92 research outputs found
Fast Polarization for Processes with Memory
Fast polarization is crucial for the performance guarantees of polar codes.
In the memoryless setting, the rate of polarization is known to be exponential
in the square root of the block length. A complete characterization of the rate
of polarization for models with memory has been missing. Namely, previous works
have not addressed fast polarization of the high entropy set under memory. We
consider polar codes for processes with memory that are characterized by an
underlying ergodic finite-state Markov chain. We show that the rate of
polarization for these processes is the same as in the memoryless setting, both
for the high and for the low entropy sets.Comment: 17 pages, 3 figures. Submitted to IEEE Transactions on Information
Theor
Channel Upgradation for Non-Binary Input Alphabets and MACs
Consider a single-user or multiple-access channel with a large output
alphabet. A method to approximate the channel by an upgraded version having a
smaller output alphabet is presented and analyzed. The original channel is not
necessarily symmetric and does not necessarily have a binary input alphabet.
Also, the input distribution is not necessarily uniform. The approximation
method is instrumental when constructing capacity achieving polar codes for an
asymmetric channel with a non-binary input alphabet. Other settings in which
the method is instrumental are the wiretap setting as well as the lossy source
coding setting.Comment: 18 pages, 2 figure
On the Construction of Polar Codes
We consider the problem of efficiently constructing polar codes over binary
memoryless symmetric (BMS) channels. The complexity of designing polar codes
via an exact evaluation of the polarized channels to find which ones are "good"
appears to be exponential in the block length. In \cite{TV11}, Tal and Vardy
show that if instead the evaluation if performed approximately, the
construction has only linear complexity. In this paper, we follow this approach
and present a framework where the algorithms of \cite{TV11} and new related
algorithms can be analyzed for complexity and accuracy. We provide numerical
and analytical results on the efficiency of such algorithms, in particular we
show that one can find all the "good" channels (except a vanishing fraction)
with almost linear complexity in block-length (except a polylogarithmic
factor).Comment: In ISIT 201
UNDER-DIVERSIFICATION AND THE ROLE OF BEST REPLY TO PATTERN
Three experiments are presented that compare alternative explanations to the coexistence of risk aversion and under-diversification in investment decisions. The participants were asked to select one of several assets under two feedback conditions. In each case, one asset was a weighted combination of the other assets, allowing for lower volatility. The frequency of choice of the composite asset was highly sensitive to feedback condition. The composite asset was the least popular asset when the feedback included information concerning forgone payoffs, and increased in frequency when the feedback was limited to the obtained payoff. These results support the assertion that under-diversification can be a product of learning from feedback and in particular best reply to pattern.Risk; Diversification; Learning
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