Aditya Siddheshwar supervised by Dr. Prasad Krishnan  received his Master of Science  in Electronics and Communication Engineering (ECE). Here’s a summary of his research work on Recursive Subproduct Codes:

Error-correcting codes are mathematical objects that are useful for mitigating errors due to noise, but they are also fundamental to other problems, such as designing and ensuring the privacy and efficiency of storage systems. Reed-Muller codes is one such family of codes that is widely used across these diverse applications, but these codes have limited flexibility in parameters like rate and length, which are required in many cases. In this thesis, we propose a new family of codes similar to Reed-Muller codes and study their properties and decoding. We study a family of subcodes of the m-dimensional product code C⊗m (‘subproduct codes’) that have a recursive Plotkin-like structure, and which include Reed-Muller (RM) codes and Dual Berman codes as special cases. We denote the codes in this family as C⊗[r,m], where 0 ≤ r ≤ m is the ‘order’ of the code. These codes allow a ‘projection’ operation that can be exploited in iterative decoding, viz., the sum of two carefully chosen subvectors of any codeword in C⊗[r,m] belongs to C⊗[r−1,m−1]. Recursive subproduct codes provide a wide range of rates and block lengths compared to RM codes while possessing several of their structural properties, such as the Plotkin-like design, the projection property, and fast ML decoding of first-order codes. Our simulation results for first-order and second order codes, that are based on a belief propagation decoder and a local graph search algorithm, show instances of subproduct codes that perform either better than or within 0.5 dB of comparable RM codes and CRC-aided Polar codes.

August 2025