AI Coding: Learning to Construct Error Correction Codes

Abstract

In this paper, we investigate an artificialintelligence (AI) driven approach to design error correction codes (ECC). Classic error-correction code design based upon coding-theoretic principles typically strives to optimize some performance-related code property such as minimum Hamming distance, decoding threshold, or subchannel reliability ordering. In contrast, AI-driven approaches, such as reinforcement learning (RL) and genetic algorithms, rely primarily on optimization methods to learn the parameters of an optimal code within a certain code family. We employ a constructor-evaluator framework, in which the code constructor can be realized by various AI algorithms and the code evaluator provides code performance metric measurements. The code constructor keeps improving the code construction to maximize code performance that is evaluated by the code evaluator. As examples, we focus on RL and genetic algorithms to construct linear block codes and polar codes. The results show that comparable code performance can be achieved with respect to the existing codes. It is noteworthy that our method can provide superior performances to classic constructions in certain cases (e.g., list decoding for polar codes). Code PerformanceCoding Theory Code Construction AI Techniques Fig. 1: Error correction code design logic improve its code performance. Equivalently, given a target error rate, we optimize code design to maximize the achievable code rate, i.e. to approach the channel capacity. A. Code design based on coding theoryClassical code construction design is built upon coding theory, in which code performance is analytically derived in terms of various types of code properties. To tune these properties is to control the code performance so that code design problems are translated into code property optimization problems.Hamming distance is an important code property for linear block codes of all lengths. For short codes, it is the dominant factor in performance, when maximum-likelihood (ML) decoding is feasible. For long codes, it is also important for performance in the high signal-to-noise ratio (SNR) regime. A linear block code can be defined by a generator matrix G or the corresponding parity check matrix H over finite fields. Directed by the knowledge of finite field algebra, the distance profile of linear block codes can be optimized, and in particular, the minimum distance. Examples include Hamming codes, Golay codes, Reed-Muller (RM) codes, quadratic residue (QR) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, Reed-Solomon (RS) codes, etc.Similar to the Hamming distance profile, free distance, another code property, is targeted for convolutional codes. Convolutional codes [2] are characterized by code rate and the memory order of the encoder. By increasing the memory order and selecting proper polynomials, larger free distance can be obtained at the expense of encoding and decoding

Reinforcement Learning for Nested Polar Code Construction

“…However, to our best knowledge, for polar codes with SCL-based decoders, theoretically optimal code construction is still an open problem. Existing constructions either directly adopt DE/GA, which are designed for SC rather than SCL, or apply genetic algorithms for SCL decodings [2], [4].…”

“…Following the "constructor-evaluator" framework [2], we propose to directly evaluate the rewards through decoding performance. Monte-Carlo (MC) simulations are conducted to output a block error rate (BLER) performance for each code construction.…”

“…Recently, artificial intelligence (AI) techniques have been applied to physical layer design. AI techniques can be a tool to design or optimize error correction codes [2], while leaving their legacy encoding and decoding architectures and implementations unchanged. Within a "constructor-evaluator" framework [2], AI algorithms such as policy gradient, genetic algorithm, and actor critic, are capable of constructing linear block codes and polar codes with as good performances as the state of the art.…”

“…AI techniques can be a tool to design or optimize error correction codes [2], while leaving their legacy encoding and decoding architectures and implementations unchanged. Within a "constructor-evaluator" framework [2], AI algorithms such as policy gradient, genetic algorithm, and actor critic, are capable of constructing linear block codes and polar codes with as good performances as the state of the art. In [3], RL and Monte Carlo tree search (MCTS) are combined to guide edge growth in LDPC code construction.…”

“…In [4], [5], genetic algorithms are used to design polar codes and LDPC codes. The main difference from [2] is that coding expert knowledge is utilized during the initialization to speed up the learning process.…”