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 <= N² of available processors, work for Barnes-Wall lattices in arbitrary dimension N=2ⁿ, correct any error up to squared unique decoding radius d_min²/4, and run in worst-case time O(N log² 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 log² N), to a fully parallel decoding circuit with polylogarithmic depth O(log² N) and polynomially many arithmetic gates.