1,087 research outputs found
Fourier Domain Decoding Algorithm of Non-Binary LDPC codes for Parallel Implementation
For decoding non-binary low-density parity check (LDPC) codes,
logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing
quantization effects of SP algorithm in conjunction with FFT. Since FFT is not
applicable in the logarithm domain, the computations required at check nodes in
the Log-SP algorithms are computationally intensive. What is worth, check nodes
usually have higher degree than variable nodes. As a result, most of the time
for decoding is used for check node computations, which leads to a bottleneck
effect. In this paper, we propose a Log-SP algorithm in the Fourier domain.
With this algorithm, the role of variable nodes and check nodes are switched.
The intensive computations are spread over lower-degree variable nodes, which
can be efficiently calculated in parallel. Furthermore, we develop a fast
calculation method for the estimated bits and syndromes in the Fourier domain.Comment: To appear in IEICE Trans. Fundamentals, vol.E93-A, no.11 November
201
Analysis and Design of Binary Message-Passing Decoders
Binary message-passing decoders for low-density parity-check (LDPC) codes are
studied by using extrinsic information transfer (EXIT) charts. The channel
delivers hard or soft decisions and the variable node decoder performs all
computations in the L-value domain. A hard decision channel results in the
well-know Gallager B algorithm, and increasing the output alphabet from hard
decisions to two bits yields a gain of more than 1.0 dB in the required signal
to noise ratio when using optimized codes. The code optimization requires
adapting the mixing property of EXIT functions to the case of binary
message-passing decoders. Finally, it is shown that errors on cycles consisting
only of degree two and three variable nodes cannot be corrected and a necessary
and sufficient condition for the existence of a cycle-free subgraph is derived.Comment: 8 pages, 6 figures, submitted to the IEEE Transactions on
Communication
Finite Length Analysis of LDPC Codes
In this paper, we study the performance of finite-length LDPC codes in the
waterfall region. We propose an algorithm to predict the error performance of
finite-length LDPC codes over various binary memoryless channels. Through
numerical results, we find that our technique gives better performance
prediction compared to existing techniques.Comment: Submitted to WCNC 201
Multilevel Decoders Surpassing Belief Propagation on the Binary Symmetric Channel
In this paper, we propose a new class of quantized message-passing decoders
for LDPC codes over the BSC. The messages take values (or levels) from a finite
set. The update rules do not mimic belief propagation but instead are derived
using the knowledge of trapping sets. We show that the update rules can be
derived to correct certain error patterns that are uncorrectable by algorithms
such as BP and min-sum. In some cases even with a small message set, these
decoders can guarantee correction of a higher number of errors than BP and
min-sum. We provide particularly good 3-bit decoders for 3-left-regular LDPC
codes. They significantly outperform the BP and min-sum decoders, but more
importantly, they achieve this at only a fraction of the complexity of the BP
and min-sum decoders.Comment: 5 pages, in Proc. of 2010 IEEE International Symposium on Information
Theory (ISIT
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