Block code

Abstract: We introduce space-time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum-likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum-likelihood decoding algorithm which is based only on linear processing at the receiver. Space-time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. The classical mathematical framework of orthogonal designs is applied to construct space-time block codes. It is shown that space-time block codes constructed in this way only exist for few sporadic values of n. Subsequently, a generalization of orthogonal designs is shown to provide space-time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK and QAM, space-time block codes are designed that achieve 1/2 of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three, and four transmit antennas, space-time block codes are designed that achieve, respectively, all, 3/4, and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well.

Abstract: We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders.

Abstract: An optimum method of coding an ensemble of messages consisting of a finite number of members is developed. A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.

Abstract: 1. Coding for Reliable Digital Transmission and Storage. 2. Introduction to Algebra. 3. Linear Block Codes. 4. Important Linear Block Codes. 5. Cyclic Codes. 6. Binary BCH Codes. 7. Nonbinary BCH Codes, Reed-Solomon Codes, and Decoding Algorithms. 8. Majority-Logic Decodable Codes. 9. Trellises for Linear Block Codes. 10. Reliability-Based Soft-Decision Decoding Algorithms for Linear Block Codes. 11. Convolutional Codes. 12. Trellis-Based Decoding Algorithms for Convolutional Codes. 13. Sequential and Threshold Decoding of Convolutional Codes. 14. Trellis-Based Soft-Decision Algorithms for Linear Block Codes. 15. Concatenated Coding, Code Decomposition ad Multistage Decoding. 16. Turbo Coding. 17. Low Density Parity Check Codes. 18. Trellis Coded Modulation. 19. Block Coded Modulation. 20. Burst-Error-Correcting Codes. 21. Automatic-Repeat-Request Strategies.