353 research outputs found
Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel
In this paper, we show that Quasi-Cyclic LDPC codes can efficiently
accommodate the hybrid iterative/ML decoding over the binary erasure channel.
We demonstrate that the quasi-cyclic structure of the parity-check matrix can
be advantageously used in order to significantly reduce the complexity of the
ML decoding. This is achieved by a simple row/column permutation that
transforms a QC matrix into a pseudo-band form. Based on this approach, we
propose a class of QC-LDPC codes with almost ideal error correction performance
under the ML decoding, while the required number of row/symbol operations
scales as , where is the number of source symbols.Comment: 6 pages, ISITA1
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
Array Convolutional Low-Density Parity-Check Codes
This paper presents a design technique for obtaining regular time-invariant
low-density parity-check convolutional (RTI-LDPCC) codes with low complexity
and good performance. We start from previous approaches which unwrap a
low-density parity-check (LDPC) block code into an RTI-LDPCC code, and we
obtain a new method to design RTI-LDPCC codes with better performance and
shorter constraint length. Differently from previous techniques, we start the
design from an array LDPC block code. We show that, for codes with high rate, a
performance gain and a reduction in the constraint length are achieved with
respect to previous proposals. Additionally, an increase in the minimum
distance is observed.Comment: 4 pages, 2 figures, accepted for publication in IEEE Communications
Letter
Circulant Arrays on Cyclic Subgroups of Finite Fields: Rank Analysis and Construction of Quasi-Cyclic LDPC Codes
This paper consists of three parts. The first part presents a large class of
new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose
parity-check matrices are constructed based on cyclic subgroups of finite
fields. Experimental results show that the codes constructed perform well over
the binary-input AWGN channel with iterative decoding using the sum-product
algorithm (SPA). The second part analyzes the ranks of the parity-check
matrices of codes constructed based on finite fields with characteristic of 2
and gives combinatorial expressions for these ranks. The third part identifies
a subclass of constructed QC-LDPC codes that have large minimum distances.
Decoding of codes in this subclass with the SPA converges very fast.Comment: 26 pages, 6 figures, submitted to IEEE Transaction on Communication
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