VLSI Implementation of a Non-Binary Decoder Based on the Analog Digital Belief Propagation

This work presents the VLSI hardware implementation of a novel Belief Propagation (BP) algorithm introduced in [G. Montorsi, “Analog digital belief propagation,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1106-1109, 2012] and named as Analog Digital Belief Propagation (ADBP). The ADBP algorithm works on factor graphs over linear models and uses messages in the form of Gaussian like probability distributions by tracking their parameters. In particular, ADBP can deal with system variables that are discrete and/or wrapped. A variant of ADBP can then be applied for the iterative decoding of a particular class of non binary codes and yields decoders with complexity independent of alphabet size M, thus allowing to construct efficient decoders for digital transmission systems with unbounded spectral efficiency. In this work, we propose some simplifications to the updating rules for ADBP algorithm that are suitable for hardware implementation. In addition, we analyze the effect of finite precision on the decoding performance of the algorithm. A careful selection of quantization scheme for input, output and intermediate variables allows us to construct a complete ADBP decoding architecture that performs close to the double precision implementation and shows a promising complexity for large values of M. Finally, synthesis results of the main processing elements of ADBP are reported for 45 nm standard cell ASIC technology.