15,909 research outputs found
Coding for Parallel Channels: Gallager Bounds for Binary Linear Codes with Applications to Repeat-Accumulate Codes and Variations
This paper is focused on the performance analysis of binary linear block
codes (or ensembles) whose transmission takes place over independent and
memoryless parallel channels. New upper bounds on the maximum-likelihood (ML)
decoding error probability are derived. These bounds are applied to various
ensembles of turbo-like codes, focusing especially on repeat-accumulate codes
and their recent variations which possess low encoding and decoding complexity
and exhibit remarkable performance under iterative decoding. The framework of
the second version of the Duman and Salehi (DS2) bounds is generalized to the
case of parallel channels, along with the derivation of their optimized tilting
measures. The connection between the generalized DS2 and the 1961 Gallager
bounds, addressed by Divsalar and by Sason and Shamai for a single channel, is
explored in the case of an arbitrary number of independent parallel channels.
The generalization of the DS2 bound for parallel channels enables to re-derive
specific bounds which were originally derived by Liu et al. as special cases of
the Gallager bound. In the asymptotic case where we let the block length tend
to infinity, the new bounds are used to obtain improved inner bounds on the
attainable channel regions under ML decoding. The tightness of the new bounds
for independent parallel channels is exemplified for structured ensembles of
turbo-like codes. The improved bounds with their optimized tilting measures
show, irrespectively of the block length of the codes, an improvement over the
union bound and other previously reported bounds for independent parallel
channels; this improvement is especially pronounced for moderate to large block
lengths.Comment: Submitted to IEEE Trans. on Information Theory, June 2006 (57 pages,
9 figures
Orthogonal Multiple Access with Correlated Sources: Feasible Region and Pragmatic Schemes
In this paper, we consider orthogonal multiple access coding schemes, where
correlated sources are encoded in a distributed fashion and transmitted,
through additive white Gaussian noise (AWGN) channels, to an access point (AP).
At the AP, component decoders, associated with the source encoders, iteratively
exchange soft information by taking into account the source correlation. The
first goal of this paper is to investigate the ultimate achievable performance
limits in terms of a multi-dimensional feasible region in the space of channel
parameters, deriving insights on the impact of the number of sources. The
second goal is the design of pragmatic schemes, where the sources use
"off-the-shelf" channel codes. In order to analyze the performance of given
coding schemes, we propose an extrinsic information transfer (EXIT)-based
approach, which allows to determine the corresponding multi-dimensional
feasible regions. On the basis of the proposed analytical framework, the
performance of pragmatic coded schemes, based on serially concatenated
convolutional codes (SCCCs), is discussed
Throughput-based Design for Polar Coded-Modulation
Typically, forward error correction (FEC) codes are designed based on the
minimization of the error rate for a given code rate. However, for applications
that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive
modulation and coding, the throughput is a more important performance metric
than the error rate. Polar codes, a new class of FEC codes with simple rate
matching, can be optimized efficiently for maximization of the throughput. In
this paper, we aim to design HARQ schemes using multilevel polar
coded-modulation (MLPCM). Thus, we first develop a method to determine a
set-partitioning based bit-to-symbol mapping for high order QAM constellations.
We simplify the LLR estimation of set-partitioned QAM constellations for a
multistage decoder, and we introduce a set of algorithms to design
throughput-maximizing MLPCM for the successive cancellation decoding (SCD).
These codes are specifically useful for non-combining (NC) and Chase-combining
(CC) HARQ protocols. Furthermore, since optimized codes for SCD are not optimal
for SC list decoders (SCLD), we propose a rate matching algorithm to find the
best rate for SCLD while using the polar codes optimized for SCD. The resulting
codes provide throughput close to the capacity with low decoding complexity
when used with NC or CC HARQ
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
Reliable Physical Layer Network Coding
When two or more users in a wireless network transmit simultaneously, their
electromagnetic signals are linearly superimposed on the channel. As a result,
a receiver that is interested in one of these signals sees the others as
unwanted interference. This property of the wireless medium is typically viewed
as a hindrance to reliable communication over a network. However, using a
recently developed coding strategy, interference can in fact be harnessed for
network coding. In a wired network, (linear) network coding refers to each
intermediate node taking its received packets, computing a linear combination
over a finite field, and forwarding the outcome towards the destinations. Then,
given an appropriate set of linear combinations, a destination can solve for
its desired packets. For certain topologies, this strategy can attain
significantly higher throughputs over routing-based strategies. Reliable
physical layer network coding takes this idea one step further: using
judiciously chosen linear error-correcting codes, intermediate nodes in a
wireless network can directly recover linear combinations of the packets from
the observed noisy superpositions of transmitted signals. Starting with some
simple examples, this survey explores the core ideas behind this new technique
and the possibilities it offers for communication over interference-limited
wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the
IEE
Source-Channel Diversity for Parallel Channels
We consider transmitting a source across a pair of independent, non-ergodic
channels with random states (e.g., slow fading channels) so as to minimize the
average distortion. The general problem is unsolved. Hence, we focus on
comparing two commonly used source and channel encoding systems which
correspond to exploiting diversity either at the physical layer through
parallel channel coding or at the application layer through multiple
description source coding.
For on-off channel models, source coding diversity offers better performance.
For channels with a continuous range of reception quality, we show the reverse
is true. Specifically, we introduce a new figure of merit called the distortion
exponent which measures how fast the average distortion decays with SNR. For
continuous-state models such as additive white Gaussian noise channels with
multiplicative Rayleigh fading, optimal channel coding diversity at the
physical layer is more efficient than source coding diversity at the
application layer in that the former achieves a better distortion exponent.
Finally, we consider a third decoding architecture: multiple description
encoding with a joint source-channel decoding. We show that this architecture
achieves the same distortion exponent as systems with optimal channel coding
diversity for continuous-state channels, and maintains the the advantages of
multiple description systems for on-off channels. Thus, the multiple
description system with joint decoding achieves the best performance, from
among the three architectures considered, on both continuous-state and on-off
channels.Comment: 48 pages, 14 figure
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