Short low-rate non-binary turbo codes

A serial concatenation of an outer non-binary turbo code with different inner binary codes is introduced and analyzed. The turbo code is based on memory-1 time-variant recursive convolutional codes over high order fields. The resulting codes possess low rates and capacity-approaching performance, thus representing an appealing solution for spread spectrum communications. The performance of the scheme is investigated on the additive white Gaussian noise channel with coherent and noncoherent detection via density evolution analysis. The proposed codes compare favorably w.r.t. other low rate constructions in terms of complexity/performance trade-off. Low error floors and performances close to the sphere packing bound are achieved down to small block sizes (k =192 information bits).