Synthesis of XOR storage schemes with different cost for minimization of memory contention

Parallel memory modules are widely used to increase memory bandwidth in parallel image processing and numerical analysis. A storage scheme, representing the way how data arrays are stored among parallel memory modules, is crucial to the system performance. XOR-schemes form one general class of storage schemes with easy address generation. In this paper, two classes of XOR-schemes are defined to make the trade-off between the cost of storage scheme implementation and the access efficiency. The column-one scheme is used to minimize the cost and the column-two scheme to reduce the memory access conflicts under moderate cost. The cost and the performance relations among different classes of XOR-schemes are found by simulation study. The general access conflict-free conditions for shifted blocks are found. The genetic algorithm is used to search the design space automatically, which is shown to be more effective than heuristics. A variety of data templates can be handled under our genetic search method, including any power-of-two templates (such as rows, columns, blocks, and crumbled blocks), diagonals, and shifted blocks, etc. The method can be used to synthesize storage schemes for different applications to minimize memory access contention and the implementation cost of the storage scheme