Soft decision decoding of linear block codes based on ordered statistics

Soft decision decoding of linear block codes has been investigated for many years and several decoding schemes based on the reordering of the received symbols according to their reliability have been proposed. In this paper, we derive the ordered statistics of the noise after ordering and develop a simple algorithm based on these ordered statistics. This algorithm consists of successive reprocessing stages. For each stage, the error performance can be evaluated. For short codes of lengths up to 64, the optimum bit error performance is achieved in two stages of reprocessing, with at most a computation complexity of o(K ²) constructed codewords. For longer codes three or more reprocessing stages are required to achieve optimum decoding. The proposed algorithm applies to any linear block code, does not require any data storage and is well suitable for parallel processing. Furthermore, the maximum number of computations required at each reprocessing stage is fixed, which prevents the overflow problem at low SNR