713 research outputs found
Statistical mechanics of error exponents for error-correcting codes
Error exponents characterize the exponential decay, when increasing message
length, of the probability of error of many error-correcting codes. To tackle
the long standing problem of computing them exactly, we introduce a general,
thermodynamic, formalism that we illustrate with maximum-likelihood decoding of
low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and
the binary symmetric channel (BSC). In this formalism, we apply the cavity
method for large deviations to derive expressions for both the average and
typical error exponents, which differ by the procedure used to select the codes
from specified ensembles. When decreasing the noise intensity, we find that two
phase transitions take place, at two different levels: a glass to ferromagnetic
transition in the space of codewords, and a paramagnetic to glass transition in
the space of codes.Comment: 32 pages, 13 figure
Application of Expurgated PPM to Indoor Visible Light Communications - Part II: Access Networks
Providing network access for multiple users in a visible light communication
(VLC) system that utilizes white light emitting diodes (LED) as sources
requires new networking techniques adapted to the lighting features. In this
paper we introduce two multiple access techniques using expurgated PPM (EPPM)
that can be implemented using LEDs and support lighting features such as
dimming. Multilevel symbols are used to provide M-ary signaling for multiple
users using multilevel EPPM (MEPPM). Using these multiple-access schemes we are
able to control the optical peak to average power ratio (PAPR) in the system,
and hereby control the dimming level. In the first technique, the M-ary data of
each user is first encoded using an optical orthogonal code (OOC) assigned to
the user, and the result is fed into a EPPM encoder to generate a multilevel
signal. The second multiple access method uses sub-sets of the EPPM
constellation to apply MEPPM to the data of each user. While the first approach
has a larger Hamming distance between the symbols of each user, the latter can
provide higher bit-rates for users in VLC systems using bandwidth-limited LEDs.Comment: Journal of Lightwave Technology. arXiv admin note: substantial text
overlap with arXiv:1308.074
Channel Detection in Coded Communication
We consider the problem of block-coded communication, where in each block,
the channel law belongs to one of two disjoint sets. The decoder is aimed to
decode only messages that have undergone a channel from one of the sets, and
thus has to detect the set which contains the prevailing channel. We begin with
the simplified case where each of the sets is a singleton. For any given code,
we derive the optimum detection/decoding rule in the sense of the best
trade-off among the probabilities of decoding error, false alarm, and
misdetection, and also introduce sub-optimal detection/decoding rules which are
simpler to implement. Then, various achievable bounds on the error exponents
are derived, including the exact single-letter characterization of the random
coding exponents for the optimal detector/decoder. We then extend the random
coding analysis to general sets of channels, and show that there exists a
universal detector/decoder which performs asymptotically as well as the optimal
detector/decoder, when tuned to detect a channel from a specific pair of
channels. The case of a pair of binary symmetric channels is discussed in
detail.Comment: Submitted to IEEE Transactions on Information Theor
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