33 citations · 160 across the 26 of their papers we have counts for
27 papers
Codes approaching the Shannon limit with polynomial complexity per information bit
Ilya Dumer, Navid Gharavi
We consider codes for channels with extreme noise that emerge in various low-power applications. Simple LDPC-type codes with parity checks of weight 3 are first studied for any dim…
Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
Yi Jiang, Ilya Dumer, Alexey A. Kovalev +1
We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds), such that each model can be obtained from the dual of the other aft…
Numerical and analytical bounds on threshold error rates for hypergraph-product codes
Alexey A. Kovalev, Sanjay Prabhakar, Ilya Dumer +1
We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple mode…
An elementary description of polarization process
Ilya Dumer
We analyze successive cancellation (SC) decoder by using two random functions. The first function is related to the likelihoods of 0 and 1 in each code position, while the second g…
On decoding algorithms for polar codes
Ilya Dumer
We survey the known list decoding algorithms for polar codes and compare their complexity. Index terms: Polar codes; Reed-Muller codes; successive cancellation decoding.
Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes
Ilya Dumer
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length and fixed order An algorithm is designed that has complexity of order a…