论文标题
具有较大Z-Distances的非对称量子串联和张量产品代码
Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances
论文作者
论文摘要
在本文中，我们通过将经典串联代码（CCS）与张量产品代码（TPC）相结合，称为不对称量子代码（TPCS），称为不对称量子量子串联和不对称量子串联产品代码（AQCTPC），这是不对称量子代码（AQC）的新结构，具有以下三个优势。首先，只有AQCTPC中的外部代码才能满足量子代码中的正交约束，并且任何经典的线性代码都可以用于内部，这使AQCTPC非常易于构建。其次，大多数AQCTPC高度退化，这意味着它们比经典的TPC对应物纠正了更多的错误。因此，我们构建了与文献中已知结果相比，具有更好参数的AQC家族。第三，只要内部和外部代码可有效地解码，AQCTPC还是可以有效地解码的。特别是，我们通过考虑错误退化，将TPCS的内部解码复杂性从$ω（N_2A^{N_1}）（a> 1）（a> 1）降低到$ O（n_2）$，通过考虑错误退化，其中$ N_1 $和$ n_2 $是内部代码和外部代码的块长度。此外，我们通过相应地使用广义CCS和TPC来概括我们的串联方案。
In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Third, AQCTPCs can be efficiently decoded although they are degenerate, provided that the inner and outer codes are efficiently decodable. In particular, we significantly reduce the inner decoding complexity of TPCs from $Ω(n_2a^{n_1})(a>1)$ to $O(n_2)$ by considering error degeneracy, where $n_1$ and $n_2$ are the block length of the inner code and the outer code, respectively. Furthermore, we generalize our concatenation scheme by using the generalized CCs and TPCs correspondingly.
