Parallel Heuristic Methods to Accelerate Best Equivocation Code Generation

In this paper, we propose parallel heuristic methods to accelerate the generation of
$(n,m)$
best equivocation code (BEC), where
$n$
and
$m$
are code and message lengths, respectively. The proposed dynamic programming (DP) method and greedy method extend a previous heuristics method by reducing the time complexity of the code generation process. The DP method produces the same codes as the previous method but incurs an overhead for data reuse. In contrast, the greedy method avoids this overhead but generates slightly different codes due to its heuristic approach. We parallelize the proposed methods by exploiting coarse-grained and fine-grained parallelisms, which achieve further acceleration on multicore CPU and graphics processing unit (GPU) systems, respectively. Experimental results demonstrate that the proposed DP and greedy methods reduce the sequential generation time to a quarter, as indicated by theoretical complexity analysis. In addition, the parallel implementation achieves linear speedup on a multicore CPU system, and the GPU implementation realizes coalesced memory accesses, resulting in
$17\times $
acceleration over the eight-core CPU implementation. We found that the greedy method produced different codes that differ from the previous and DP methods; however, the generated codes had higher equivocation rates than those generated by a naive random method. We believe that the proposed parallel methods can effectively accelerate BEC generation for large
$m$
and
$n$
values, especially with larger values of
$n$
relative to
$m$
.