Results 1 
8 of
8
Universal algorithms for channel decoding of uncompressed sources
 IEEE TRANS. INFORM. THEORY
, 2008
"... In many applications, an uncompressed source stream is systematically encoded by a channel code (which ignores the source redundancy) for transmission over a discrete memoryless channel. The decoder knows the channel and the code but does not know the source statistics. This paper proposes several ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
In many applications, an uncompressed source stream is systematically encoded by a channel code (which ignores the source redundancy) for transmission over a discrete memoryless channel. The decoder knows the channel and the code but does not know the source statistics. This paper proposes several universal channel decoders that take advantage of the source redundancy without requiring prior knowledge of its statistics.
The Information Lost in Erasures
, 2008
"... We consider sources and channels with memory observed through erasure channels. In particular, we examine the impact of sporadic erasures on the fundamental limits of lossless data compression, lossy data compression, channel coding, and denoising. We define the erasure entropy of a collection of ra ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
(Show Context)
We consider sources and channels with memory observed through erasure channels. In particular, we examine the impact of sporadic erasures on the fundamental limits of lossless data compression, lossy data compression, channel coding, and denoising. We define the erasure entropy of a collection of random variables as the sum of entropies of the individual variables conditioned on all the rest. The erasure entropy measures the information content carried by each symbol knowing its context. The erasure entropy rate is shown to be the minimal amount of bits per erasure required to recover the lost information in the limit of small erasure probability. When we allow recovery of the erased symbols within a prescribed degree of distortion, the fundamental tradeoff is described by the erasure rate–distortion function which we characterize. We show that in the regime of sporadic erasures, knowledge at the encoder of the erasure locations does not lower the rate required to achieve a given distortion. When no additional encoded information is available, the erased information is reconstructed solely on the basis of its context by a denoiser. Connections between erasure entropy and discrete denoising are developed. The decrease of the capacity of channels with memory due to sporadic memoryless erasures is also characterized in wide generality.
Discrete Universal Filtering via Hidden Markov Modelling
"... Abstract — We consider the discrete universal filtering problem, where the components of a discrete signal emitted by an unknown source and corrupted by a known DMC are to be causally estimated. We derive a family of filters which we show to be universally asymptotically optimal in the sense of achi ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract — We consider the discrete universal filtering problem, where the components of a discrete signal emitted by an unknown source and corrupted by a known DMC are to be causally estimated. We derive a family of filters which we show to be universally asymptotically optimal in the sense of achieving the optimum filtering performance when the clean signal is stationary, ergodic, and satisfies an additional mild positivity condition. Our schemes are based on approximating the noisy signal by a hidden Markov process (HMP) via maximumlikelihood (ML) estimation, followed by use of the wellknown forward recursions for HMP state estimation. We show that as the data length increases, and as the number of states in the HMP approximation increases, our family of filters attain the performance of the optimal distributiondependent filter. I.
Discrete denoising with shifts
 IEEE Trans. Inf. Theory
, 2007
"... We introduce SDUDE, a new algorithm for denoising DMCcorrupted data. The algorithm, which generalizes the recently introduced DUDE (Discrete Universal DEnoiser) of Weissman et al., aims to compete with a genie that has access, in addition to the noisy data, also to the underlying clean data, and c ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We introduce SDUDE, a new algorithm for denoising DMCcorrupted data. The algorithm, which generalizes the recently introduced DUDE (Discrete Universal DEnoiser) of Weissman et al., aims to compete with a genie that has access, in addition to the noisy data, also to the underlying clean data, and can choose to switch, up to m times, between sliding window denoisers in a way that minimizes the overall loss. When the underlying data form an individual sequence, we show that the SDUDE performs essentially as well as this genie, provided that m is sublinear in the size of the data. When the clean data is emitted by a piecewise stationary process, we show that the SDUDE achieves the optimum distributiondependent performance, provided that the same sublinearity condition is imposed on the number of switches. To further substantiate the universal optimality of the SDUDE, we show that when the number of switches is allowed to grow linearly with the size of the data, any (sequence of) scheme(s) fails to compete in the above senses. Using dynamic programming, we derive an efficient implementation of the SDUDE, which has complexity (time and memory) growing only linearly with the data size and the number of switches m. Preliminary experimental results are presented, suggesting that SDUDE has the capacity to significantly improve on the performance attained by the original DUDE in applications where the nature of the data abruptly changes in time (or space), as is often the case in practice. Index Terms Discrete denoising, competitive analysis, individual sequence, universal algorithms, piecewise stationary processes, dynamic programming, discrete memoryless channel (DMC), switching experts, forwardbackward recursions. 1
6. (algorithm) Discrete Universal DEnoiser
"... 3. (slang) A term of address for a man. 4. (archaic) A dandy, a man who is very concerned about his dress and appearance. 5. (slang) A cool person of either sex. ..."
Abstract
 Add to MetaCart
(Show Context)
3. (slang) A term of address for a man. 4. (archaic) A dandy, a man who is very concerned about his dress and appearance. 5. (slang) A cool person of either sex.
6. (algorithm) Discrete Universal Denoiser
"... 3. (slang) A term of address for a man. 4. (archaic) A dandy, a man who is very concerned about his dress and appearance. 5. (slang) A cool person of either sex. ..."
Abstract
 Add to MetaCart
(Show Context)
3. (slang) A term of address for a man. 4. (archaic) A dandy, a man who is very concerned about his dress and appearance. 5. (slang) A cool person of either sex.
unknown title
"... Abstract — We introduce SDUDE, a new algorithm for denoising DMCcorrupted data. The algorithm, which generalizes the recently introduced DUDE (Discrete Universal DEnoiser) of Weissman et al., aims to compete with a genie that has access, in addition to the noisy data, also to the underlying clean ..."
Abstract
 Add to MetaCart
Abstract — We introduce SDUDE, a new algorithm for denoising DMCcorrupted data. The algorithm, which generalizes the recently introduced DUDE (Discrete Universal DEnoiser) of Weissman et al., aims to compete with a genie that has access, in addition to the noisy data, also to the underlying clean data, and can choose to switch, up to m times, between sliding window denoisers in a way that minimizes the overall loss. When the underlying data form an individual sequence, we show that the SDUDE performs essentially as well as this genie, provided that m is sublinear in the size of the data. When the clean data is emitted by a piecewise stationary process, we show that the SDUDE achieves the optimum distributiondependent performance, provided that the same sublinearity condition is imposed on the number of switches. To further substantiate the universal optimality of the SDUDE, we show that when the number of switches is allowed to grow linearly with the size of the data, any (sequence of) scheme(s) fails to compete in the above senses. Using dynamic programming, we derive an efficient implementation of the SDUDE, which has complexity (time and memory) growing only linearly with the data size and the number of switches m. Preliminary experimental results are presented, suggesting that SDUDE has the capacity to significantly improve on the performance attained by the original DUDE in applications where the nature of the data abruptly changes in time (or space), as is often the case in practice. I.
Approved for External PublicationUniversal Algorithms for Channel Decoding of Uncompressed Sources ∗
, 2008
"... sourcechannel ..."
(Show Context)