10,166 research outputs found
Efficient Termination of Spatially-Coupled Codes
Spatially-coupled low-density parity-check codes attract much attention due
to their capacity-achieving performance and a memory-efficient sliding-window
decoding algorithm. On the other hand, the encoder needs to solve large linear
equations to terminate the encoding process. In this paper, we propose modified
spatially-coupled codes. The modified (\dl,\dr,L) codes have less rate-loss,
i.e., higher coding rate, and have the same threshold as (\dl,\dr,L) codes
and are efficiently terminable by using an accumulator
Nonbinary Spatially-Coupled LDPC Codes on the Binary Erasure Channel
We analyze the asymptotic performance of nonbinary spatially-coupled
low-density parity-check (SC-LDPC) codes built on the general linear group,
when the transmission takes place over the binary erasure channel. We propose
an efficient method to derive an upper bound to the maximum a posteriori
probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP
performance of regular LDPC codes improves with the alphabet size. We then
consider nonbinary SC-LDPC codes. We show that the same threshold saturation
effect experienced by binary SC-LDPC codes occurs for the nonbinary codes,
hence we conjecture that the BP threshold for large termination length
approaches the MAP threshold of the underlying regular ensemble.Comment: Submitted to IEEE International Conference on Communications 201
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
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
Optimized Bit Mappings for Spatially Coupled LDPC Codes over Parallel Binary Erasure Channels
In many practical communication systems, one binary encoder/decoder pair is
used to communicate over a set of parallel channels. Examples of this setup
include multi-carrier transmission, rate-compatible puncturing of turbo-like
codes, and bit-interleaved coded modulation (BICM). A bit mapper is commonly
employed to determine how the coded bits are allocated to the channels. In this
paper, we study spatially coupled low-density parity check codes over parallel
channels and optimize the bit mapper using BICM as the driving example. For
simplicity, the parallel bit channels that arise in BICM are replaced by
independent binary erasure channels (BECs). For two parallel BECs modeled
according to a 4-PAM constellation labeled by the binary reflected Gray code,
the optimization results show that the decoding threshold can be improved over
a uniform random bit mapper, or, alternatively, the spatial chain length of the
code can be reduced for a given gap to capacity. It is also shown that for
rate-loss free, circular (tail-biting) ensembles, a decoding wave effect can be
initiated using only an optimized bit mapper
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