Improved error exponent for time-invariant and periodically time-variant convolutional codes

An improved upper bound on the error probability (first error event) of time-invariant convolutional codes, and the resulting error exponent, is derived. The improved error bound depends on both the delay of the code K and its width (the number of symbols that enter the delay line in parallel) b. Determining the error exponent of time-invariant convolutional codes is an open problem. While the previously known bounds on the error probability of time-invariant codes led to the block-coding exponent, we obtain a better error exponent (strictly better for b>1). In the limit b→∞ our error exponent equals the Yudkin-Viterbi (1967, 1971, 1965) exponent derived for time-variant convolutional codes. These results are also used to derive an improved error exponent for periodically time-variant codes