33 citations · 160 across the 26 of their papers we have counts for
13 papers · 1 filter
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…
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…
Soft decision decoding of Reed-Muller codes: recursive lists
Ilya Dumer, Kirill Shabunov
Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of…
Recursive List Decoding for Reed-Muller Codes
Ilya Dumer, Kirill Shabunov
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and s…