A novel structure of variable rate non-binary LDPC codes for MIMO channels

Slow decoding convergence and performance loss are two main drawbacks of the conventional variable rate non-binary LDPC codes based on puncturing. To alleviate these problems, we study in this paper the variable rate non-binary LDPC code that has a mother code of high rate and a series of lower rate codes obtained from the concept of shortening. A novel shortening technique to construct variable rate non-binary LDPC codes is proposed in this paper. By using this technique, the performance loss between variable rate code and independently-designed code, in MIMO channels, at any given rate no longer exists and the decoding convergence of the proposed scheme is very fast, e.g., only 5 iterations on average to achieve BER of 10⁻⁵. Moreover, the proposed shortening is done in symbol-wise manner (inherently low-complexity) which is more suitable for realistic MIMO communications.