Rate-Compatible Non-Binary LDPC Codes Concatenated with Multiplicative Repetition Codes

We propose non-binary LDPC codes concatenated with multiplicative repetition codes. To the best of the authors' knowledge, for the transmissions over the memoryless binary-input output-symmetric channels, 2(m)-ary the (2,d(c))-regular LDPC code for m similar to 8 and d(c) >= 3 is the best code so far among codes with moderate code length. By multiplicatively repeating the 2(m)-ary (2,3)-regular LDPC code of rate 1/3, we construct rate-compatible codes of lower rates 1/6,1/9,1/12, .... Surprisingly, such simple low-rate codes outperform the best low-rate binary codes so far.