Linear code construction for the 2-user binary adder channel

This paper deals with the construction of a class of binary uniquely decodable code pairs (C₁, C₂) for the two-user binary adder channel (2-BAC), where C₁ is a linear code. The generator matrix G for code C₁ has the property that 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 the Hadamard product of any two rows of G is the all-zero n-tuple. The proposed 2-BAC codes achieve the upper bound for the sum rate when the rate of C₁ is greater than or equal to 1/2. Block and bit synchronization is assumed between the users and the receiver