Design of capacity-approaching irregular low-density parity-check codes
Design of capacity-approaching irregular low-density parity-check codes
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DOI：
10.1109/18.910578
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发表时间：
2001-02-01
影响因子：
2.5
通讯作者：
Urbanke, RL
中科院分区：
文献类型：
--
作者：
Richardson, TJ;Shokrollahi, MA;Urbanke, RL
我们设计的低密度奇偶校验（LDPC）码，执行率非常接近香农容量的代码是建立在高度不规则的二分图与精心挑选的度模式的两侧。本文在文献[1]的基础上对这类码进行了理论分析，在通信信道是对称的假设下，证明了图的消息节点的概率密度具有一定的对称性，并利用这一对称性证明了在无圈的假设下，消息密度总是随着迭代次数趋于无穷而收敛。此外，我们证明了一个稳定性条件，这意味着一个上界的错误的分数，置信传播解码器可以纠正时，适用于从一个二分图与给定的degreedistribution.Our代码诱导的代码被发现，通过优化的度结构的底层graphs。我们开发了几种策略来执行这种优化。我们还提出了一些模拟结果的代码发现，这表明代码的性能是非常接近的渐近理论界。
We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1], Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph possess a certain symmetry, Using this symmetry property we then show that, under the assumption of no cycles, the message densities always converge as the number of iterations tends to infinity. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a belief-propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution.Our codes are found by optimizing the degree structure of the underlying graphs. We develop several strategies to perform this optimization. We also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds.