Rate compatible product codes

High rate product codes with large block lengths have been shown to achieve a BER of 10^-5 within 0.27 dB of Shannon´s channel capacity over an AWGN channel with iterative decoding algorithms. We propose a simple construction of rate compatible low rate codes from relatively high rate product codes. The resulting codes of rates 0.72, 0.63, and 0.57 outperform turbo codes of the same rate and comparable complexity at a BER >10^-4 for a block length of 676 bits. A family of rate compatible product codes is then applied to an adaptive ARQ scheme and achieves a throughput larger than the computational cutoff rate for SNR <5.5 dB