, and error floor.