21,983 research outputs found
Stall Pattern Avoidance in Polynomial Product Codes
Product codes are a concatenated error-correction scheme that has been often
considered for applications requiring very low bit-error rates, which demand
that the error floor be decreased as much as possible. In this work, we
consider product codes constructed from polynomial algebraic codes, and propose
a novel low-complexity post-processing technique that is able to improve the
error-correction performance by orders of magnitude. We provide lower bounds
for the error rate achievable under post processing, and present simulation
results indicating that these bounds are tight.Comment: 4 pages, 2 figures, GlobalSiP 201
Improved Decoding of Staircase Codes: The Soft-aided Bit-marking (SABM) Algorithm
Staircase codes (SCCs) are typically decoded using iterative bounded-distance
decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is
proposed, which partially uses soft information from the channel. The proposed
algorithm is based on marking certain number of highly reliable and highly
unreliable bits. These marked bits are used to improve the
miscorrection-detection capability of the SCC decoder and the error-correcting
capability of BDD. For SCCs with -error-correcting
Bose-Chaudhuri-Hocquenghem component codes, our algorithm improves upon
standard SCC decoding by up to ~dB at a bit-error rate (BER) of
. The proposed algorithm is shown to achieve almost half of the gain
achievable by an idealized decoder with this structure. A complexity analysis
based on the number of additional calls to the component BDD decoder shows that
the relative complexity increase is only around at a BER of .
This additional complexity is shown to decrease as the channel quality
improves. Our algorithm is also extended (with minor modifications) to product
codes. The simulation results show that in this case, the algorithm offers
gains of up to ~dB at a BER of .Comment: 10 pages, 12 figure
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
Density Evolution for Deterministic Generalized Product Codes with Higher-Order Modulation
Generalized product codes (GPCs) are extensions of product codes (PCs) where
coded bits are protected by two component codes but not necessarily arranged in
a rectangular array. It has recently been shown that there exists a large class
of deterministic GPCs (including, e.g., irregular PCs, half-product codes,
staircase codes, and certain braided codes) for which the asymptotic
performance under iterative bounded-distance decoding over the binary erasure
channel (BEC) can be rigorously characterized in terms of a density evolution
analysis. In this paper, the analysis is extended to the case where
transmission takes place over parallel BECs with different erasure
probabilities. We use this model to predict the code performance in a coded
modulation setup with higher-order signal constellations. We also discuss the
design of the bit mapper that determines the allocation of the coded bits to
the modulation bits of the signal constellation.Comment: invited and accepted paper for the special session "Recent Advances
in Coding for Higher Order Modulation" at the International Symposium on
Turbo Codes & Iterative Information Processing, Brest, France, 201
Analysis and Design of Tuned Turbo Codes
It has been widely observed that there exists a fundamental trade-off between
the minimum (Hamming) distance properties and the iterative decoding
convergence behavior of turbo-like codes. While capacity achieving code
ensembles typically are asymptotically bad in the sense that their minimum
distance does not grow linearly with block length, and they therefore exhibit
an error floor at moderate-to-high signal to noise ratios, asymptotically good
codes usually converge further away from channel capacity. In this paper, we
introduce the concept of tuned turbo codes, a family of asymptotically good
hybrid concatenated code ensembles, where asymptotic minimum distance growth
rates, convergence thresholds, and code rates can be traded-off using two
tuning parameters, {\lambda} and {\mu}. By decreasing {\lambda}, the asymptotic
minimum distance growth rate is reduced in exchange for improved iterative
decoding convergence behavior, while increasing {\lambda} raises the asymptotic
minimum distance growth rate at the expense of worse convergence behavior, and
thus the code performance can be tuned to fit the desired application. By
decreasing {\mu}, a similar tuning behavior can be achieved for higher rate
code ensembles.Comment: Accepted for publication in IEEE Transactions on Information Theor
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