Decoding a family of dense codes using the Sum-Product Algorithm

Cortex codes are a family of block codes with good minimum distance properties whose parity-check matrices are very dense. Digital implementations of Cortex decoders using standard decoding algorithms have not shown an acceptable performance. Motivated by the encoder structure, a new bipartite graph is introduced and exemplified for the Cortex construction of the extended Hamming code. The Cortex graph has longer girth and approximately 80% less cycles than the Tanner graph. A Cortex and an LDPC-like decoder were implemented for the same code using identical PMOS-based Gilbert multipliers. This makes them the first reported analog decoders using mainly PMOS transistors. The Cortex outperforms the LDPC-like decoder in bit error rate and at the same time saves 44% of die surface. The results are supported using data from a test chip designed for a 0.25 mum CMOS process.