Progressive algebraic Chase decoding algorithms for Reed–Solomon codes

Abstract

This study proposes a progressive algebraic Chase decoding (PACD) algorithm for Reed–Solomon (RS) codes. On the basis of the received information, 2 η (η > 0) interpolation test-vectors are constructed for the interpolation-based algebraic Chase decoding. A test-vector reliability function is defined to assess their potential for yielding the intended message. The algebraic Chase decoding will then be performed progressively granting priority to decode the test-vectors that are more likely to yield the message, and is then terminated once it is found. Consequently, the decoding complexity can be adapted to the quality of the received information. An enhanced-PACD (E-PACD) algorithm is further proposed by coupling the PACD algorithm with the adaptive belief propagation (ABP) decoding. The ABP decoding generates new test-vectors for the PACD algorithm by enhancing the received information. It improves the Chase decoding performance without increasing the decoding complexity exponentially. It is shown that the E-PACD algorithm's complexity can be significantly reduced by utilising the existing interpolation information of the previous Chase decodings'. Our performance evaluations show that the two proposed decoders outperform a number of existing algebraic decoding approaches. Complexity and memory analyses of the PACD algorithm are also presented, demonstrating that this is an efficient RS decoding strategy.