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Abstract

A message in the form of a sequence of bits is encoded into relatively short, non-binary signals. The message (or vector) is divided into two halves. The encoder first determines an encoding of the message into a vector half the length of the eventual encoded vector. The half-length vector forms the first half of the encoded, and is negated to form the second half of the encoded vector. An identical synchronization signal is added to both halves of the encoded vector. The synchronization signal is used to compensate for the possibility that the received vector (or message) is cyclically rotated from the original vector. During decoding, the decoder first obtains the synchronization signal by adding the two halves of the vector together, canceling the encoded message. The synchronization signal is used to find the original cyclical shift of the vector. The decoder obtains the half-length encoded message vector by taking the difference between the two halves of the aligned full-length encoded vector. After decoding the vector into a bit sequence, the encoder re-encodes that bit sequence and compares the resulting vector with the original vector to determine whether the original vector truly encoded a message or was simply a noise signal.

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First Claim