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0807.3566[abs pdf]
- Title:
Stabilizer Quantum Codes: A Unified View based on Forney-style Factor
Graphs
Authors:
Pascal O. Vontobel
Quantum error-correction codes (QECCs) are a vital ingredient of quantum
computation and communication systems. In that context it is highly desirable
to design QECCs that can be represented by graphical models which possess a
structure that enables efficient and close-to-optimal iterative decoding. In
this paper we focus on stabilizer QECCs, a class of QECCs whose construction is
rendered non-trivial by the fact that the stabilizer label code, a code that is
associated with a stabilizer QECC, has to satisfy a certain self-orthogonality
condition. In order to design graphical models of stabilizer label codes that
satisfy this condition, we extend a duality result for Forney-style factor
graphs (FFGs) to the stabilizer label code framework. This allows us to
formulate a simple FFG design rule for constructing stabilizer label codes, a
design rule that unifies several earlier stabilizer label code constructions.
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