Talk: V. Arvind Rameshwar (September 26, 2023 at 11:00 AM, Seminar room N2409)
Coding Schemes Using Constrained Subcodes Over Input-Constrained Channels
V. Arvind Rameshwar
Department of Electrical Communication Engineering
Indian Institute of Science, Bengaluru.
In this talk, we shall discuss some of our recent work on designing coding schemes for input-constrained memoryless symmetric channels with binary inputs. The (hard) constraints that we work with include runlength limited (RLL) constraints, charge constraints, and weight-based constraints. Such input-constrained channels are common models for intersymbol interference in communication and physical effects in storage media. The simple idea behind our coding schemes is the use of constrained subcodes of capacity-achieving codes, such as Reed-Muller (RM) codes, which ensures vanishing probabilities of decoding error in the large blocklength limit. We first illustrate the design of such constrained codes, using subcodes of RM codes or their variants, for a specific RLL constraint, and briefly present analytically computable achievable rates. Next, we attempt to address the general issue of computing the rates of constrained subcodes of arbitrary linear codes, via elementary Fourier-analytic techniques. Our techniques illustrate the somewhat surprising observation that the Fourier transforms related to many non-linear constraints are computable analytically, or numerically via fast algorithms. Finally, we shall discuss an interesting sampling-based algorithm for approximately computing the rates of arbitrarily constrained subcodes of RM codes. Importantly, this approach allows us to arrive at robust rate estimates of the weight distribution of moderate-blocklength RM codes – a problem that is still wide open.
V. Arvind Rameshwar received the B.E. (Hons.) degree in Electronics and Communication Engineering from BITS Pilani University, India, in 2018. He is now a Research Associate at the Department of Electrical Communication Engineering, Indian Institute of Science, Bengaluru, having submitted his PhD thesis in July 2023. He is a recipient of the Prime Minister's Research Fellowship 2020 and was part of teams that won Qualcomm Innovation Fellowships India 2020, 2022, and 2023. His recent paper, co-authored with his advisor, was a recipient of the Jack Keil Wolf ISIT Student Paper Award 2023. His other works 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 non-standard channels.