Decoding method and decoding device for a CDMA transmission system for demodulating a received signal available in serial code concatenation

A decoding method for demodulating a received signal available in serial code concatenation in a code-division multiple access transmission system, a two-step coding being carried out at the transmitting end of the transmission system, a first step of the two-step coding including a Hadamard orthogonal multi-step inner code, a second step of the two-step coding including an outer error-correcting code of a predefined rate, the method comprising:

• providing a soft-in/soft-out decoder in a receiver of the transmission system, a first decoder step of the soft-in/soft-out decoder including an inner decoder, a second decoder step of the soft-in/soft-out decoder including an outer decoder;
• and
• processing soft values as reliability information at an output and an input of the soft-in/soft-out decoder, a soft output of the inner decoder being a soft input for the outer decoder, a channel reliability information output from a preceding demodulation being an input for the inner decoder,
• wherein the first decoder step of the soft-in/soft-out decoder and the second decoder step of the soft-in/soft-out decoder are configured to decode the received signal coded in the two-step coding,
• wherein the receiver includes a coherent receiver structure, wherein a soft input of the inner decoder includes a-priori information for systematic bits of Walsh functions of the inner code, and wherein the inner code includes a Hadamard code, the Hadamard code being decoded by:
• adding an a-priori information vector L(u) for systematic bits of a Walsh function of the Hadamard code to an input vector Lc·y from a channel;
• performing a fast Hadamard transformation so as to provide a fast Hadamard transform resultant vector w;
• then generating exponential functions with ½·wj as an argument, wj being a respective element of the vector w;
• and
• adding, dividing and expressing logarithmically elements of a result vector z for each symbol ûK to be decoded according to the equation:
• ln ⁢ ⁢ ∑ j , u k = + 1 N - 1 ⁢ z j ∑ j , u k = - 1 N - 1 ⁢ z j = ⁢ ln ⁢ ⁢ ∑ j , u k = + 1 N - 1 ⁢ exp ⁡ ( 1 2 ⁢ ⁢ w j ) ∑ j , u k = - 1 N - 1 ⁢ exp ⁡ ( 1 2 ⁢ ⁢ w j ) = ⁢ ln ⁢ ( ∑ j , u k = + 1 N - 1 ⁢ exp ⁡ ( 1 2 ⁢ ⁢ w j ) ) Term ⁢ ⁢ 1 - ln ⁢ ⁢ ( ∑ j , u k = - 1 N - 1 ⁢ exp ⁡ ( 1 2 ⁢ ⁢ w j ) ) Term ⁢ ⁢ 2
• zj being a respective element of the resultant vector z, j being a respective vector element index, N being a size of the Walsh functions of the inner code;
• wherein, with respect to Term 1 and Term 2 of the equation, for each step at least one maximum is used so as to provide a simplified decoder instruction of the equation, the simplified decoder instruction expressed by the relation:
• ⁢ ≈ ⁢ ln ⁢ ⁢ ( max j , u k = + 1 ⁢ [ exp ⁡ ( 1 2 ⁢ ⁢ w j ) ] ) - ln ⁢ ⁢ ( max j , u k = - 1 ⁢ [ exp ⁡ ( 1 2 ⁢ ⁢ w j ) ] ) = ⁢ 1 2 ⁢ max j , u k = + 1 ⁢ [ w j ] - 1 2 ⁢ max j , u k = - 1 ⁢ [ w j ]
• so that L I ⁡ ( u ^ k ) ≅ 1 2 · max j , u k = + 1 ⁢ ( w j ′ ) - 1 2 · max j , u k = - 1 ⁢ ( w j ′ ) ,
• wj being a respective element of the vector w, LI(ûk) being the soft output of the inner decoder, u being a bit, y being a vector.