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Quantum Serial Turbo Codes

Poulin, David and Tillich, Jean-Pierre and Ollivier, Harold (2009) Quantum Serial Turbo Codes. IEEE Transactions on Information Theory, 55 (6). pp. 2776-2798. ISSN 0018-9448.

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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.

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Additional Information:© Copyright 2009 IEEE. Manuscript received March 04, 2008; revised February 02, 2009. Current version published May 20, 2009. The work of D. Poulin was supported in part by the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information, by the National Science Foundation under Grant PHY-0456720, and by the Natural Sciences and Engineering Research Council of Canada. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 2008.
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Gordon and Betty Moore FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of CanadaUNSPECIFIED
Subject Keywords:Belief propagation, convolutional codes, iterative decoding, quantum error correction, turbo codes
Issue or Number:6
Record Number:CaltechAUTHORS:20090821-124920284
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15231
Deposited By: George Porter
Deposited On:09 Sep 2009 16:14
Last Modified:03 Oct 2019 00:56

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