Light Code: Light Analytical and Neural Codes for Channels With Feedback
Sravan Kumar Ankireddy, Krishna R. Narayanan, Hyeji Kim
Abstract
The design of reliable and efficient codes for channels with feedback remains a longstanding challenge in communication theory. While significant improvements have been achieved by leveraging deep learning techniques, neural codes often suffer from high computational costs, a lack of interpretability, and limited practicality in resource-constrained settings. We focus on designing low-complexity coding schemes that are interpretable and more suitable for communication systems. We advance both analytical and neural codes. First, we demonstrate that P<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ower</small> B<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">last</small>, an analytical coding scheme inspired by Schalkwijk-Kailath (SK) and Gallager-Nakiboğlu (GN) schemes, achieves notable reliability improvements over both SK and GN schemes, outperforming neural codes in high signal-to-noise ratio (SNR) regions. Next, to enhance reliability in low-SNR regions, we propose L<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ight</small> C<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ode</small>, a lightweight neural code that achieves state-of-the-art reliability while using a fraction of memory and compute compared to existing deep-learning-based codes. Finally, we systematically analyze the learned codes, establishing connections between L<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ight</small> C<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ode</small> and P<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ower</small> B<sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">last</small>, identifying components crucial for performance, and providing interpretation aided by linear regression analysis.