TY - GEN
T1 - Decoding turbo codes based on their parity-check matrices
AU - Jiang, Fan
AU - Psota, Eric
AU - Pérez, Lance C.
PY - 2007
Y1 - 2007
N2 - The turbo iterative decoding algorithm only performs well for turbo codes with relatively small memories. Moreover, its decoding complexity becomes prohibitively large when the turbo encoders have very large memories. The sumproduct and linear programming decoding algorithms are based on the parity-check matrices of the codes. They are widely used to decode low-density parity-check codes. These algorithms do not suffer the limitations of the turbo iterative decoding algorithm. In order to apply them to the turbo codes, the parity-check matrices of turbo codes must be found. By treating turbo codes as serially concatenated codes, the generator and paritycheck matrices of the turbo codes are derived in this paper. Turbo codes with low-density parity-check matrices are then designed based on the derived results. Provided these matrices, turbo codes are decoded using the sum-product algorithms. Preliminary results show that the sum-product decoding of turbo codes performs slightly worse than sum-product decoding of conventional low-density parity-check codes. However, since the encoding of turbo codes has less complexity than the straightforward encoding of low-density parity-check codes, this loss in performance may be justified by the drastically decreased encoding complexity. The availability of the parity-check matrices of turbo codes also makes them ready to be decoded by the linear programming decoding algorithm which is optimum for the given linear constraints.
AB - The turbo iterative decoding algorithm only performs well for turbo codes with relatively small memories. Moreover, its decoding complexity becomes prohibitively large when the turbo encoders have very large memories. The sumproduct and linear programming decoding algorithms are based on the parity-check matrices of the codes. They are widely used to decode low-density parity-check codes. These algorithms do not suffer the limitations of the turbo iterative decoding algorithm. In order to apply them to the turbo codes, the parity-check matrices of turbo codes must be found. By treating turbo codes as serially concatenated codes, the generator and paritycheck matrices of the turbo codes are derived in this paper. Turbo codes with low-density parity-check matrices are then designed based on the derived results. Provided these matrices, turbo codes are decoded using the sum-product algorithms. Preliminary results show that the sum-product decoding of turbo codes performs slightly worse than sum-product decoding of conventional low-density parity-check codes. However, since the encoding of turbo codes has less complexity than the straightforward encoding of low-density parity-check codes, this loss in performance may be justified by the drastically decreased encoding complexity. The availability of the parity-check matrices of turbo codes also makes them ready to be decoded by the linear programming decoding algorithm which is optimum for the given linear constraints.
UR - http://www.scopus.com/inward/record.url?scp=34548139795&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34548139795&partnerID=8YFLogxK
U2 - 10.1109/SSST.2007.352352
DO - 10.1109/SSST.2007.352352
M3 - Conference contribution
AN - SCOPUS:34548139795
SN - 1424411262
SN - 9781424411269
T3 - Proceedings of the Annual Southeastern Symposium on System Theory
SP - 221
EP - 224
BT - Proceedings of the Thirty-Ninth Southeastern Symposium on System Theory, SSST
T2 - 2007 39th Southeastern Symposium on System Theory, SSST
Y2 - 4 March 2007 through 6 March 2007
ER -