Abstmct-We investigate the performance of single and multiple parity codes in magnetic recording systems. We evaluate the codes with respect t o Bit Error Rate as well as ECC failure rate. While multiple parity codes outperform the single parity code in Bit Error Rate, their performance is worse with respect to the ECC failure rate.

Optimization of sup-norm-type performance functions over the space of H ∞ functions is an area of extensive research. In electrical engineering, it is central to the subject of H ∞ design, while in several complex variables, it is often required to produce analytic discs with valuable properties. It has been known for many years that an H ∞-type optimum is frequency independent (flat). In this paper, we study simultaneous (Pareto) optimization of several competing performances Γ 1 ,. .. , Γ l. We find under strong assumptions on the performance functions that if we are optimizing over N functions (f 1 ,. .. , f N) in H ∞ and have l performance measures with l ≤ N , then at a nondegenerate Pareto optimum (f * 1 ,. .. , f * N), every performance is flat. Besides flatness, there are other gradient-alignment conditions which must hold at an optimum. The article presents these and thus gives the precise first-derivative test for a natural class of H ∞ Pareto optima. Such optimality conditions are valuable for assessing how iterations in a computer run are progressing. Also, in the traditional case, optimality conditions have been the base of highly sucessful computer algorithms; see [

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