Sampling-based estimates of the sizes of constrained subcodes of Reed-Muller codes
VA Rameshwar, S Jain… - 2024 National Conference …, 2024 - ieeexplore.ieee.org
This paper develops an algorithmic approach for obtaining approximate, numerical
estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which
satisfy a given constraint. Our algorithm is based on a statistical physics technique for
estimating the partition functions of spin systems, which in turn makes use of a sampler that
produces RM codewords according to a Gibbs distribution. The Gibbs distribution is
designed so that it is biased towards codewords that respect the constraint. We apply our …
estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which
satisfy a given constraint. Our algorithm is based on a statistical physics technique for
estimating the partition functions of spin systems, which in turn makes use of a sampler that
produces RM codewords according to a Gibbs distribution. The Gibbs distribution is
designed so that it is biased towards codewords that respect the constraint. We apply our …
Sampling-Based Estimates of the Sizes of Constrained Subcodes of Reed-Muller Codes
This paper develops an algorithmic approach for obtaining approximate, numerical
estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which
satisfy a given constraint. Our algorithm is based on a statistical physics technique for
estimating the partition functions of spin systems, which in turn makes use of a sampler that
produces RM codewords according to a Gibbs distribution. The Gibbs distribution is
designed so that it is biased towards codewords that respect the constraint. We apply our …
estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which
satisfy a given constraint. Our algorithm is based on a statistical physics technique for
estimating the partition functions of spin systems, which in turn makes use of a sampler that
produces RM codewords according to a Gibbs distribution. The Gibbs distribution is
designed so that it is biased towards codewords that respect the constraint. We apply our …
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