IEEE TRANSACTIONS ON COMMUNICATIONS. VOL 50. NO. 1 JANUARY 2002 1000001000100 Fig 4. Example of a parity-check matrix P for an(n, k.t.j)=(20. 5. 3. 4)regular LDPC code with code rate 1/4, block length n= 20, column weight t=3, and row weight 工FFT LDPC Coded MPSK Bits Encoder Bits Modulator symbola/S/p 工F LETT Fig. 5. Transmitter structure of an LDPC-based STC-OF DM system with multiple antennas. The LDPC codes have the following advantages for the to minimize the loss in the effective length between the binary STC-OFDM system considered here. 1)the LdPC decoder LDPC code bits and the modulated StC code symbols, which usually has a lower computational complexity than the is caused by the MPSK(or MQAM)modulation turbo-code decoder. In addition to this, since the decoding As an example, consider a regular binary LDPC code with complexity of each iteration in an LDPC decoder is much column weight t =3, rate R= 1/2 and block-length n less than a turbo-code decoder, a finer resolution in the per- 1024, the minimum distance is around 100 [11]. The STC based formance-complexity tradeoff can be obtained by varying the on this LDPC code is configured with a QPsk modulator and maximum number of iterations. Moreover, the decoding of two transmitter antennas, therefore the effective length of this LDPC is highly parallelizable. 2)The minimum distance of LDPC-based STC is at least 25, which is more than enough binary LDPC codes increases linearly with the block length to satisfy the minimum effective length requirement for a two with probability close to 1 [11]. 3)It is easier to design a transmitter antenna (N=2)OFDM system in a Six-tap(L=6) competitive LDPC code with any block-length and any code frequency-selective fading channel. Together with its built-in rate, which makes it easier for the LDPC-based STC to scale random interleaver, this LdPC code can well satisfy the two according to different system requirements (e.g, different coding design principles mentioned earlier and therefore is an number of antennas or different information rate). 4)LDPC empirically good STC for the OFDM system considered in this codes do not typically show an error floor, which is suitable for paper. Since the minimum distance of binary LDPC codes in short-frame applications. 5)Due to the random generation of crease linearly with the block length, further performance im parity-check matrix(or equivalently the encoder matrix), the provement is possible by increasing the block length. Note that, coded bits have been effectively interleaved; therefore, no extra we do not claim the optimality of the proposed LDPC-based interleaver is needed STC, but rather, we argue that with its low decoding complexity, The transmitter structure of an LDPC-based STC-OFDM flexible scalability and high performance, the LDPC-based STO system is illustrated in Fig. 5. Denote the set of all possible is a promising coding technique for reliable high-speed data STC symbols, which is up to a constant Vy of the traditional communication in multiple-antenna OFDM systems with fre constellation, e.g., MPSK or MQAM (recall that the additive quency-and time-selective fading noise is assumed to have unit variance). The(PKlog2l e)c Data Burst sructure encoder into(NPKlog2 12) coded bits and then the binary As in a typical data communication scenario, communication LDPC coded bits are modulated into(NPK) STC symbols is carried out in a burst manner. a data burst is illustrated in by an MPSK (or MQAM)modulator. These(NPK STC Fig. 6. It spans(Pa+ 1)OFDM words, with the first OFDM into N streams; the (PK)STC symbols of each stream are oFD( ntaining known pilot symbols.The mbols, which correspond to an STC code word, are split word words contain q STC code words transmitted from one particular transmitter antenna at K subcarriers and over P adjacent OFDM slots. Note that, in such VI TURBO RECEIVER a bit-interleaved coded-modulation system proposed above, the In this section, we consider receiver design for the proposed built-in random interleaver of the LDPC codes is also helpful LDPC-based STC-OFDM system. Even with ideal CSl, the80 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 50, NO. 1, JANUARY 2002 Fig. 4. Example of a parity-check matrix P for an (n; k; t; j)=(20; 5; 3; 4) regular LDPC code with code rate 1=4, block length n = 20, column weight t = 3, and row weight j = 4. Fig. 5. Transmitter structure of an LDPC-based STC-OFDM system with multiple antennas. The LDPC codes have the following advantages for the STC-OFDM system considered here. 1) the LDPC decoder usually has a lower computational complexity than the turbo-code decoder. In addition to this, since the decoding complexity of each iteration in an LDPC decoder is much less than a turbo-code decoder, a finer resolution in the per￾formance-complexity tradeoff can be obtained by varying the maximum number of iterations. Moreover, the decoding of LDPC is highly parallelizable. 2) The minimum distance of binary LDPC codes increases linearly with the block length with probability close to 1 [11]. 3) It is easier to design a competitive LDPC code with any block-length and any code rate, which makes it easier for the LDPC-based STC to scale according to different system requirements (e.g., different number of antennas or different information rate). 4) LDPC codes do not typically show an error floor, which is suitable for short-frame applications. 5) Due to the random generation of parity-check matrix (or equivalently the encoder matrix), the coded bits have been effectively interleaved; therefore, no extra interleaver is needed. The transmitter structure of an LDPC-based STC-OFDM system is illustrated in Fig. 5. Denote the set of all possible STC symbols, which is up to a constant of the traditional constellation, e.g., MPSK or MQAM (recall that the additive noise is assumed to have unit variance). The ( ) information bits are first encoded by a rate 1 LDPC encoder into ( ) coded bits and then the binary LDPC coded bits are modulated into ( ) STC symbols by an MPSK (or MQAM) modulator. These ( ) STC symbols, which correspond to an STC code word, are split into streams; the ( ) STC symbols of each stream are transmitted from one particular transmitter antenna at subcarriers and over adjacent OFDM slots. Note that, in such a bit-interleaved coded-modulation system proposed above, the built-in random interleaver of the LDPC codes is also helpful to minimize the loss in the effective length between the binary LDPC code bits and the modulated STC code symbols, which is caused by the MPSK (or MQAM) modulation. As an example, consider a regular binary LDPC code with column weight 3, rate 1 2 and block-length 1024, the minimum distance is around 100 [11]. The STC based on this LDPC code is configured with a QPSK modulator and two transmitter antennas, therefore the effective length of this LDPC-based STC is at least 25, which is more than enough to satisfy the minimum effective length requirement for a two transmitter antenna ( 2) OFDM system in a six-tap ( 6) frequency-selective fading channel. Together with its built-in random interleaver, this LDPC code can well satisfy the two coding design principles mentioned earlier and therefore is an empirically good STC for the OFDM system considered in this paper. Since the minimum distance of binary LDPC codes in￾crease linearly with the block length, further performance im￾provement is possible by increasing the block length. Note that, we do not claim the optimality of the proposed LDPC-based STC; but rather, we argue that with its low decoding complexity, flexible scalability and high performance, the LDPC-based STC is a promising coding technique for reliable high-speed data communication in multiple-antenna OFDM systems with fre￾quency- and time-selective fading. C. Data Burst Structure As in a typical data communication scenario, communication is carried out in a burst manner. A data burst is illustrated in Fig. 6. It spans ( 1) OFDM words, with the first OFDM word containing known pilot symbols. The remaining ( ) OFDM words contain STC code words. VI. TURBO RECEIVER In this section, we consider receiver design for the proposed LDPC-based STC-OFDM system. Even with ideal CSI, the op-