In this talk, we shall discuss some recent work on coding schemes for binary input-constrained channels. The (hard) constraints that we work with, find application in alleviating intersymbol interference (ISI) in magnetic and optical recording, in simultaneous energy and information transfer, and in synchronization and timing markers for multimedia streams. In the first part of the talk, the focus will be on constrained coding schemes for memoryless, stochastic noise channels, which are common models in information theory for communication and storage media. We will illustrate the construction of run length-limited (RLL) constrained coding schemes over such channels, using variants of Reed-Muller codes, which are known to achieve the capacities of binary memoryless symmetric (BMS) channels. Next, we discuss a recipe, based on the Fourier-analysis of Boolean functions, which helps us compute (analytically or numerically) the sizes of arbitrarily constrained subcodes of general linear codes. This, in turn, can aid in the calculation of rates achieved by constrained subcodes of linear codes, over input-constrained channels. In the second part of the talk, our interest shifts to input-constrained, adversarial (or worst-case) bit-flip error and erasure channels. In this model, there is a combinatorial upper bound on the number of errors or erasures that affect the constrained codeword. We obtain good numerical upper bounds on the sizes of constrained codes with a prescribed error resilience, via linear programming bounds for constrained systems, which beat the state of the art.
V. Arvind Rameshwar received the B.E. (Hons.) degree in Electronics and Communication Engineering from BITS Pilani University, India, in 2018. He is currently pursuing the Ph.D. degree at the Department of Electrical Communication Engineering, of IISc, Bengaluru. He is a recipient of the Prime Minister's Research Fellowship 2020 and was part of teams that won Qualcomm Innovation Fellowships India 2020 and 2022. His papers, co-authored with his advisor, have won student paper awards at the National Conference on Communications (NCC) 2021 and the IEEE International Conference on Signal Processing and Communications (SPCOM) 2022. His research interests lie in information theory and coding for channels with memory.