ARRAY CODES OVER RINGS AND THEIR TRELLIS DECODING

A class of array codes over rings of integers modulo-q with good Eucli dean distance properties is introduced. Depending on the design, these codes can have linear or nonlinear properties. An extension of a simp le algorithm to design a low-complexity trellis diagram for array code s over GF(2) introduced recently is developed for array codes over rin gs. These codes over rings are compared to the corresponding codes ove r GF(2), where particular attention is given to the coding gain, spect ral efficiency, codebook size and trellis complexity. It is shown that array codes over Z(4) and Z(8) provide a twofold and threefold increa se, respectively, in spectral efficiency as well as a higher coding ga in over uncoded transmission and a much larger codebook than that obta ined with the same array codes over GF(2) for similar code parameters.