Rate-compatible non-binary LDPC codes concatenated with multiplicative repetition codes

Abstract

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, 2m-ary the (2,dc)-regular LDPC code for m ∼ 8 and dc ≥ 3 is the best code so far among codes with moderate code length. By multiplicatively repeating the 2m-ary (2,3)-regular LDPC code of rate ⅓, 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.