Error-Correcting Codes for Automatic Control

Systems with automatic feedback control may consist of several remote devices, connected only by unreliable communication channels. It is necessary in these conditions to have a method for accurate, real-time state estimation in the presence of channel noise. This problem is addressed, for the case of polynomial-growth-rate state spaces, through a new type of error-correcting code that is online and computationally efficient. This solution establishes a constructive analog, for some applications in estimation and control, of the Shannon coding theorem

An investigation of error characteristics and coding performance

The performance of forward error correcting coding schemes on errors anticipated for the Earth Observation System (EOS) Ku-band downlink are studied. The EOS transmits picture frame data to the ground via the Telemetry Data Relay Satellite System (TDRSS) to a ground-based receiver at White Sands. Due to unintentional RF interference from other systems operating in the Ku band, the noise at the receiver is non-Gaussian which may result in non-random errors output by the demodulator. That is, the downlink channel cannot be modeled by a simple memoryless Gaussian-noise channel. From previous experience, it is believed that those errors are bursty. The research proceeded by developing a computer based simulation, called Communication Link Error ANalysis (CLEAN), to model the downlink errors, forward error correcting schemes, and interleavers used with TDRSS. To date, the bulk of CLEAN was written, documented, debugged, and verified. The procedures for utilizing CLEAN to investigate code performance were established and are discussed

Self-concatenated code design and its application in power-efficient cooperative communications

In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions

The statistical mechanics of turbo codes

The "turbo codes", recently proposed by Berrou et. al. are written as a disordered spin Hamiltonian. It is shown that there is a threshold Theta such that for signal to noise ratios v^2 / w^2 > Theta, the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitly long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations.Comment: 23 pages, 6 figures: Fig.2 has been replaced (in the preceding version it was identical to Fig.1

Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January 2006 - First review: June 200