Generalized Pre-Processor for Block and Convolutional Codes

The design could be simplified by taking advantageof the structures of the codes.

NASA's Jet Propulsion Laboratory, Pasadena, California

A generalized data processor, proposed for use in the reception of binary-phase-shift-keyed (BPSK) radio signals, provides preliminary estimates of the block and convolutionally encoded symbols that are meant to be conveyed by the BPSK modulation. In a process denoted information-reduced maximum a posteriori (MAP) phase estimation, an estimate of the instantaneous symbol (and thus of the instantaneous phase modulation) is used to reduce the amount of randomness and information by converting the received modulated carrier to an approximation of an unmodulated carrier. The resulting partially reconstructed carrier is then fed as input to a MAP phase estimator to improve phase-tracking performance. The basic principles of information-reduced MAP phase estimation were described in somewhat more detail in "Information-Reduced Carrier Synchronization for Coded PSK Operation at Low-SNR" (NPO-20261), NASA Tech Briefs, Vol. 22, No. 10 (October 1998), page 64.

A detailed description of the generalized pre-processor can be found in the TMO Progress Report 42-144, October 2000, "Generalized Pre-Processor for Block and Convolutionally Coded Signals." Here we present a brief summary of the generalized pre-processor (see figure), which makes use of the algebraic structures of block and convolutional codes. In the coherent mode of operation, this pre-processor decomposes the received code words by use of orthogonal Hadamard basis functions and generates a vector of coefficients of length K (where K is the number of bits per code symbol) for each received block. Next, the coefficient vector is multiplied by a signal-weighting matrix to generate a vector of log-likelihood functions. The largest component of this decision vector is identified, and its index used to reconstruct the decoded code word.

The structure of the pre-processor remains essentially the same for any linear code of a given block length, except for the signal-weighting matrix, which is unique to each code. The signal-weighting matrix is pre-computed for each coding scheme by first generating the set of code words, then multiplying the Hadamard matrix by the coefficient matrix representing all possible code words.

The proposed generalized pre-processor was tested in computational simulations. The results showed that under representative conditions, including signal-to-noise ratios ranging from -5 to -10 dB, the increase in carrier-phase-estimation performance is equivalent to the improvement afforded by strengthening the received signal by 5 to 6 dB.

This Simplified Version of the Pre-Processor performs Hadamard decomposition and signal reconstruction.

This work was done by Victor Vilnrotter, Clement Lee, and Norman Lay of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Electronic Components and Systems category.

Refer to NPO-30129, volume and number of this NASA Tech Briefs issue, and the page number.

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