644 research outputs found
Distance Properties of Short LDPC Codes and their Impact on the BP, ML and Near-ML Decoding Performance
Parameters of LDPC codes, such as minimum distance, stopping distance,
stopping redundancy, girth of the Tanner graph, and their influence on the
frame error rate performance of the BP, ML and near-ML decoding over a BEC and
an AWGN channel are studied. Both random and structured LDPC codes are
considered. In particular, the BP decoding is applied to the code parity-check
matrices with an increasing number of redundant rows, and the convergence of
the performance to that of the ML decoding is analyzed. A comparison of the
simulated BP, ML, and near-ML performance with the improved theoretical bounds
on the error probability based on the exact weight spectrum coefficients and
the exact stopping size spectrum coefficients is presented. It is observed that
decoding performance very close to the ML decoding performance can be achieved
with a relatively small number of redundant rows for some codes, for both the
BEC and the AWGN channels
Update-Efficiency and Local Repairability Limits for Capacity Approaching Codes
Motivated by distributed storage applications, we investigate the degree to
which capacity achieving encodings can be efficiently updated when a single
information bit changes, and the degree to which such encodings can be
efficiently (i.e., locally) repaired when single encoded bit is lost.
Specifically, we first develop conditions under which optimum
error-correction and update-efficiency are possible, and establish that the
number of encoded bits that must change in response to a change in a single
information bit must scale logarithmically in the block-length of the code if
we are to achieve any nontrivial rate with vanishing probability of error over
the binary erasure or binary symmetric channels. Moreover, we show there exist
capacity-achieving codes with this scaling.
With respect to local repairability, we develop tight upper and lower bounds
on the number of remaining encoded bits that are needed to recover a single
lost bit of the encoding. In particular, we show that if the code-rate is
less than the capacity, then for optimal codes, the maximum number
of codeword symbols required to recover one lost symbol must scale as
.
Several variations on---and extensions of---these results are also developed.Comment: Accepted to appear in JSA
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
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