Theoretical Method of Calculating Raw Bit-Error-Rate of 2:N Constant-Weight Block Code for Multilayered Waveguide Holographic Memory

Abstract

We present an expression for the probability density functions of the ON and OFF pixels of a 2:N constant-weight block code to estimate the raw bit error rate (BER). We also show that they are similar to Gaussian ones through an analysis of an actual code image reconstructed from a multilayered waveguide holographic memory. From these results, we show that this expression for estimating the raw BER can be obtained using averages and standard deviations of the ON and OFF pixels. Finally, we demonstrate that the relationship between the signal-to-noise ratio and the raw BER derived from the expression for estimating the raw BER closely fits simulation results. This expression is useful for roughly estimating the value of the raw BER from the averages and standard deviations of the ON and OFF pixels.