Asymptotic Upper Bounds on the Minimum Distance of Trellis Codes
A.R. Calderbank, James E. Mazo, Victor K. Wei · IEEE Transactions on Communications · 1985
A trellis code is a "sliding window" method of encoding a binary data stream as a sequence of signal points in Rn. When a trellis code is used to encode data at the rate ofkbits/channel symbol, each channel input depends not only on the most recent block ofkbits to enter the encoder, but will also depend on a set of ν bits preceding this block. The ν bits determine the state of the encoder and the most recent block ofkbits generates the channel symbol conditional on the encoder state. The performance of a trellis code depends on a suitably defined minimum distance property of that code. This paper obtains upper bounds on this minimum distance that are better than any previously known.