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 in this paper. The improved error bound depends on both the delay of the code and its width (the number of symbols that enter the delay line in parallel) . 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 1). In the limit our error exponent equals the Yudkin–Viterbi exponent derived for time-variant convolutional codes. These results are also used to derive an improved error exponent for periodically time-variant codes.