133,983 research outputs found
Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security
We present information-theoretic definitions and results for analyzing
symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when
perfect secrecy is not attained. We adopt two lines of analysis, one based on
lossless source coding, and another akin to rate-distortion theory. We start by
presenting a new information-theoretic metric for security, called symbol
secrecy, and derive associated fundamental bounds. We then introduce
list-source codes (LSCs), which are a general framework for mapping a key
length (entropy) to a list size that an eavesdropper has to resolve in order to
recover a secret message. We provide explicit constructions of LSCs, and
demonstrate that, when the source is uniformly distributed, the highest level
of symbol secrecy for a fixed key length can be achieved through a construction
based on minimum-distance separable (MDS) codes. Using an analysis related to
rate-distortion theory, we then show how symbol secrecy can be used to
determine the probability that an eavesdropper correctly reconstructs functions
of the original plaintext. We illustrate how these bounds can be applied to
characterize security properties of symmetric-key encryption schemes, and, in
particular, extend security claims based on symbol secrecy to a functional
setting.Comment: Submitted to IEEE Transactions on Information Theor
LDPC Code Design for the BPSK-constrained Gaussian Wiretap Channel
A coding scheme based on irregular low-density parity-check (LDPC) codes is
proposed to send secret messages from a source over the Gaussian wiretap
channel to a destination in the presence of a wiretapper, with the restriction
that the source can send only binary phase-shift keyed (BPSK) symbols. The
secrecy performance of the proposed coding scheme is measured by the secret
message rate through the wiretap channel as well as the equivocation rate about
the message at the wiretapper. A code search procedure is suggested to obtain
irregular LDPC codes that achieve good secrecy performance in such context.Comment: submitted to IEEE GLOBECOM 2011 - Communication Theory Symposiu
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
A unary error correction code for the near-capacity joint source and channel coding of symbol values from an infinite set
A novel Joint Source and Channel Code (JSCC) is proposed, which we refer to as the Unary Error Correction (UEC) code. Unlike existing JSCCs, our UEC facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality. Conventionally, these symbols are conveyed using Separate Source and Channel Codes (SSCCs), but we demonstrate that the residual redundancy that is retained following source coding results in a capacity loss, which is found to have a value of 1.11 dB in a particular practical scenario. By contrast, the proposed UEC code can eliminate this capacity loss, or reduce it to an infinitesimally small value. Furthermore, the UEC code has only a moderate complexity, facilitating its employment in practical low-complexity applications
Bilayer Protograph Codes for Half-Duplex Relay Channels
Despite encouraging advances in the design of relay codes, several important
challenges remain. Many of the existing LDPC relay codes are tightly optimized
for fixed channel conditions and not easily adapted without extensive
re-optimization of the code. Some have high encoding complexity and some need
long block lengths to approach capacity. This paper presents a high-performance
protograph-based LDPC coding scheme for the half-duplex relay channel that
addresses simultaneously several important issues: structured coding that
permits easy design, low encoding complexity, embedded structure for convenient
adaptation to various channel conditions, and performance close to capacity
with a reasonable block length. The application of the coding structure to
multi-relay networks is demonstrated. Finally, a simple new methodology for
evaluating the end-to-end error performance of relay coding systems is
developed and used to highlight the performance of the proposed codes.Comment: Accepted in IEEE Trans. Wireless Com
Source coding with escort distributions and Renyi entropy bounds
We discuss the interest of escort distributions and R\'enyi entropy in the
context of source coding. We first recall a source coding theorem by Campbell
relating a generalized measure of length to the R\'enyi-Tsallis entropy. We
show that the associated optimal codes can be obtained using considerations on
escort-distributions. We propose a new family of measure of length involving
escort-distributions and we show that these generalized lengths are also
bounded below by the R\'enyi entropy. Furthermore, we obtain that the standard
Shannon codes lengths are optimum for the new generalized lengths measures,
whatever the entropic index. Finally, we show that there exists in this setting
an interplay between standard and escort distributions
Optimal coding and the origins of Zipfian laws
The problem of compression in standard information theory consists of
assigning codes as short as possible to numbers. Here we consider the problem
of optimal coding -- under an arbitrary coding scheme -- and show that it
predicts Zipf's law of abbreviation, namely a tendency in natural languages for
more frequent words to be shorter. We apply this result to investigate optimal
coding also under so-called non-singular coding, a scheme where unique
segmentation is not warranted but codes stand for a distinct number. Optimal
non-singular coding predicts that the length of a word should grow
approximately as the logarithm of its frequency rank, which is again consistent
with Zipf's law of abbreviation. Optimal non-singular coding in combination
with the maximum entropy principle also predicts Zipf's rank-frequency
distribution. Furthermore, our findings on optimal non-singular coding
challenge common beliefs about random typing. It turns out that random typing
is in fact an optimal coding process, in stark contrast with the common
assumption that it is detached from cost cutting considerations. Finally, we
discuss the implications of optimal coding for the construction of a compact
theory of Zipfian laws and other linguistic laws.Comment: in press in the Journal of Quantitative Linguistics; definition of
concordant pair corrected, proofs polished, references update
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