Wireless channel is not very conducive towards error-free raw data transmission. On the other hand the tremendous growth in wireless services has made the channel bandwidth a scarce resource and effective utilization of this resource is mandatory. Thus it is instructive to know the limits of a wireless channel. Shannonâ s theorems on channel capacity have been used so far to find the maximum rate at which data can be transmitted over any noisy channel. The theorem calculates the minimum signal to noise ratio (SNR) required to transmit data across a channel with zero probability of sequence error. However the result is practically inhibitive, as it requires encoding and decoding of infinite length code sequences. Practical finite codes never achieve this zero error limit. For practical code design bit-error-rate is often a preferred metric over sequence error rate. However there is no satisfactory method to compare the Shannonâ s capacity results with the bit error rate performance of the practical codes. We introduce the notion of distorted channel capacity to bridge this gap. This measure defines the capacity of a channel when a particular bit-error-rate is allowed. It can also be used as a benchmark to measure the â goodnessâ of a code. Our results show that most of the practical codes lie far beyond the capacity limit. We see that Turbo codes and the convolutional codes come close to this achievable at a prohibitively large computational cost. Specifically, for the convolutional codes the performance improves with large constraint length codes. However the optimal decoding complexity of the convolutional codes grow exponentially with this parameter. We propose a suboptimal decoding technique that has linear complexity in the size of the constraint length and provides close to optimal performance. We further extend our results to a multiuser environment. The optimal joint decoding complexity of multiple users data symbols is exponential in the number of users. Our proposed iterative joint interference cancellation and decoding technique provides computational gain without performance loss.