Uniquely decodable signature sequences over the noisy adder channel

Abstract

Signature sequences that are uniquely decodable (UD) can be used to identify active terminals by the observation of their sums. Such sequences provide a solution to the problem of finding which m-out-of-t users are active in grant-free access methods that use physical layer network coding (PLNC). Although the existence of such sequences has been assumed in previous works, their explicit construction is presented here for the first time, along with a performance assessment when the observed sums are disturbed by noise. UD sequences are defined as sets of integers that satisfy the unique-sum property. The construction of the sets is algebraically defined depending on two Galois fields with related dimensions. We use the BoseChowla-Lindström approach to computationally find such integer sets that are obtained with reasonable computational complexity. In comparison with orthogonal binary real sequences, these sequences use fewer bits in equivalent setups. The binary signature sequences are mapped to some binary antipodal modulation and assessed in the multiple access adder channel (MAAC) disturbed by noise. Both hard and soft maximum likelihood detectors are used to assess the probability of misidentifying an active user.