Exchange of Limits: Why Iterative Decoding Works
Exchange of Limits: Why Iterative Decoding Works
复制标题
极限交换：为什么迭代解码有效
DOI：
10.1109/tit.2011.2111730
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发表时间：
2008
影响因子：
2.5
通讯作者：
R. Urbanke
中科院分区：
文献类型：
--
作者：
Satish Babu Korada;R. Urbanke
我们考虑使用低密度奇偶校验码和消息传递解码在二进制输入无内存输出对称信道上进行通信。这种组合对于固定迭代次数的渐近（在长度上）性能由密度演化给出。让迭代次数趋于无穷，我们得到密度演化（DE）阈值，这是最大的信道参数，使误码概率作为迭代的函数趋于零。在实践中，我们经常使用短代码并执行大量迭代。因此，考虑如果在标准分析中我们交换块长度和迭代次数发散到无穷大的顺序会发生什么，这是很有趣的。特别是，我们可以问两个极限是否给出相同的阈值。尽管经验观察强烈表明，交换限制对所有通道参数都有效，但我们将讨论限制在DE阈值以下的通道参数。具体地说，我们表明，只要消息可靠性是有界的，并且满足其他技术条件，无论如何采取限制，误码概率都会消失到一个重要的阈值。当变量节点的最小度至少为5时，该阈值等于DE阈值，对于更小的度，该阈值严格小于DE阈值。
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of iterations is given by density evolution. Letting the number of iterations tend to infinity we get the density evolution (DE) threshold, the largest channel parameter so that the bit error probability tends to zero as a function of the iterations. In practice, we often work with short codes and perform a large number of iterations. It is, therefore, interesting to consider what happens if in the standard analysis we exchange the order in which the blocklength and the number of iterations diverge to infinity. In particular, we can ask whether both limits give the same threshold. Although empirical observations strongly suggest that the exchange of limits is valid for all channel parameters, we limit our discussion to channel parameters below the DE threshold. Specifically, we show that as long as the message reliabilities are bounded and other technical conditions are met, the bit error probability vanishes up to a nontrivial threshold regardless of how the limit is taken. This threshold is equal to the DE threshold when the minimum degree of the variable nodes is at least five and strictly less than the DE threshold for smaller degrees.