Joint optimization of multi-rate LDPC code ensembles for the AWGN channel based on shortening and puncturing

In most communication systems, being able to adapt the error protection strength of the physical layer is essential to ensure the functionality of the system in potentially strongly varying conditions. Traditional forward error correction code design focuses on the optimization of codes with a fixed code rate for a worst-case channel condition. So-called rate-compatible codes, on the other hand, are tailored to support multiple code rates. In this paper we present an optimization strategy for a rate-compatible system based on shortening and puncturing of Low-Density Parity-Check (LDPC) codes. While the technique itself is well known, we propose a novel joint optimization of the resulting multi-rate LDPC code ensemble at all rates. This joint optimization achieves close to capacity decoding thresholds over an arbitrarily wide range of target code rates using only a single encoder and decoder implementation.