3,421 research outputs found
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
Achievable Information Rates for Coded Modulation with Hard Decision Decoding for Coherent Fiber-Optic Systems
We analyze the achievable information rates (AIRs) for coded modulation
schemes with QAM constellations with both bit-wise and symbol-wise decoders,
corresponding to the case where a binary code is used in combination with a
higher-order modulation using the bit-interleaved coded modulation (BICM)
paradigm and to the case where a nonbinary code over a field matched to the
constellation size is used, respectively. In particular, we consider hard
decision decoding, which is the preferable option for fiber-optic communication
systems where decoding complexity is a concern. Recently, Liga \emph{et al.}
analyzed the AIRs for bit-wise and symbol-wise decoders considering what the
authors called \emph{hard decision decoder} which, however, exploits \emph{soft
information} of the transition probabilities of discrete-input discrete-output
channel resulting from the hard detection. As such, the complexity of the
decoder is essentially the same as the complexity of a soft decision decoder.
In this paper, we analyze instead the AIRs for the standard hard decision
decoder, commonly used in practice, where the decoding is based on the Hamming
distance metric. We show that if standard hard decision decoding is used,
bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As
a result, contrary to the conclusion by Liga \emph{et al.}, binary decoders
together with the BICM paradigm are preferable for spectrally-efficient
fiber-optic systems. We also design binary and nonbinary staircase codes and
show that, in agreement with the AIRs, binary codes yield better performance.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201
Coordinated design of coding and modulation systems
The joint optimization of the coding and modulation systems employed in telemetry systems was investigated. Emphasis was placed on formulating inner and outer coding standards used by the Goddard Spaceflight Center. Convolutional codes were found that are nearly optimum for use with Viterbi decoding in the inner coding of concatenated coding systems. A convolutional code, the unit-memory code, was discovered and is ideal for inner system usage because of its byte-oriented structure. Simulations of sequential decoding on the deep-space channel were carried out to compare directly various convolutional codes that are proposed for use in deep-space systems
Feedback Communication Systems with Limitations on Incremental Redundancy
This paper explores feedback systems using incremental redundancy (IR) with
noiseless transmitter confirmation (NTC). For IR-NTC systems based on {\em
finite-length} codes (with blocklength ) and decoding attempts only at {\em
certain specified decoding times}, this paper presents the asymptotic expansion
achieved by random coding, provides rate-compatible sphere-packing (RCSP)
performance approximations, and presents simulation results of tail-biting
convolutional codes.
The information-theoretic analysis shows that values of relatively close
to the expected latency yield the same random-coding achievability expansion as
with . However, the penalty introduced in the expansion by limiting
decoding times is linear in the interval between decoding times. For binary
symmetric channels, the RCSP approximation provides an efficiently-computed
approximation of performance that shows excellent agreement with a family of
rate-compatible, tail-biting convolutional codes in the short-latency regime.
For the additive white Gaussian noise channel, bounded-distance decoding
simplifies the computation of the marginal RCSP approximation and produces
similar results as analysis based on maximum-likelihood decoding for latencies
greater than 200. The efficiency of the marginal RCSP approximation facilitates
optimization of the lengths of incremental transmissions when the number of
incremental transmissions is constrained to be small or the length of the
incremental transmissions is constrained to be uniform after the first
transmission. Finally, an RCSP-based decoding error trajectory is introduced
that provides target error rates for the design of rate-compatible code
families for use in feedback communication systems.Comment: 23 pages, 15 figure
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