Short codes for ADMM-based decoding

Modern communication systems are required to operate in different regimes depending on the channel state, size, and purpose of the message. Considering today’s widely used coding schemes, it is known that different code designs and decoding algorithms are optimal for different regimes. From the point of view of technical implementation, it is convenient to have a unified scheme of coding and decoding for the whole range of possible modes. For the solution of this problem it is necessary to consider decoding algorithms based on new principles and code constructions optimized for them. Intensive research in recent years has shown that iterative algorithms based on the Alternating Direction Method of Multipliers (ADMM) have good performance and are a perspective direction of research. In this paper, we consider short code constructions optimized for both classical decoding algorithms (successive cancellation and message-passing based algorithms) and ADMM-based algorithms, and compare their performance using numerical simulation methods.