129,164 research outputs found
Lossy Compression via Sparse Linear Regression: Performance under Minimum-distance Encoding
We study a new class of codes for lossy compression with the squared-error
distortion criterion, designed using the statistical framework of
high-dimensional linear regression. Codewords are linear combinations of
subsets of columns of a design matrix. Called a Sparse Superposition or Sparse
Regression codebook, this structure is motivated by an analogous construction
proposed recently by Barron and Joseph for communication over an AWGN channel.
For i.i.d Gaussian sources and minimum-distance encoding, we show that such a
code can attain the Shannon rate-distortion function with the optimal error
exponent, for all distortions below a specified value. It is also shown that
sparse regression codes are robust in the following sense: a codebook designed
to compress an i.i.d Gaussian source of variance with
(squared-error) distortion can compress any ergodic source of variance less
than to within distortion . Thus the sparse regression ensemble
retains many of the good covering properties of the i.i.d random Gaussian
ensemble, while having having a compact representation in terms of a matrix
whose size is a low-order polynomial in the block-length.Comment: This version corrects a typo in the statement of Theorem 2 of the
published pape
Code Design for Non-Coherent Detection of Frame Headers in Precoded Satellite Systems
In this paper we propose a simple method for generating short-length
rate-compatible codes over that are robust to non-coherent
detection for -PSK constellations. First, a greedy algorithm is used to
construct a family of rotationally invariant codes for a given constellation.
Then, by properly modifying such codes we obtain codes that are robust to
non-coherent detection. We briefly discuss the optimality of the constructed
codes for special cases of BPSK and QPSK constellations. Our method provides an
upper bound for the length of optimal codes with a given desired non-coherent
distance. We also derive a simple asymptotic upper bound on the frame error
rate (FER) of such codes and provide the simulation results for a selected set
of proposed codes. Finally, we briefly discuss the problem of designing binary
codes that are robust to non-coherent detection for QPSK constellation.Comment: 11 pages, 5 figure
Quickest Sequence Phase Detection
A phase detection sequence is a length- cyclic sequence, such that the
location of any length- contiguous subsequence can be determined from a
noisy observation of that subsequence. In this paper, we derive bounds on the
minimal possible in the limit of , and describe some sequence
constructions. We further consider multiple phase detection sequences, where
the location of any length- contiguous subsequence of each sequence can be
determined simultaneously from a noisy mixture of those subsequences. We study
the optimal trade-offs between the lengths of the sequences, and describe some
sequence constructions. We compare these phase detection problems to their
natural channel coding counterparts, and show a strict separation between the
fundamental limits in the multiple sequence case. Both adversarial and
probabilistic noise models are addressed.Comment: To appear in the IEEE Transactions on Information Theor
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