Non-binary split LDPC codes defined over finite groups

Abstract

In this paper, we propose a practically implementable decoding algorithm for split LDPC codes with parity constraints defined over finite groups. The proposed decoding algorithm generalizes the orders of the variable and check nodes such that it may have messages of different order at the various nodes. This gives us a further degree of freedom in terms of better code construction. Using the binary image of the parity check matrix, we define the function node which maps lower order messages to higher order and vice-versa. In order to have a reduced compexity decoder which is practically implementable, we use the truncated messages concept at the check nodes and evaluate its performance. We show improved performance in the error floor region as compared to other non-split low complexity decoding algorithms.