211,474 research outputs found
A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences
Given the widespread use of lossless compression algorithms to approximate
algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression
algorithms fall short at characterizing patterns other than statistical ones
not different to entropy estimations, here we explore an alternative and
complementary approach. We study formal properties of a Levin-inspired measure
calculated from the output distribution of small Turing machines. We
introduce and justify finite approximations that have been used in some
applications as an alternative to lossless compression algorithms for
approximating algorithmic (Kolmogorov-Chaitin) complexity. We provide proofs of
the relevant properties of both and and compare them to Levin's
Universal Distribution. We provide error estimations of with respect to
. Finally, we present an application to integer sequences from the Online
Encyclopedia of Integer Sequences which suggests that our AP-based measures may
characterize non-statistical patterns, and we report interesting correlations
with textual, function and program description lengths of the said sequences.Comment: As accepted by the journal Complexity (Wiley/Hindawi
Statistical Pruning for Near Maximum Likelihood Detection of MIMO Systems
We show a statistical pruning approach for maximum
likelihood (ML) detection of multiple-input multiple-output
(MIMO) systems. We present a general pruning strategy for
sphere decoder (SD), which can also be applied to any tree search
algorithms. Our pruning rules are effective especially for the case
when SD has high complexity. Three specific pruning rules are
given and discussed. From analyzing the union bound on the
symbol error probability, we show that the diversity order of the
deterministic pruning is only one by fixing the pruning probability.
By choosing different pruning probability distribution
functions, the statistical pruning can achieve arbitrary diversity
orders and SNR gains. Our statistical pruning strategy thus
achieves a flexible trade-off between complexity and performance
Simplified Multiuser Detection for SCMA with Sum-Product Algorithm
Sparse code multiple access (SCMA) is a novel non-orthogonal multiple access
technique, which fully exploits the shaping gain of multi-dimensional
codewords. However, the lack of simplified multiuser detection algorithm
prevents further implementation due to the inherently high computation
complexity. In this paper, general SCMA detector algorithms based on
Sum-product algorithm are elaborated. Then two improved algorithms are
proposed, which simplify the detection structure and curtail exponent
operations quantitatively in logarithm domain. Furthermore, to analyze these
detection algorithms fairly, we derive theoretical expression of the average
mutual information (AMI) of SCMA (SCMA-AMI), and employ a statistical method to
calculate SCMA-AMI based specific detection algorithm. Simulation results show
that the performance is almost as well as the based message passing algorithm
in terms of both BER and AMI while the complexity is significantly decreased,
compared to the traditional Max-Log approximation method
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