We describe a new family of parallelizable bounded distance decoding
algorithms for the Barnes-Wall lattices, and analyze their decoding
complexity.
The algorithms are parameterized by the number
*p = 4*^{k} <= N^{2}
of available processors, work for Barnes-Wall lattices in arbitrary
dimension *N=2*^{n},
correct any error up to squared unique decoding radius
*d*_{min}^{2}/4, and run in worst-case time
*O(N log*^{2} N / p^{1/2}).
Depending on the value of the parameter *p*,
this yields efficient
decoding algorithms ranging from a fast sequential algorithm
with quasi-linear decoding complexity
*O(N log*^{2} N),
to a fully parallel decoding circuit with polylogarithmic depth
*O(log*^{2} N) and polynomially many arithmetic gates.