Bounds of the Probability and of the Number of Correctable Errors for Nonblock Codes

Upper bounds are derived for the number of correctable errors for nonblock codes. Explicit expressions are given for the upper limits of the power of a code as the decoding delay $\tau\to\infty$ for the case where a fixed number $t$ of errors may occur in the interval $\tau$, and for the case where the number of errors $t=\alpha\tau$ increases linearly with $\tau$. These bounds are similar to the Hamming and Elias bounds for block codes. The upper limit of the error probability is also calculated for nonblock transmission over a binary symmetric memoryless channel: the exponential term of this limit is the same as the exponential term for block codes of length $\tau$. It is shown that for transmission rates tending to zero, the exponential term of the error probability converges to the exponential term of the error probability for block transmission at zero rate. It is shown that many estimates also remain valid when feedback is present.