Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Urbanke, Rudiger"'
Autor:
Głuch, Grzegorz, Urbanke, Rudiger
We introduce a new notion of complexity of functions and we show that it has the following properties: (i) it governs a PAC Bayes-like generalization bound, (ii) for neural networks it relates to natural notions of complexity of functions (such as th
Externí odkaz:
http://arxiv.org/abs/2303.07874
Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of decoding
Externí odkaz:
http://arxiv.org/abs/1705.05497
Autor:
Hassani, S. Hamed, Urbanke, Rudiger
Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless output-symmetric channel. One of the few drawbacks of the original polar code construction is that it is not universal. This means that the code
Externí odkaz:
http://arxiv.org/abs/1307.7223
Consider a binary-input memoryless output-symmetric channel $W$. Such a channel has a capacity, call it $I(W)$, and for any $R
Externí odkaz:
http://arxiv.org/abs/1304.4778
The XOR-satisfiability (XORSAT) problem deals with a system of $n$ Boolean variables and $m$ clauses. Each clause is a linear Boolean equation (XOR) of a subset of the variables. A $K$-clause is a clause involving $K$ distinct variables. In the rando
Externí odkaz:
http://arxiv.org/abs/1303.0540
For a given family of spatially coupled codes, we prove that the LP threshold on the BSC of the graph cover ensemble is the same as the LP threshold on the BSC of the derived spatially coupled ensemble. This result is in contrast with the fact that t
Externí odkaz:
http://arxiv.org/abs/1301.6410
Autor:
Hassani, S. Hamed, Urbanke, Rudiger
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the performan
Externí odkaz:
http://arxiv.org/abs/1209.4612
We consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy
Externí odkaz:
http://arxiv.org/abs/1205.2876
We study a new encoding scheme for lossy source compression based on spatially coupled low-density generator-matrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distor
Externí odkaz:
http://arxiv.org/abs/1202.4959
We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction. We investigate their phase diagram at zero temperature using the survey propagation formalism and the interpolati
Externí odkaz:
http://arxiv.org/abs/1112.6320