14,605 research outputs found
Lossy Compression via Sparse Linear Regression: Computationally Efficient Encoding and Decoding
We propose computationally efficient encoders and decoders for lossy
compression using a Sparse Regression Code. The codebook is defined by a design
matrix and codewords are structured linear combinations of columns of this
matrix. The proposed encoding algorithm sequentially chooses columns of the
design matrix to successively approximate the source sequence. It is shown to
achieve the optimal distortion-rate function for i.i.d Gaussian sources under
the squared-error distortion criterion. For a given rate, the parameters of the
design matrix can be varied to trade off distortion performance with encoding
complexity. An example of such a trade-off as a function of the block length n
is the following. With computational resource (space or time) per source sample
of O((n/\log n)^2), for a fixed distortion-level above the Gaussian
distortion-rate function, the probability of excess distortion decays
exponentially in n. The Sparse Regression Code is robust in the following
sense: for any ergodic source, the proposed encoder achieves the optimal
distortion-rate function of an i.i.d Gaussian source with the same variance.
Simulations show that the encoder has good empirical performance, especially at
low and moderate rates.Comment: 14 pages, to appear in IEEE Transactions on Information Theor
MIMO Detection for High-Order QAM Based on a Gaussian Tree Approximation
This paper proposes a new detection algorithm for MIMO communication systems
employing high order QAM constellations. The factor graph that corresponds to
this problem is very loopy; in fact, it is a complete graph. Hence, a
straightforward application of the Belief Propagation (BP) algorithm yields
very poor results. Our algorithm is based on an optimal tree approximation of
the Gaussian density of the unconstrained linear system. The finite-set
constraint is then applied to obtain a loop-free discrete distribution. It is
shown that even though the approximation is not directly applied to the exact
discrete distribution, applying the BP algorithm to the loop-free factor graph
outperforms current methods in terms of both performance and complexity. The
improved performance of the proposed algorithm is demonstrated on the problem
of MIMO detection
Integer-Forcing Linear Receivers
Linear receivers are often used to reduce the implementation complexity of
multiple-antenna systems. In a traditional linear receiver architecture, the
receive antennas are used to separate out the codewords sent by each transmit
antenna, which can then be decoded individually. Although easy to implement,
this approach can be highly suboptimal when the channel matrix is near
singular. This paper develops a new linear receiver architecture that uses the
receive antennas to create an effective channel matrix with integer-valued
entries. Rather than attempting to recover transmitted codewords directly, the
decoder recovers integer combinations of the codewords according to the entries
of the effective channel matrix. The codewords are all generated using the same
linear code which guarantees that these integer combinations are themselves
codewords. Provided that the effective channel is full rank, these integer
combinations can then be digitally solved for the original codewords. This
paper focuses on the special case where there is no coding across transmit
antennas and no channel state information at the transmitter(s), which
corresponds either to a multi-user uplink scenario or to single-user V-BLAST
encoding. In this setting, the proposed integer-forcing linear receiver
significantly outperforms conventional linear architectures such as the
zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed
receiver attains the optimal diversity-multiplexing tradeoff for the standard
MIMO channel with no coding across transmit antennas. It is further shown that
in an extended MIMO model with interference, the integer-forcing linear
receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on
Information Theor
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