This paper identifies convolutional codes (CCs) used in conjunction with a CC-specific cyclic redundancy check (CRC) code as a promising paradigm for short blocklength codes. The resulting CRC-CC concatenated code naturally permits the use of the serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The CC of interest is of rate-$1/\omega$ and is either zero-terminated (ZT) or tail-biting (TB). For CRC-CC concatenated code designs, we show how to find the optimal CRC polynomial for a given ZTCC or TBCC. Our complexity analysis reveals that SLVD decoding complexity is a function of the terminating list rank, which converges to one at high SNR. This behavior allows the performance gains of SLVD to be achieved with a small increase in average complexity at the SNR operating point of interest. With a sufficiently large CC constraint length, the performance of CRC-CC concatenated code under SLVD approaches the random-coding union (RCU) bound as the CRC size is increased while average decoding complexity does not increase significantly. TB encoding further reduces the backoff from the RCU bound by avoiding the termination overhead. As a result, several CRC-TBCC codes outperform the RCU bound at moderate SNR values while permitting decoding with relatively low complexity.
翻译:本文指出,与CC专用的自行车冗余检查(CRC)代码一起使用的革命代码(CCs)与CC专用的自行车冗余检查(CRC)代码是短长代码的一个有希望的范例。由此形成的CRC-CC混合代码自然允许使用序列列表Viterbi解码(SLVD)实现最大类似解码(SLVD)的功能。CC的利率为1美元/千美加元,在SNRC运行点的平均复杂性略微提高的情况下实现。对于CRC-CC组合的代码设计而言,我们展示了如何为给定的ZTCC或TBCC找到最佳的CRC多元性。我们复杂的分析显示,SLVD解码复杂性是终止列表等级的函数,与SLVBC解码相交集。SLDCC的绩效增长幅度小于1美元/千美加美加元,而CFCCFC的常规和CRCFC的稳定性越低,而CRCFC的稳定性越低。