Vector symbol decoding with list inner symbol decisions

Abstract Error correcting codes can play a key role in improving the efficiency and reliability of wireless communications. Concatenated codes have the advantages that: 1) breaking the task into stages simplifies decoding, and 2) performance is good against clustered bit errors, fading and bursty interference. Reed-Solomon codes (maximum distance codes) have been popular as an outer code of concatenated codes because of their feature of maximum minimum distance between code words. Recently, block Vector Symbol Decoding (VSD) has been introduced. Block VSD has been shown to achieve in many cases a better decoder success probability than Reed-Solomon code decoding. VSD decoding is a fairly simple technique applicable to a broad class of codes. Recently it has been shown capable of using multiple choices provided by the inner decoder or by macrodiversity inner symbol decoding, at little or no addition in complexity. In this present paper, we extend the work on VSD to a method of using VSD with (n-1)/n outer convolutional codes and list of two inner symbol decisions. The convolutional technique has the advantage over the block technique in that most corrections are almost immediate based on observation of only one or a few syndromes. (Some error events require consideration of significantly larger numbers of syndromes, however.) A method for computing the parity check matrix for (n-1)/n nonsystematic convolutional codes, which is essential for VSD, is also presented. In addition, the detail of the decoding steps is described. Performance simulations are made for a simplified fading channel with a rate 2/3 terminated nonsystematic convolutional outer code. The inner code per outer symbol is also a terminated convolutional code, using list Viterbi decoding (LVA) to provide the list decision choices. It is found that the decoding failure probability of the whole received sequence and the post-decoded inner symbol error probability is about two orders of magnitude lower than that of a maximum distance code decoder of the same symbol length and data rate.