Structural Analysis of Quantum Turbo Codes

Iñiguez de Gordoa Pouso

Jean–Pierre Tillich

Iryna Andriyanova, Jean–Pierre Tillich

Hailin Xiao, Ju Ni, Wu Xie +1 more

As in classical coding theory, turbo product codes (TPCs) through serially concatenated block codes can achieve approximatively Shannon capacity limit and have low decoding complexity. However, special requirements in the quantum setting severely limit the structures of turbo product codes (QTPCs). To design a good structure for QTPCs, we present a new construction of QTPCs with the interleaved serial concatenation of [Formula: see text]-type quantum convolutional codes (QCCs). First, [Formula: see text]-type QCCs are proposed by exploiting the theory of CSS-type quantum stabilizer codes and QCCs, and the description and the analysis of encoder circuit are greatly simplified in the form of Hadamard gates and C-NOT gates. Second, the interleaved coded matrix of QTPCs is derived by quantum permutation SWAP gate definition. Finally, we prove the corresponding relation on the minimum Hamming distance of QTPCs associated with classical TPCs, and describe the state diagram of encoder and decoder of QTPCs that have a highly regular structure and simple design idea.

Daniele Capirone, Giacomo Como, Fabio Fagnani +1 more

A class of serial turbo codes admitting low-density parity-check (LDPC) representation is considered. Their parity matrix has a random and a structured part. Thanks to their turbo structure, these codes are linear-time encodable, while they can be decoded as LDPC codes. An ensemble analysis for the error floor region, on the line of classical results for serial turbo codes, suggests a design parameter. Simulation results using usual LDPC message-passing show poor performance and no dependence on such parameter. A different block-wise decoding algorithm is proposed, which considerably improves performance. With this new decoding scheme, simulations confirm the theoretical design parameters in the medium-high SNR region.

Sankalpa Khadka