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Girth Analysis and Design of Periodically Time-Varying SC-LDPC Codes

机译：周期性时代SC-LDPC码的周长分析与设计

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摘要

Time-varying spatially coupled low-density parity-check (SC-LDPC) codes with very large period are characterized by significantly better error rate performance and girth properties than their time-invariant counterparts, but the number of parameters they require to be described is usually very large and unpractical. Time-invariant SC-LDPC codes, which can be seen as periodically time-varying codes with unitary period, are represented through a small number of parameters and designed exploiting few degrees of freedom, but their error rate performance and girth properties are sub-optimal. In this paper, we show that the limits of time-invariant SC-LDPC codes can be overcome by transforming them into time-varying SC-LDPC codes with very small period. In particular, we show that periodically time-varying SC-LDPC codes with small period may exhibit significantly better girth properties than the corresponding time-invariant codes by exploiting a larger number of degrees of freedom in the code design, which however scale at most linearly with the product of the code period and the size of the considered base matrix.
机译：具有非常大的时段的时变空间耦合的低密度奇偶校验（SC-LDPC）代码的特征在于，比其时间不变对应物显着更好地更好地更好的错误率性能和周长属性，但是要描述的参数数量是通常非常大而不公司。可以通过少量参数表示可以被视为具有单一时期的周期性的SC-LDPC代码，并设计利用少量自由度，但它们的错误率性能和周长属性是子最优的。在本文中，我们表明，通过将它们转换为具有非常小的时期的时变的SC-LDPC代码，可以克服时间不变的SC-LDPC代码的极限。特别地，我们表明，通过利用代码设计中的更大数量的自由度，周期性地，具有小时期的SC-LDPC代码具有比相应的时间不变码显着更好的周围性能。然而，它以最具线性缩放使用代码周期的乘积和所考虑的基础矩阵的大小。

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