# Real-Time Decoder Architecture for LDPC–CPM

## TL;DR

This paper explores efficient decoding methods for LDPC codes combined with CPM modulation used in aeronautical telemetry.

## Contribution

A real-time decoder architecture is proposed for LDPC-CPM systems with fixed complexity and adjustable performance-complexity trade-offs.

## Key findings

- LDPC-CPM decoders face a significant peak to average ratio in global iterations.
- A reference simulation can evaluate many system designs efficiently.
- The proposed decoder achieves good performance with fixed complexity.

## Abstract

This paper examines the iterative decoding of low-density parity check (LDPC) codes concatenated with continuous phase modulation (CPM). As relevant case studies, we focus on the family of three CPM waveforms that are embodied in the IRIG-106 aeronautical telemetry standard. Two of these CPMs have recently had LDPC codes designed for them for the first time, and thus the decoding complexity of these new schemes is of interest when considering adoption into the standard. We provide comprehensive numerical results that characterize the performance and iteration statistics of the joint LDPC–CPM decoder. These results identify the most advantageous decoder configurations and also expose a key design challenge, which is that LDPC-CPM decoders must deal with a large “peak to average” ratio in terms of global iterations. We show how a properly designed reference simulation can be used as a design tool to explore the performance of a large range of candidate systems without need for further simulation. We develop a real-time decoder architecture with fixed complexity and show how such a decoder can still achieve a relatively large maximum number of global iterations by introducing a trade-off between decoding latency and maximum global iterations. Our discussion shows that this scheme is generally applicable to LDPC-based schemes. We conclude with a comprehensive design study that demonstrates the accuracy of our methodology and its attractive performance–complexity trade-off.