6,612 research outputs found
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
Generalized Stability Condition for Generalized and Doubly-Generalized LDPC Codes
In this paper, the stability condition for low-density parity-check (LDPC)
codes on the binary erasure channel (BEC) is extended to generalized LDPC
(GLDPC) codes and doublygeneralized LDPC (D-GLDPC) codes. It is proved that, in
both cases, the stability condition only involves the component codes with
minimum distance 2. The stability condition for GLDPC codes is always expressed
as an upper bound to the decoding threshold. This is not possible for D-GLDPC
codes, unless all the generalized variable nodes have minimum distance at least
3. Furthermore, a condition called derivative matching is defined in the paper.
This condition is sufficient for a GLDPC or DGLDPC code to achieve the
stability condition with equality. If this condition is satisfied, the
threshold of D-GLDPC codes (whose generalized variable nodes have all minimum
distance at least 3) and GLDPC codes can be expressed in closed form.Comment: 5 pages, 2 figures, to appear in Proc. of IEEE ISIT 200
Compressed sensing using sparse binary measurements: a rateless coding perspective
Compressed Sensing (CS) methods using sparse binary measurement matrices and iterative message-passing re- covery procedures have been recently investigated due to their low computational complexity and excellent performance. Drawing much of inspiration from sparse-graph codes such as Low-Density Parity-Check (LDPC) codes, these studies use analytical tools from modern coding theory to analyze CS solutions. In this paper, we consider and systematically analyze the CS setup inspired by a class of efficient, popular and flexible sparse-graph codes called rateless codes. The proposed rateless CS setup is asymptotically analyzed using tools such as Density Evolution and EXIT charts and fine-tuned using degree distribution optimization techniques
Bounds on the map threshold of iterative decoding systems with erasure noise
Iterative decoding and codes on graphs were first devised by Gallager in 1960, and then rediscovered by Berrou, Glavieux and Thitimajshima in 1993. This technique plays an important role in modern communications, especially in coding theory and practice. In particular, low-density parity-check (LDPC) codes, introduced by Gallager in the 1960s, are the class of codes at the heart of iterative coding. Since these codes are quite general and exhibit good performance under message-passing decoding, they play an important role in communications research today. A thorough analysis of iterative decoding systems and the relationship between maximum a posteriori (MAP) and belief propagation (BP) decoding was initiated by Measson, Montanari, and Urbanke. This analysis is based on density evolution (DE), and extrinsic information transfer (EXIT) functions, introduced by ten Brink. Following their work, this thesis considers the MAP decoding thresholds of three iterative decoding systems. First, irregular repeat-accumulate (IRA) and accumulaterepeataccumulate (ARA) code ensembles are analyzed on the binary erasure channel (BEC). Next, the joint iterative decoding of LDPC codes is studied on the dicode erasure channel (DEC). The DEC is a two-state intersymbol-interference (ISI) channel with erasure noise, and it is the simplest example of an ISI channel with erasure noise. Then, we introduce a slight generalization of the EXIT area theorem and apply the MAP threshold bound for the joint decoder. Both the MAP and BP erasure thresholds are computed and compared with each other. The result quantities the loss due to iterative decoding Some open questions include the tightness of these bounds and the extensions to non-erasure channels
Reconfigurable rateless codes
We propose novel reconfigurable rateless codes, that are capable of not only varying the block length but also adaptively modify their encoding strategy by incrementally adjusting their degree distribution according to the prevalent channel conditions without the availability of the channel state information at the transmitter. In particular, we characterize a reconfigurable ratelesscode designed for the transmission of 9,500 information bits that achieves a performance, which is approximately 1 dB away from the discrete-input continuous-output memoryless channel’s (DCMC) capacity over a diverse range of channel signal-to-noise (SNR) ratios
Improving soft FEC performance for higher-order modulations via optimized bit channel mappings
Soft forward error correction with higher-order modulations is often
implemented in practice via the pragmatic bit-interleaved coded modulation
paradigm, where a single binary code is mapped to a nonbinary modulation. In
this paper, we study the optimization of the mapping of the coded bits to the
modulation bits for a polarization-multiplexed fiber-optical system without
optical inline dispersion compensation. Our focus is on protograph-based
low-density parity-check (LDPC) codes which allow for an efficient hardware
implementation, suitable for high-speed optical communications. The
optimization is applied to the AR4JA protograph family, and further extended to
protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full
field simulations via the split-step Fourier method are used to verify the
analysis. The results show performance gains of up to 0.25 dB, which translate
into a possible extension of the transmission reach by roughly up to 8%,
without significantly increasing the system complexity.Comment: This paper was published in Optics Express and is made available as
an electronic reprint with the permission of OSA. The paper can be found at
the following URL on the OSA website:
http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-1454
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