9,552 research outputs found
Integer-Forcing Source Coding
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for
decoding multiple integer linear combinations from the output of a Gaussian
multiple-input multiple-output channel. This work applies the IF approach to
arrive at a new low-complexity scheme, IF source coding, for distributed lossy
compression of correlated Gaussian sources under a minimum mean squared error
distortion measure. All encoders use the same nested lattice codebook. Each
encoder quantizes its observation using the fine lattice as a quantizer and
reduces the result modulo the coarse lattice, which plays the role of binning.
Rather than directly recovering the individual quantized signals, the decoder
first recovers a full-rank set of judiciously chosen integer linear
combinations of the quantized signals, and then inverts it. In general, the
linear combinations have smaller average powers than the original signals. This
allows to increase the density of the coarse lattice, which in turn translates
to smaller compression rates. We also propose and analyze a one-shot version of
IF source coding, that is simple enough to potentially lead to a new design
principle for analog-to-digital converters that can exploit spatial
correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor
Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
Quantum convolutional codes, like their classical counterparts, promise to
offer higher error correction performance than block codes of equivalent
encoding complexity, and are expected to find important applications in
reliable quantum communication where a continuous stream of qubits is
transmitted. Grassl and Roetteler devised an algorithm to encode a quantum
convolutional code with a "pearl-necklace encoder." Despite their theoretical
significance as a neat way of representing quantum convolutional codes, they
are not well-suited to practical realization. In fact, there is no
straightforward way to implement any given pearl-necklace structure. This paper
closes the gap between theoretical representation and practical implementation.
In our previous work, we presented an efficient algorithm for finding a
minimal-memory realization of a pearl-necklace encoder for
Calderbank-Shor-Steane (CSS) convolutional codes. This work extends our
previous work and presents an algorithm for turning a pearl-necklace encoder
for a general (non-CSS) quantum convolutional code into a realizable quantum
convolutional encoder. We show that a minimal-memory realization depends on the
commutativity relations between the gate strings in the pearl-necklace encoder.
We find a realization by means of a weighted graph which details the
non-commutative paths through the pearl-necklace. The weight of the longest
path in this graph is equal to the minimal amount of memory needed to implement
the encoder. The algorithm has a polynomial-time complexity in the number of
gate strings in the pearl-necklace encoder.Comment: 16 pages, 5 figures; extends paper arXiv:1004.5179v
On vocabulary size of grammar-based codes
We discuss inequalities holding between the vocabulary size, i.e., the number
of distinct nonterminal symbols in a grammar-based compression for a string,
and the excess length of the respective universal code, i.e., the code-based
analog of algorithmic mutual information. The aim is to strengthen inequalities
which were discussed in a weaker form in linguistics but shed some light on
redundancy of efficiently computable codes. The main contribution of the paper
is a construction of universal grammar-based codes for which the excess lengths
can be bounded easily.Comment: 5 pages, accepted to ISIT 2007 and correcte
Constructions of Quantum Convolutional Codes
We address the problems of constructing quantum convolutional codes (QCCs)
and of encoding them. The first construction is a CSS-type construction which
allows us to find QCCs of rate 2/4. The second construction yields a quantum
convolutional code by applying a product code construction to an arbitrary
classical convolutional code and an arbitrary quantum block code. We show that
the resulting codes have highly structured and efficient encoders. Furthermore,
we show that the resulting quantum circuits have finite depth, independent of
the lengths of the input stream, and show that this depth is polynomial in the
degree and frame size of the code.Comment: 5 pages, to appear in the Proceedings of the 2007 IEEE International
Symposium on Information Theor
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