In recent years, the invention of Turbo codes has spurred much interest in the coding community. Turbo codes are capable of approaching channel capacity closely at a decoding complexity much lower than previously thought possible. Although decoding complexity is relatively low, Turbo codes are still too complex to implement for many practical systems. This work is focused on low complexity channel coding schemes with Turbo-like performance. The issue of complexity is tackled by using single parity check (SPC) codes, arguably the simplest codes known. The SPC codes are used as component codes in multiple parallel and multiple serial concatenated structures to achieve high performance. An elegant technique for improving error performance by increasing the dimensionality of the code without changing the block length and code rate is presented. For high bandwidth efficiency applications, concatenated SPC codes are combined with 16-QAM Bit Interleaved Coded Modulation (BICM) to achieve excellent performance. Analytical and simulation results show that concatenated SPC codes are capable of achieving Turbo-like performances at a complexity which is approximately 10 times less than that of a 16-state Turbo code. A simple yet accurate generalised bounding method is derived for BICM systems employing large signal constellations. This bound works well over a wide range of SNRs for common signal constellations in the independent Rayleigh fading channel. Moreover, the bounding method is independent of the type and code rate of channel coding scheme. In addition to the primary aim of the research, an improved decoder structure for serially concatenated codes has been designed, and a sub-optimal, soft-in-soft-out iterative technique for decoding systematic binary algebraic block codes has been developed.