By inserting interleavers between intermediate stages of the polar encoder, a new class of polar codes, termed interleaved polar (i-polar) codes, is proposed. By the uniform interleaver assumption, we derive the weight enumerating function (WEF) and the input-output weight enumerating function (IOWEF) averaged over the ensemble of i-polar codes. The average WEF can be used to calculate the upper bound on the average block error rate (BLER) of a code selected at random from the ensemble of i-polar codes. Also, we propose a concatenated coding scheme that employs $P$ high rate codes as the outer code and $Q$ i-polar codes as the inner code with an interleaver in between. The average WEF of the concatenated code is derived based on the uniform interleaver assumption. Simulation results show that BLER upper bounds can well predict BLER performance levels of the concatenated codes. The results show that the performance of the proposed concatenated code with $P=Q=2$ is better than that of the CRC-aided i-polar code with $P=Q=1$ of the same length and code rate at high signal-to-noise ratios (SNRs). Moreover, the proposed concatenated code allows multiple decoders to operate in parallel, which can reduce the decoding latency and hence is suitable for ultra-reliable low-latency communications (URLLC).

中文翻译：

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交错极性 (I-Polar) 码

通过在极坐标编码器的中间级之间插入交织器，提出了一类新的极坐标码，称为交织极坐标 (i-polar) 码。通过均匀交织器假设，我们推导出权重枚举函数 (WEF) 和输入输出权重枚举函数 (IOWEF) 在 i-polar 码集合上的平均值。平均 WEF 可用于计算从 i-polar 码集合中随机选择的码的平均误块率 (BLER) 的上限。此外，我们提出了一种使用的级联编码方案 $P$ 高速率码作为外码和 $Q$ i-polar 代码作为内部代码，中间有一个交织器。级联码的平均 WEF 是基于均匀交织器假设得出的。仿真结果表明，BLER 上限可以很好地预测级联码的 BLER 性能水平。结果表明，所提出的连接代码的性能与 $P=Q=2$ 优于 CRC 辅助的 i-polar 码 $P=Q=1$ 在高信噪比 (SNR) 下具有相同的长度和码率。此外，所提出的级联码允许多个解码器并行操作，这可以减少解码延迟，因此适用于超可靠低延迟通信（URLLC）。