Computationally efficient soft-decision decoding of linear block codes based on ordered statistics

This paper presents a novel approach to soft decision decoding for binary linear block codes. The basic idea of this approach is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is tightly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the tradeoff between performance and decoding complexity is provided. The proposed decoding is based on the reordering of the received symbols according to their reliability measure. In the paper, the statistics of the noise after ordering are evaluated. Based on these statistics, two monotonic properties which dictate the reprocessing strategy are derived. Each codeword is decoded in two steps: 1) hard-decision decoding based on reliability information and 2) reprocessing of the hard-decision-decoded codeword in successive stages until the desired performance is achieved. The reprocessing is based on the monotonic properties of the ordering and is carried out using a cost function. A new resource test tightly related to the reprocessing strategy is introduced to reduce the number of computations at each reprocessing stage. For short codes of lengths -15 32 or medium codes with 32 < S 5 64 with rate R 2 0.6, nearoptimum bit error performance is achieved in two stages of reprocessing with at most a computation complexity of o( I<' ) constructed codewords, where I< is the dimension of the code. For longer codes, three or more reprocessing stages are required to achieve near-optimum decoding. However, most of the coding gain is obtained within the first two reprocessing stages for error performances of practical interest. The proposed decoding algorithm applies to any binary linear 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 buffer overtlow at low SNR.