1,961 research outputs found
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
Turbo Decoding and Detection for Wireless Applications
A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannonâs visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannonâs capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted
Can Punctured Rate-1/2 Turbo Codes Achieve a Lower Error Floor than their Rate-1/3 Parent Codes?
In this paper we concentrate on rate-1/3 systematic parallel concatenated
convolutional codes and their rate-1/2 punctured child codes. Assuming
maximum-likelihood decoding over an additive white Gaussian channel, we
demonstrate that a rate-1/2 non-systematic child code can exhibit a lower error
floor than that of its rate-1/3 parent code, if a particular condition is met.
However, assuming iterative decoding, convergence of the non-systematic code
towards low bit-error rates is problematic. To alleviate this problem, we
propose rate-1/2 partially-systematic codes that can still achieve a lower
error floor than that of their rate-1/3 parent codes. Results obtained from
extrinsic information transfer charts and simulations support our conclusion.Comment: 5 pages, 7 figures, Proceedings of the 2006 IEEE Information Theory
Workshop, Chengdu, China, October 22-26, 200
Turbo-Detected Unequal Error Protection Irregular Convolutional Codes Designed for the Wideband Advanced Multirate Speech Codec
Abstractâsince the different bits of multimedia information, such as speech and video, have different error sensitivity, efficient unequalprotection channel coding schemes have to be used to ensure that the perceptually more important bits benefit from more powerful protection. Furthermore, in the context of turbo detection the channel codes should also match the characteristics of the channel for the sake of attaining a good convergence performance. In this paper, we address this design dilemma by using irregular convolutional codes (IRCCs) which constitute a family of different-rate subcodes. we benefit from the high design flexibility of IRCCs and hence excellent convergence properties are maintained while having unequal error protection capabilities matched to the requirements of the source. An EXIT chart based design procedure is proposed and used in the context of protecting the different-sensitivity speech bits of the wideband AMR speech codec. As a benefit, the unequalprotection system using IRCCs exhibits an SNR advantage of about 0.4dB over the equal-protection system employing regular convolutional codes, when communicating over a Gaussian channel
Entanglement-assisted quantum turbo codes
An unexpected breakdown in the existing theory of quantum serial turbo coding
is that a quantum convolutional encoder cannot simultaneously be recursive and
non-catastrophic. These properties are essential for quantum turbo code
families to have a minimum distance growing with blocklength and for their
iterative decoding algorithm to converge, respectively. Here, we show that the
entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in
the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can
possess both of the aforementioned desirable properties. We give several
examples of EAQ convolutional encoders that are both recursive and
non-catastrophic and detail their relevant parameters. We then modify the
quantum turbo decoding algorithm of Poulin et al., in order to have the
constituent decoders pass along only "extrinsic information" to each other
rather than a posteriori probabilities as in the decoder of Poulin et al., and
this leads to a significant improvement in the performance of unassisted
quantum turbo codes. Other simulation results indicate that
entanglement-assisted turbo codes can operate reliably in a noise regime 4.73
dB beyond that of standard quantum turbo codes, when used on a memoryless
depolarizing channel. Furthermore, several of our quantum turbo codes are
within 1 dB or less of their hashing limits, so that the performance of quantum
turbo codes is now on par with that of classical turbo codes. Finally, we prove
that entanglement is the resource that enables a convolutional encoder to be
both non-catastrophic and recursive because an encoder acting on only
information qubits, classical bits, gauge qubits, and ancilla qubits cannot
simultaneously satisfy them.Comment: 31 pages, software for simulating EA turbo codes is available at
http://code.google.com/p/ea-turbo/ and a presentation is available at
http://markwilde.com/publications/10-10-EA-Turbo.ppt ; v2, revisions based on
feedback from journal; v3, modification of the quantum turbo decoding
algorithm that leads to improved performance over results in v2 and the
results of Poulin et al. in arXiv:0712.288
Distributed Turbo-Like Codes for Multi-User Cooperative Relay Networks
In this paper, a distributed turbo-like coding scheme for wireless networks
with relays is proposed. We consider a scenario where multiple sources
communicate with a single destination with the help of a relay. The proposed
scheme can be regarded as of the decode-and-forward type. The relay decodes the
information from the sources and it properly combines and re-encodes them to
generate some extra redundancy, which is transmitted to the destination. The
amount of redundancy generated by the relay can simply be adjusted according to
requirements in terms of performance, throughput and/or power. At the
destination, decoding of the information of all sources is performed jointly
exploiting the redundancy provided by the relay in an iterative fashion. The
overall communication network can be viewed as a serially concatenated code.
The proposed distributed scheme achieves significant performance gains with
respect to the non-cooperation system, even for a very large number of users.
Furthermore, it presents a high flexibility in terms of code rate, block length
and number of users.Comment: Submitted to ICC 201
Concatenated Space Time Block Codes and TCM, Turbo TCM Convolutional as well as Turbo Codes
Space-time block codes provide substantial diversity advantages for multiple transmit antenna systems at a low decoding complexity. In this paper, we concatenate space-time codes with Convolutional Codes (CC), Turbo Convolutional codes (TC), Turbo BCH codes (TBCH), Trellis Coded Modulation (TCM) and Turbo Trellis Coded Modulation (TTCM) schemes for achieving a high coding gain. The associated performance and complexity of the coding schemes is compared
Good Concatenated Code Ensembles for the Binary Erasure Channel
In this work, we give good concatenated code ensembles for the binary erasure
channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code
ensembles formed by the serial concatenation of a repetition code with multiple
accumulators, and the hybrid concatenated code (HCC) ensembles recently
introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics,
Lausanne, Switzerland) consisting of an outer multiple parallel concatenated
code serially concatenated with an inner accumulator. We introduce stopping
sets for iterative constituent code oriented decoding using maximum a
posteriori erasure correction in the constituent codes. We then analyze the
asymptotic stopping set distribution for RMA and HCC ensembles and show that
their stopping distance hmin, defined as the size of the smallest nonempty
stopping set, asymptotically grows linearly with the block length. Thus, these
code ensembles are good for the BEC. It is shown that for RMA code ensembles,
contrary to the asymptotic minimum distance dmin, whose growth rate coefficient
increases with the number of accumulate codes, the hmin growth rate coefficient
diminishes with the number of accumulators. We also consider random puncturing
of RMA code ensembles and show that for sufficiently high code rates, the
asymptotic hmin does not grow linearly with the block length, contrary to the
asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov
bound as the rate increases. Finally, we give iterative decoding thresholds for
the different code ensembles to compare the convergence properties.Comment: To appear in IEEE Journal on Selected Areas in Communications,
special issue on Capacity Approaching Code
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