7,573 research outputs found
Pseudocodewords of Tanner graphs
This papers presents a detailed analysis of pseudocodewords of Tanner graphs.
Pseudocodewords arising on the iterative decoder's computation tree are
distinguished from pseudocodewords arising on finite degree lifts. Lower bounds
on the minimum pseudocodeword weight are presented for the BEC, BSC, and AWGN
channel. Some structural properties of pseudocodewords are examined, and
pseudocodewords and graph properties that are potentially problematic with
min-sum iterative decoding are identified. An upper bound on the minimum degree
lift needed to realize a particular irreducible lift-realizable pseudocodeword
is given in terms of its maximal component, and it is shown that all
irreducible lift-realizable pseudocodewords have components upper bounded by a
finite value that is dependent on the graph structure. Examples and
different Tanner graph representations of individual codes are examined and the
resulting pseudocodeword distributions and iterative decoding performances are
analyzed. The results obtained provide some insights in relating the structure
of the Tanner graph to the pseudocodeword distribution and suggest ways of
designing Tanner graphs with good minimum pseudocodeword weight.Comment: To appear in Nov. 2007 issue of IEEE Transactions on Information
Theor
List decoding - random coding exponents and expurgated exponents
Some new results are derived concerning random coding error exponents and
expurgated exponents for list decoding with a deterministic list size . Two
asymptotic regimes are considered, the fixed list-size regime, where is
fixed independently of the block length , and the exponential list-size,
where grows exponentially with . We first derive a general upper bound
on the list-decoding average error probability, which is suitable for both
regimes. This bound leads to more specific bounds in the two regimes. In the
fixed list-size regime, the bound is related to known bounds and we establish
its exponential tightness. In the exponential list-size regime, we establish
the achievability of the well known sphere packing lower bound. Relations to
guessing exponents are also provided. An immediate byproduct of our analysis in
both regimes is the universality of the maximum mutual information (MMI) list
decoder in the error exponent sense. Finally, we consider expurgated bounds at
low rates, both using Gallager's approach and the Csisz\'ar-K\"orner-Marton
approach, which is, in general better (at least for ). The latter
expurgated bound, which involves the notion of {\it multi-information}, is also
modified to apply to continuous alphabet channels, and in particular, to the
Gaussian memoryless channel, where the expression of the expurgated bound
becomes quite explicit.Comment: 28 pages; submitted to the IEEE Trans. on Information Theor
Successive Integer-Forcing and its Sum-Rate Optimality
Integer-forcing receivers generalize traditional linear receivers for the
multiple-input multiple-output channel by decoding integer-linear combinations
of the transmitted streams, rather then the streams themselves. Previous works
have shown that the additional degree of freedom in choosing the integer
coefficients enables this receiver to approach the performance of
maximum-likelihood decoding in various scenarios. Nonetheless, even for the
optimal choice of integer coefficients, the additive noise at the equalizer's
output is still correlated. In this work we study a variant of integer-forcing,
termed successive integer-forcing, that exploits these noise correlations to
improve performance. This scheme is the integer-forcing counterpart of
successive interference cancellation for traditional linear receivers.
Similarly to the latter, we show that successive integer-forcing is capacity
achieving when it is possible to optimize the rate allocation to the different
streams. In comparison to standard successive interference cancellation
receivers, the successive integer-forcing receiver offers more possibilities
for capacity achieving rate tuples, and in particular, ones that are more
balanced.Comment: A shorter version was submitted to the 51st Allerton Conferenc
Communication for Generating Correlation: A Unifying Survey
The task of manipulating correlated random variables in a distributed setting
has received attention in the fields of both Information Theory and Computer
Science. Often shared correlations can be converted, using a little amount of
communication, into perfectly shared uniform random variables. Such perfect
shared randomness, in turn, enables the solutions of many tasks. Even the
reverse conversion of perfectly shared uniform randomness into variables with a
desired form of correlation turns out to be insightful and technically useful.
In this survey article, we describe progress-to-date on such problems and lay
out pertinent measures, achievability results, limits of performance, and point
to new directions.Comment: A review article to appear in IEEE Transactions on Information Theor
An Achievable rate region for the user interference channel based on coset codes
We consider the problem of communication over a three user discrete
memoryless interference channel (IC). The current known coding techniques
for communicating over an arbitrary IC are based on message splitting,
superposition coding and binning using independent and identically distributed
(iid) random codebooks. In this work, we propose a new ensemble of codes -
partitioned coset codes (PCC) - that possess an appropriate mix of empirical
and algebraic closure properties. We develop coding techniques that exploit
algebraic closure property of PCC to enable efficient communication over
IC. We analyze the performance of the proposed coding technique to derive
an achievable rate region for the general discrete IC. Additive and
non-additive examples are identified for which the derived achievable rate
region is the capacity, and moreover, strictly larger than current known
largest achievable rate regions based on iid random codebooks.Comment: New examples for which coset codes yield strictly larger achievable
rate regions in comparison to those achievable using unstructured iid codes
are identified. The issue of aligning interference at multiple receiver
terminals addressed through an example. Revised submission to IEEE Trans. on
Information Theor
Outage Behavior of Discrete Memoryless Channels (DMCs) Under Channel Estimation Errors
Communication systems are usually designed by assuming perfect channel state
information (CSI). However, in many practical scenarios, only a noisy estimate
of the channel is available, which may strongly differ from the true channel.
This imperfect CSI scenario is addressed by introducing the notion of
estimation-induced outage (EIO) capacity. We derive a single-letter
characterization of the maximal EIO rate and prove an associated coding theorem
and its strong converse for discrete memoryless channels (DMCs). The
transmitter and the receiver rely on the channel estimate and the statistics of
the estimate to construct codes that guarantee reliable communication with a
certain outage probability. This ensures that in the non-outage case the
transmission meets the target rate with small error probability, irrespective
of the quality of the channel estimate. Applications of the EIO capacity to a
single-antenna (non-ergodic) Ricean fading channel are considered. The EIO
capacity for this case is compared to the EIO rates of a communication system
in which the receiver decodes by using a mismatched ML decoder. The effects of
rate-limited feedback to provide the transmitter with quantized CSI are also
investigated.Comment: To appear in IEEE Transactions on Information Theory, Sep. 200
Cross-layer Optimization for Ultra-reliable and Low-latency Radio Access Networks
In this paper, we propose a framework for cross-layer optimization to ensure
ultra-high reliability and ultra-low latency in radio access networks, where
both transmission delay and queueing delay are considered. With short
transmission time, the blocklength of channel codes is finite, and the Shannon
Capacity cannot be used to characterize the maximal achievable rate with given
transmission error probability. With randomly arrived packets, some packets may
violate the queueing delay. Moreover, since the queueing delay is shorter than
the channel coherence time in typical scenarios, the required transmit power to
guarantee the queueing delay and transmission error probability will become
unbounded even with spatial diversity. To ensure the required
quality-of-service (QoS) with finite transmit power, a proactive packet
dropping mechanism is introduced. Then, the overall packet loss probability
includes transmission error probability, queueing delay violation probability,
and packet dropping probability. We optimize the packet dropping policy, power
allocation policy, and bandwidth allocation policy to minimize the transmit
power under the QoS constraint. The optimal solution is obtained, which depends
on both channel and queue state information. Simulation and numerical results
validate our analysis, and show that setting packet loss probabilities equal is
a near optimal solution.Comment: The manuscript has been accepted by IEEE transactions on wireless
communication
Symmetrised Characterisation of Noisy Quantum Processes
A major goal of developing high-precision control of many-body quantum
systems is to realise their potential as quantum computers. Probably the most
significant obstacle in this direction is the problem of "decoherence": the
extreme fragility of quantum systems to environmental noise and other control
limitations. The theory of fault-tolerant quantum error correction has shown
that quantum computation is possible even in the presence of decoherence
provided that the noise affecting the quantum system satisfies certain
well-defined theoretical conditions. However, existing methods for noise
characterisation have become intractable already for the systems that are
controlled in today's labs. In this paper we introduce a technique based on
symmetrisation that enables direct experimental characterisation of key
properties of the decoherence affecting a multi-body quantum system. Our method
reduces the number of experiments required by existing methods from exponential
to polynomial in the number of subsystems. We demonstrate the application of
this technique to the optimisation of control over nuclear spins in the solid
state.Comment: About 12 pages, 5 figure
Joint Source-Channel Coding with Time-Varying Channel and Side-Information
Transmission of a Gaussian source over a time-varying Gaussian channel is
studied in the presence of time-varying correlated side information at the
receiver. A block fading model is considered for both the channel and the side
information, whose states are assumed to be known only at the receiver. The
optimality of separate source and channel coding in terms of average end-to-end
distortion is shown when the channel is static while the side information state
follows a discrete or a continuous and quasiconcave distribution. When both the
channel and side information states are time-varying, separate source and
channel coding is suboptimal in general. A partially informed encoder lower
bound is studied by providing the channel state information to the encoder.
Several achievable transmission schemes are proposed based on uncoded
transmission, separate source and channel coding, joint decoding as well as
hybrid digital-analog transmission. Uncoded transmission is shown to be optimal
for a class of continuous and quasiconcave side information state
distributions, while the channel gain may have an arbitrary distribution. To
the best of our knowledge, this is the first example in which the uncoded
transmission achieves the optimal performance thanks to the time-varying nature
of the states, while it is suboptimal in the static version of the same
problem. Then, the optimal \emph{distortion exponent}, that quantifies the
exponential decay rate of the expected distortion in the high SNR regime, is
characterized for Nakagami distributed channel and side information states, and
it is shown to be achieved by hybrid digital-analog and joint decoding schemes
in certain cases, illustrating the suboptimality of pure digital or analog
transmission in general.Comment: Submitted to IEEE Transactions on Information Theor
Secure Diversity-Multiplexing Tradeoff of Zero-Forcing Transmit Scheme at Finite-SNR
In this paper, we address the finite Signal-to-Noise Ratio (SNR)
Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output
(MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends
to send the secret information in the orthogonal space of the eavesdropper
channel, is used. First, we introduce the secrecy multiplexing gain at
finite-SNR that generalizes the definition at high-SNR. Then, we provide upper
and lower bounds on the outage probability under secrecy constraint, from which
secrecy diversity gain estimates of ZF are derived. Through asymptotic
analysis, we show that the upper bound underestimates the secrecy diversity
gain, whereas the lower bound is tight at high-SNR, and thus its related
diversity gain estimate is equal to the actual asymptotic secrecy diversity
gain of the MIMO wiretap channel.Comment: 10 pages and 5 figures. To appear IEEE Transactions on Communications
201
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