New syndrome decoding techniques for the (n,k) convolutional codes

This paper presents a new syndrome decoding algorithm for the (n,k) convolutional codes (CCs). The construction of the trellis diagram of this algorithm is simpler than the syndrome decoding algorithms of Schalkwijk, Vinck and De Paepe. The new algorithm is based on the general solution of the syndrome equation, a linear diophantine equation for the error polynomial vector E(D). The set of diophantine solutions is a coset of the CC. In this error coset a recursive, Viterbi-like, algorithm is developed to find the minimum weight error vector E(D). An example, illustrating the new decoding algorithm is given for the binary nonsystematic (3,1) CC.