Concatenated Signal Codes with Applications to Compute and Forward

We present a new coding scheme based on concatenating a newly introduced class of lattice codes called signal codes with interleaved Low Density Parity Check (LDPC)codes. These codes are shown to possess a special algebraic structure which makes them suitable for recovering linear combinations (over a finite field) of the transmitted signals in a multiple access channel. This facilitates their use as a coding scheme for the recently proposed compute and forward paradigm. The decoding algorithm is based on an appropriate combination of the stack decoder with a message passing algorithm. Simulation results show that our proposed scheme can approach the uniform input AWGN capacity within 1.5 db, which is a 2 db improvement compared to using only signal codes when decoding using a stack algorithm with the same stack size. Simulation results for our proposed scheme applied to compute and forward are also presented.