Quantum computation and quantum information
Quantum computation and quantum information
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
On the iterative decoding of sparse quantum codes
Quantum Information & Computation
Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding
IEEE Transactions on Information Theory
Sparse-graph codes for quantum error correction
IEEE Transactions on Information Theory
The private classical capacity and quantum capacity of a quantum channel
IEEE Transactions on Information Theory
On Quantum and Classical BCH Codes
IEEE Transactions on Information Theory
Convolutional and Tail-Biting Quantum Error-Correcting Codes
IEEE Transactions on Information Theory
Quantum convolutional coding with shared entanglement: general structure
Quantum Information Processing
On the iterative decoding of sparse quantum codes
Quantum Information & Computation
On the construction of stabilizer codes with an arbitrary binary matrix
Quantum Information Processing
A class of quantum low-density parity check codes by combining seed graphs
Quantum Information Processing
Dualities and identities for entanglement-assisted quantum codes
Quantum Information Processing
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In this paper, we present a theory of quantum serial turbo codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum low-density parity-check (LDPC) codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Second, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice.We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular, its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoders have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be noncatastrophic and nonrecursive. While the resulting families of turbo codes have bounded minimum distance, from a pragmatic point of view, the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes.With well-chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.