In this work we propose RELDEC, a novel approach for sequential decoding of moderate length low-density parity-check (LDPC) codes. The main idea behind RELDEC is that an optimized decoding policy is subsequently obtained via reinforcement learning based on a Markov decision process (MDP). In contrast to our previous work, where an agent learns to schedule only a single check node (CN) within a group (cluster) of CNs per iteration, in this work we train the agent to schedule all CNs in a cluster, and all clusters in every iteration. That is, in each learning step of RELDEC an agent learns to schedule CN clusters sequentially depending on a reward associated with the outcome of scheduling a particular cluster. We also modify the state space representation of the MDP, enabling RELDEC to be suitable for larger block length LDPC codes than those studied in our previous work. Furthermore, to address decoding under varying channel conditions, we propose agile meta-RELDEC (AM-RELDEC) that employs meta-reinforcement learning. The proposed RELDEC scheme significantly outperforms standard flooding and random sequential decoding for a variety of LDPC codes, including codes designed for 5G new radio.

Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this article, we consider nested array-based spatially coupled low-density parity-check (SC-LDPC) codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. Since the parity-check matrices of different nested sub-codes partially overlap, the optimization of one nested sub-code imposes constraints on the optimization of the other sub-codes. To tackle these constraints, a multi-step optimization process is applied first to one of the nested codes, then sequential optimization of the remaining nested codes is carried out based on the constraints imposed by the previously optimized sub-codes. Results show that the order of optimization has a significant impact on the number of dominant absorbing sets in the Tanner graph of the code, resulting in a trade-off between the performance of a nested code structure and its optimization sequence: the code which is optimized without constraints has fewer harmful structures than the code which is optimized with constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes are completely removed using our proposed optimization strategy.

The multi-armed bandit (MAB) problem refers to the dilemma encountered by a gambler when deciding which arm of a multi-armed slot machine to pull in order to maximize the total reward earned in a sequence of pulls. In this paper, we model the scheduling of a node-wise sequential LDPC decoder as a Markov decision process, where the underlying Tanner graph is viewed as a slot machine with multiple arms corresponding to the check nodes. A fictitious gambler decides which check node to pull (schedule) next by observing a reward associated with each pull. This interaction enables the gambler to discover an optimized scheduling policy that aims to reach a codeword output by propagating the fewest possible messages. Based on this policy, we contrive a novel MAB-based node-wise scheduling (MABNS) algorithm to perform sequential decoding of LDPC codes. Simulation results show that the MAB-NS scheme, aided by an appropriate scheduling policy, outperforms traditional scheduling schemes in terms of complexity and bit error probability.

We show in this work that reinforcement learning can be successfully applied to decoding short to moderate length sparse graph-based channel codes. Specifically, we focus on low-density parity check (LDPC) codes, which for example have been standardized in the context of 5G cellular communication systems due to their excellent error correcting performance. These codes are typically decoded via belief propagation iterative decoding on the corresponding bipartite (Tanner) graph of the code via flooding, i.e., all check and variable nodes in the Tanner graph are updated at once. In contrast, in this paper we utilize a sequential update policy which selects the optimum check node (CN) scheduling in order to improve decoding performance. In particular, we model the CN update process as a multi-armed bandit process with dependent arms and employ a Q-learning scheme for optimizing the CN scheduling policy. In order to reduce the learning complexity, we propose a novel graph-induced CN clustering approach to partition the state space in such a way that dependencies between clusters are minimized. Our results show that compared to other decoding approaches from the literature, the proposed reinforcement learning scheme not only significantly improves the decoding performance, but also reduces the decoding complexity dramatically once the scheduling policy is learned.

Linear nested codes, where two or more subcodes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled LDPC codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. The presented multi-step optimization process is applied first to one of the nested codes, then an optimization of the remaining nested codes is carried out based on these code constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes can be completely removed using our proposed optimization strategy.

We consider binary spatially coupled (SC) low density measurement matrices for low complexity reconstruction of sparse signals via the interval passing algorithm (IPA). The IPA is known to fail due to the presence of harmful sub-structures in the Tanner graph of a binary sparse measurement matrix, so called termatiko sets. In this work we construct array-based (AB) SC sparse measurement matrices via algebraic lifts of graphs, such that the number of termatiko sets in the Tanner graph is minimized. To this end, we show for the column-weight-three case that the most critical termatiko sets can be removed by eliminating all length-12 cycles associated with the Tanner graph, via algebraic lifting. As a consequence, IPA-based reconstruction with SC measurement matrices is able to provide an almost error free reconstruction for significantly denser signal vectors compared to uncoupled AB LDPC measurement matrices.