yage
" ... whereas subsequent constructions interpret the message as the values of the polynomial at the first k points a 1 , … , a k {displaystyle a_{1},dots ,a_{k}} and obtain the polynomial p by interpolating these values with a polynomial of degree less than k ..."
There’s no interpolation happening when performing error correction since there’s no ’guessing’You are mistaken. Interpolation is "guessing" by definition (in this context) and interpolation is part of the CD standard.
The proper bits are either recovered or the data stream is so corrupted that some errors remain. In the latter case, the player may mute the output or cease playback.That’s how a data disc works because it has to be bit perfect. But it’s not how digital audio works at all. The Reed-Solomon error correction code is part of the CD standard and, as MC noted, it’s all part of the fun math that makes digital audio:
" ... whereas subsequent constructions interpret the message as the values of the polynomial at the first k points a 1 , … , a k {displaystyle a_{1},dots ,a_{k}} and obtain the polynomial p by interpolating these values with a polynomial of degree less than k ..."