Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances

• URL: http://arxiv.org/abs/2012.00226v2
• Date: Fri, 12 Mar 2021 04:58:58 GMT
• Title: Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances
• Authors: Jihao Fan, Jun Li, Jianxin Wang, Zhihui Wei and Min-Hsiu Hsieh
• Abstract summary: We present a new construction of asymmetric quantum codes (AQCs) by combining classical tensord codes (CCs) with tensor product codes (TPCs) Most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical counterparts. We generalize our concatenation scheme by using the generalized CCs and TPCs.
• Score: 27.90363292358871
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\Omega(n_2a^{n_1})(a>1)$ 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.

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