56,819 research outputs found

    Trellis phase codes for power-bandwith efficient satellite communications

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    Support work on improved power and spectrum utilization on digital satellite channels was performed. Specific attention is given to the class of signalling schemes known as continuous phase modulation (CPM). The specific work described in this report addresses: analytical bounds on error probability for multi-h phase codes, power and bandwidth characterization of 4-ary multi-h codes, and initial results of channel simulation to assess the impact of band limiting filters and nonlinear amplifiers on CPM performance

    Multi-Error-Correcting Amplitude Damping Codes

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    We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This allows us to use concatenated codes with quantum erasure-correcting codes as outer codes for correcting multiple amplitude damping errors. Our new codes are degenerate stabilizer codes and have parameters which are better than the amplitude damping codes obtained by any previously known construction.Comment: 5 pages. Submitted to ISIT 201

    Multilevel Coded Modulation for Unequal Error Protection and Multistage Decoding—Part II: Asymmetric Constellations

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    In this paper, multilevel coded asymmetric modulation with multistage decoding and unequal error protection (UEP) is discussed. These results further emphasize the fact that unconventional signal set partitionings are more promising than traditional (Ungerboeck-type) partitionings, to achieve UEP capabilities with multilevel coding and multistage decoding. Three types of unconventional partitionings are analyzed for asymmetric 8-PSK and 16-QAM constellations over the additive white Gaussian noise channel to introduce design guidelines. Generalizations to other PSK and QAM type constellations follow the same lines. Upper bounds on the bit-error probability based on union bound arguments are first derived. In some cases, these bounds become loose due to the large overlappings of decision regions associated with asymmetric constellations and unconventional partitionings. To overcome this problem, simpler and tighter approximated bounds are derived. Based on these bounds, it is shown that additional refinements can be achieved in the construction of multilevel UEP codes, by introducing asymmetries in PSK and QAM signal constellations

    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
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