257 research outputs found
Bit-Interleaved Coded Modulation Revisited: A Mismatched Decoding Perspective
We revisit the information-theoretic analysis of bit-interleaved coded
modulation (BICM) by modeling the BICM decoder as a mismatched decoder. The
mismatched decoding model is well-defined for finite, yet arbitrary, block
lengths, and naturally captures the channel memory among the bits belonging to
the same symbol. We give two independent proofs of the achievability of the
BICM capacity calculated by Caire et al. where BICM was modeled as a set of
independent parallel binary-input channels whose output is the bitwise
log-likelihood ratio. Our first achievability proof uses typical sequences, and
shows that due to the random coding construction, the interleaver is not
required. The second proof is based on the random coding error exponents with
mismatched decoding, where the largest achievable rate is the generalized
mutual information. We show that the generalized mutual information of the
mismatched decoder coincides with the infinite-interleaver BICM capacity. We
also show that the error exponent -and hence the cutoff rate- of the BICM
mismatched decoder is upper bounded by that of coded modulation and may thus be
lower than in the infinite-interleaved model. We also consider the mutual
information appearing in the analysis of iterative decoding of BICM with EXIT
charts. We show that the corresponding symbol metric has knowledge of the
transmitted symbol and the EXIT mutual information admits a representation as a
pseudo-generalized mutual information, which is in general not achievable. A
different symbol decoding metric, for which the extrinsic side information
refers to the hypothesized symbol, induces a generalized mutual information
lower than the coded modulation capacity.Comment: submitted to the IEEE Transactions on Information Theory. Conference
version in 2008 IEEE International Symposium on Information Theory, Toronto,
Canada, July 200
Computational Intelligence and Complexity Measures for Chaotic Information Processing
This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value
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