Symbol-by-Symbol MAP Decoding of Nonbinary Codes

Symbol-by-symbol maximum a posteriori (MAP) decoding algorithms for linear nonbinary block and convolutional codes over both extension fields GF(q = p a ) and integer rings Z q are presented. Equivalent MAP decoding rules employing the dual code are given which are computationally more efficient for high-rate codes. The suitability of the proposed algorithms is demonstrated by applying them to a parallel concatenated coding scheme with nonbinary component codes. 1 Introduction Recently, symbol-by-symbol MAP decoding has regained attention with the presentation of powerful concatenated "turbo"-(de)coding schemes [1][2]. Turbo codes are of interest in a wide range of telecommunications applications and were originally composed of two binary component codes in conjunction with binary modulation. Approaches have been undertaken to combine turbo codes with higher order modulation, where binary component codes [3] or Ungerboecklike codes[4] can be used. In this article we discuss symbol-..