A Novel Short Block Length Coding Method for Arbitrary Channels

Overview

Forward error correction (FEC) is a vital part of digital communication systems, and it is especially important in aerospace communications, where transmit power resources may be scarce. Presently, there is still room for FEC improvement for transmissions over complex channels and for short block-lengths. For these cases, I developed an algorithm to incrementally improve the signal set. Specifically, to transmit k information bits in n channel uses, I started with a random set of 2k codewords in n-dimensional hyperspace representing all possible k-bit messages. A codeword’s n coordinates represent the n wave amplitudes used to transmit the associated message. n each iteration, the probability pij of the receiver confusing a transmission of codeword ci with codeword cj is obtained via simulation for all codeword pairs. Then, ci is “pushed away” from cj through hyperspace by a distance that increases with pij. The aggregate update of the codeword ci, then, is the vector sum of all such “pushes” emanating from the other codewords Updating all the codewords similarly and conducting power normalization constitutes one iteration. Simulation testing demonstrated that this technique’s performance matched that of the well-known (7, 4) Hamming codes over additive white Gaussian noise channels and exceeded Hamming code performance over Rayleigh fading channels, halving the required transmit power. In fact, the use of empirically-generated probabilities of error allows this approach to be applied for any complex channel for which optimal codes may not be known, especially for short block-length coding.

Competition history

• JSHS 2022 Category not listed

Resources

• National JSHS abstract book ↗

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