Multiple Hybrid Concatenated Single Parity Check Codes

Concatenated codes have not only the generally known serial and parallel concatenated coding structures, but also the uncommon hybrid concatenated coding structure. Utilizing SPC codes as constituent codes, this paper considers the three coding structures in a uniform way. A uniform description of the three coding structures is illustrated and a kind of generalized iterative decoding structure suitable for the three coding structures is also presented. In addition, the comparison of upper bounds to the bit-error-probability for multiple concatenated SPC codes is performed with the three coding structures. The bounds and simulation results show that different coding structures have different but regular performance variation: (1) the performance of various hybrid concatenated SPC codes is always lying in between the performance of parallel and serial concatenated SPC codes; (2) when code rate increases, the performance crossover between parallel and serial concatenated SPC codes moves to lower bit-error rate (BER) region and their performance difference decreases.