Uniquely Decodable Code-Division via Augmented Sylvester-Hadamard Matrices

Abstract: We consider the problem of designing binary antipodal uniquely decodable (errorless) code sets for overloaded codedivision multiplexing applications where the number of signals K is larger than the code length L. Our proposed errorless code set design aims at identifying the maximum number of columns that can be potentially appended to a Sylvester-Hadamard matrix of order L, while maintaining the errorless code property. In particular, we derive formally the maximum number of columns that may be appended to the Sylvester-Hadamard matrix of order L = 8 and use this result as a seed to produce an infinite sequence of designs in increasing L. In the noiseless transmission case, a simple algorithm is developed to uniquely decode all signals. In additive white Gaussian noise (AWGN), a slab-sphere decoding scheme can be utilized for efficient and effective decoding.

ArmenianMathematics

Audience: general audience

( slides )

Yerevan Mathematical Colloquium

Series comments: "Yerevan Mathematical Colloquium" invites survey talks aimed at a general mathematical audience, that emphasize proof methods, relations between branches of mathematics, possible applications, and open problems.