Two-Phase Channel Quantization and Mapping

• Published in: IEEE transactions on communications Vol. 73; no. 1; pp. 363 - 377
• Main Authors: Philosof, Tal, Kissos, Lior, Doubchak, Ariel, Dergachov, Jenny, Berman, Amit
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; channel capacity; Channel quantization; Communications systems; Constraints; Decoding; Dynamic programming; Flash memories; Heuristic algorithms; Information systems; Mapping; mutual information maximization; Optimization; Quantization (signal); Reflective binary codes; Thresholds; Viterbi algorithm
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2024.3439428

Channel quantization is commonly used in non-volatile memories and front-end communication systems. The general setting of channel quantization and mapping involves two phases: a contiguous quantization subject to a specified number of thresholds, referred to as the threshold-constrained, and a mapping with restricted output cardinality. The latter constraint stems from limitations in data throughput and the complexity of post-processing. The objective of this study is to maximize mutual information at the output of the channel quantization and mapping block. We demonstrate that, given a predefined mapping, an optimal solution exists for threshold-constrained using a dynamic programming algorithm. This approach is particularly suitable for non-volatile memory architectures, where the read process involves establishing read thresholds modeled as contiguous quantization. The incorporation of mapping is crucial due to constraints on output cardinality. Furthermore, we provide sufficient conditions for achieving the global optimal solution to the general channel quantization and mapping problem, which involves joint optimization of contiguous quantization and mapping.