On phase-locked loops and Kalman filters

Driessen (1994) and Christiansen (1994) independently showed that for a specific dynamic model, the proportional-integral phase-locked loop (PLL) has the same structure as the Kalman filter. In this paper, closed-form expressions of the corresponding Kalman gain values are derived both in acquisition and tracking modes of the PLL     

Punctured recursive convolutional encoders and their applicationsin turbo codes

Puncturing is the predominant strategy to construct high code rate convolutional encoders, and infinite impulse response (IIR) convolutional encoders are an essential building block in turbo codes. In this paper, various properties of convolutional encoders with these characteristics are developed. In particular the closed-form representation of a punctured convolutional encoder and its generator matrix is constructed, necessary and sufficient conditions are given such that the punctured encoders retain the IIR property, and various lower bounds on distance properties, such as effective free distance, are developed. Finally, necessary and sufficient conditions are given on the inverse puncturing problem: representing a known convolutional encoder as a punctured encoder     

Application of Kalman filters with a loop delay in synchronization

Discrete-time Kalman filters under a loop-delay constraint suffer performance loss and cease to be optimal. In this letter, modified Kalman filters are proposed to compensate for loop delay. The proposed filter performance is similar to a Kalman predictor. The results are applied to synchronizer loop-filter, design. Closed form expressions for both the update gain and the performance values are derived for first- and second-order disturbance models     

The (d,k) subcode of a linear block code

A simple technique employing linear block codes to construct (d,k) error-correcting block codes is considered. This scheme allows asymptotically reliable transmission at rate R over a BSC channel with capacity C_BSC provided R ⩽C_d,k-(1+C_BSC), where C_d,k is the maximum entropy of a (d,k ) source. For the same error-correcting capability, the loss in code rate incurred by a multiple-error correcting (d,k) code resulting from this scheme is no greater than that incurred by the parent linear block code. The single-error correcting code is asymptotically optimal. A modification allows the correction of single bit-shaft errors as well. Decoding can be accomplished using off-the-shelf decoders. A systematic (but suboptimal) encoding scheme and detailed case studies are provided