Functions and Architectures for LDPC Decoding

Implementation of belief propagation for low-density parity-check codes involves selection of functions possessing manageable dynamic range, topologic considerations for aggregation of these functions such that nodes of varying degree can be efficiently realized, and message passing architectures that offer various alternatives for flexibility and throughput. This paper discusses each of these topics and contrasts optimal and sub-optimal techniques where appropriate. In particular, optimal functions for producing extrinsic messages in the absence of an inverse function are described and compared to sub-optimal approaches that do not compute a full set of extrinsic messages. In addition we describe structured and universal message passing architectures and discuss scenarios where application of each may be appropriate.