88,001 research outputs found
Combining the Burrows-Wheeler Transform and RCM-LDGM Codes for the Transmission of Sources with Memory at High Spectral Efficiencies
In this paper, we look at the problem of implementing high-throughput Joint SourceChannel (JSC) coding schemes for the transmission of binary sources with memory over AWGN channels. The sources are modeled either by a Markov chain (MC) or a hidden Markov model (HMM). We propose a coding scheme based on the Burrows-Wheeler Transform (BWT) and the parallel concatenation of Rate-Compatible Modulation and Low-Density Generator Matrix (RCM-LDGM) codes. The proposed scheme uses the BWT to convert the original source with memory into a set of independent non-uniform Discrete Memoryless (DMS) binary sources, which are then separately encoded, with optimal rates, using RCM-LDGM codes
Polar Coding for Secret-Key Generation
Practical implementations of secret-key generation are often based on
sequential strategies, which handle reliability and secrecy in two successive
steps, called reconciliation and privacy amplification. In this paper, we
propose an alternative approach based on polar codes that jointly deals with
reliability and secrecy. Specifically, we propose secret-key capacity-achieving
polar coding schemes for the following models: (i) the degraded binary
memoryless source (DBMS) model with rate-unlimited public communication, (ii)
the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m
broadcast model and (iv) the Markov tree model with uniform marginals. For
models (i) and (ii) our coding schemes remain valid for non-degraded sources,
although they may not achieve the secret-key capacity. For models (i), (ii) and
(iii), our schemes rely on pre-shared secret seed of negligible rate; however,
we provide special cases of these models for which no seed is required.
Finally, we show an application of our results to secrecy and privacy for
biometric systems. We thus provide the first examples of low-complexity
secret-key capacity-achieving schemes that are able to handle vector
quantization for model (ii), or multiterminal communication for models (iii)
and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information
Theory; parts of the results were presented at the 2013 IEEE Information
Theory Worksho
Scaling Exponent and Moderate Deviations Asymptotics of Polar Codes for the AWGN Channel
This paper investigates polar codes for the additive white Gaussian noise
(AWGN) channel. The scaling exponent of polar codes for a memoryless
channel with capacity characterizes the closest gap
between the capacity and non-asymptotic achievable rates in the following way:
For a fixed , the gap between the capacity
and the maximum non-asymptotic rate achieved by a length- polar code
with average error probability scales as , i.e.,
.
It is well known that the scaling exponent for any binary-input
memoryless channel (BMC) with is bounded above by ,
which was shown by an explicit construction of polar codes. Our main result
shows that remains to be a valid upper bound on the scaling exponent
for the AWGN channel. Our proof technique involves the following two ideas: (i)
The capacity of the AWGN channel can be achieved within a gap of
by using an input alphabet consisting of
constellations and restricting the input distribution to be uniform; (ii) The
capacity of a multiple access channel (MAC) with an input alphabet consisting
of constellations can be achieved within a gap of by
using a superposition of binary-input polar codes. In addition, we
investigate the performance of polar codes in the moderate deviations regime
where both the gap to capacity and the error probability vanish as grows.
An explicit construction of polar codes is proposed to obey a certain tradeoff
between the gap to capacity and the decay rate of the error probability for the
AWGN channel.Comment: 24 page
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