A Note on Comparison of Error Correction Codes

Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different error correction codes. We present results on the comparison of block error correction codes using the representation of error correction code as a linear experiment. In this case the code comparison is based on the Loewner matrix ordering of respective code matrices. Next, we demonstrate the bit-error rate code performance comparison based on the representation of the codes as dichotomies, in which case the comparison is based on the matrix majorization ordering of their respective equivalent code matrices.