Linear code construction for the 2-user binary adder channel

摘要

This paper deals with the construction of a class of binaryuniquely decodable code pairs (C₁, C₂) for thetwo-user binary adder channel (2-BAC), where C₁ is a linearcode. The generator matrix G for code C₁ has the propertythat any of its columns has at most a single 1 among its K elements.These codes are called strongly orthogonal codes in the sense that theHadamard product of any two rows of G is the all-zero n-tuple. Theproposed 2-BAC codes achieve the upper bound for the sum rate when therate of C₁ is greater than or equal to 1/2. Block and bitsynchronization is assumed between the users and the receiver