Joint Low Density Parity-Check Coding and Linear Precoding for Rayleigh Fading Channels

We introduce a serially concatenated scheme consisting of outer low density parity-check (LDPC) coding and inner complex field linear precoding (LP) for reliable communications over wireless fading channels. We compare the ergodic capacities of the uncorrelated Rayleigh flat fading channel with and without LP, and show that for constellation-constrained inputs LP can bring considerable signal-to-noise ratio (SNR) gains even with precoders of size as small as 2 or 4. We further derive both optimal and low-complexity sub-optimal iterative decoding algorithms and employ extrinsic information transfer (EXIT) charts to approximately evaluate threshold values of their performance. Simulations reveal that when BPSK is used, the novel LDPC-LP scheme results in up to 1.3 dB (1.0 dB) gain at rate frac12for regular (irregular) codes with a medium block size.