713 research outputs found

    Statistical mechanics of error exponents for error-correcting codes

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    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

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    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

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    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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