6,922 research outputs found
Enhanced Feedback Iterative Decoding of Sparse Quantum Codes
Decoding sparse quantum codes can be accomplished by syndrome-based decoding
using a belief propagation (BP) algorithm.We significantly improve this
decoding scheme by developing a new feedback adjustment strategy for the
standard BP algorithm. In our feedback procedure, we exploit much of the
information from stabilizers, not just the syndrome but also the values of the
frustrated checks on individual qubits of the code and the channel model.
Furthermore we show that our decoding algorithm is superior to belief
propagation algorithms using only the syndrome in the feedback procedure for
all cases of the depolarizing channel. Our algorithm does not increase the
measurement overhead compared to the previous method, as the extra information
comes for free from the requisite stabilizer measurements.Comment: 10 pages, 11 figures, Second version, To be appeared in IEEE
Transactions on Information Theor
An Iteratively Decodable Tensor Product Code with Application to Data Storage
The error pattern correcting code (EPCC) can be constructed to provide a
syndrome decoding table targeting the dominant error events of an inter-symbol
interference channel at the output of the Viterbi detector. For the size of the
syndrome table to be manageable and the list of possible error events to be
reasonable in size, the codeword length of EPCC needs to be short enough.
However, the rate of such a short length code will be too low for hard drive
applications. To accommodate the required large redundancy, it is possible to
record only a highly compressed function of the parity bits of EPCC's tensor
product with a symbol correcting code. In this paper, we show that the proposed
tensor error-pattern correcting code (T-EPCC) is linear time encodable and also
devise a low-complexity soft iterative decoding algorithm for EPCC's tensor
product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that
T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a
1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB
T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same
decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor
Product Code with Application to Data Storage
Iterative decoding for MIMO channels via modified sphere decoding
In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiantenna systems employing space-time codes, however, it is not clear what is the best way to obtain the soft information required of the iterative scheme with low complexity. In this paper, we propose a modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence. The new algorithm solves a nonlinear integer least squares problem and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity. Performance of the algorithm, combined with convolutional, turbo, and low-density parity check codes, is demonstrated on several multiantenna channels. The results for systems that employ space-time modulation schemes seem to indicate that the best performing schemes are those that support the highest mutual information between the transmitted and received signals, rather than the best diversity gain
Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient
technique to obtain high diversity and coding gain on a block-fading MIMO
channel. Its maximum-likelihood (ML) performance is computed under ideal
interleaving conditions, which enables a global optimization taking into
account channel coding. Thanks to a diversity upperbound derived from the
Singleton bound, an appropriate choice of the time dimension of the space-time
coding is possible, which maximizes diversity while minimizing complexity.
Based on the analysis, an optimized interleaver and a set of linear precoders,
called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed
precoders have good performance with respect to the state of the art and exist
for any number of transmit antennas and any time dimension. With turbo codes,
they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January
2006 - First review: June 200
Rewriting Flash Memories by Message Passing
This paper constructs WOM codes that combine rewriting and error correction
for mitigating the reliability and the endurance problems in flash memory. We
consider a rewriting model that is of practical interest to flash applications
where only the second write uses WOM codes. Our WOM code construction is based
on binary erasure quantization with LDGM codes, where the rewriting uses
message passing and has potential to share the efficient hardware
implementations with LDPC codes in practice. We show that the coding scheme
achieves the capacity of the rewriting model. Extensive simulations show that
the rewriting performance of our scheme compares favorably with that of polar
WOM code in the rate region where high rewriting success probability is
desired. We further augment our coding schemes with error correction
capability. By drawing a connection to the conjugate code pairs studied in the
context of quantum error correction, we develop a general framework for
constructing error-correction WOM codes. Under this framework, we give an
explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201
Iterative channel equalization, channel decoding and source decoding
The performance of soft source decoding is evaluated over dispersive AWGN channels. By employing source codes having error-correcting capabilities, such as Reversible Variable-Length Codes (RVLCs) and Variable-Length Error-Correcting (VLEC) codes, the softin/soft-out (SISO) source decoder benefits from exchanging information with the MAP equalizer, and effectively eliminates the inter-symbol interference (ISI) after a few iterations. It was also found that the soft source decoder is capable of significantly improving the attainable performance of the turbo receiver provided that channel equalization, channel decoding and source decoding are carried out jointly and iteratively. At SER = 10-4, the performance of this three-component turbo receiver is about 2 dB better in comparison to the benchmark scheme carrying out channel equalization and channel decoding jointly, but source decoding separately. At this SER value, the performance of the proposed scheme is about 1 dB worse than that of the ½-rate convolutional coded non-dispersive AWGN channel.<br/
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
Self-concatenated code design and its application in power-efficient cooperative communications
In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions
- …