Baseband Receiver Design for Wireless MIMO-OFDM Communications, 2nd Edition

Chapter 4

Error-Correcting Codes

Error-correcting codes apply some redundant information in the transmitted signal so that errors and/or erasures incurred during transmission can be identified and even corrected. Applying the soft-input soft-output decoders, some powerful codes such as turbo codes and low-density parity-check codes can further enhance the error correction performance.

4.1 Introduction

All communication links are reliable only to a certain extent, and wireless communication systems are no exception. Digital modulation has the advantage that an error made during the transmission can be recovered, since binary information can be regenerated from a corrupted version. The major apparatus for error removal is error-correcting codes, and they play an indispensable role in all wireless communication systems.

An error-correcting code encoder generates redundant information according to the message information. The message and the redundant information are transmitted or stored, during which time they may be corrupted. The decoder exploits the redundancy in the received and garbled data and determines the original message information being sent or stored.

Intuitively, the encoder puts a limit on the number of codewords since some of the data in a codeword are computed from the message and cannot change freely. Therefore, not all possible 2ⁿ n-bit vectors are legitimate codewords. For instance, if the encoder uses k message bits to generate an n-bit codeword, then only ...