Approximating the protection offered by a channel code in terms of bit error rate

In many joint source-channel coding applications, there is a need to assess the performance of a system on a given channel, with different combinations of channel codes. What is interesting is to know some measure of the overall bit error rate, in order to design the source and/or channel codes accordingly. We propose here an approximation of the bit error rate of the cascade of a linear block code and a memoryless binary channel. With this approximation, both of these components can be considered in this respect as a single binary symmetric channel, with known transition probability, and can be used as such for further processing. We also show some possible applications in joint source-channel coding schemes.