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Iterative Codes The discovery of turbo codes has been an important breakthrough in improving performance of many communication systems. Turbo codes effectively achieve random coding and thereby allow reliable communication at data rates near capacity in many channels, yet they posses enough structure to enable practical encoding and decoding. One significant characteristic of turbo codes is the interleaver gain, which is substantially different from the traditional coding approach of improving distance properties. This appears to make turbo coding applicable to a broad class of communication channels with different signal and noise/interference characteristics. Impressive coding gains and simulation performances of turbo codes on various channels, including the magnetic recording channel, have been demonstrated by several researchers. However, there still exist some serious obstacles, such as high complexity and large memory requirements for the decoding operation. Low-density parity-check (LDPC) codes have also attracted interest as a viable alternative to various forms of turbo codes. LDPC codes are based on using a sparse, non-systematic parity check matrix. Their performance has been shown to be comparable to that achieved by using turbo codes. In fact, irregular LDPC codes with large block lengths have been shown to outperform turbo codes. Decoding of LDPC codes can be done by iterative exchange of soft information between the channel decoder and LDPC decoder, as is done in turbo equalization. The LDPC decoder uses the sum-product algorithm, which is also know as the message-passing algorithm or as belief propagation. While decoding can be performed using a massively parallel architecture, complexity of encoder is very high in LDPC codes. A practical solution to this problem is to force the parity check matrix to have an identity matrix as its left-hand side submatrix. The effect is that both the generator matrix and the parity check matrix are sparse, leading to both simple encoding and decoding. Unlike in usual LDPC codes, the parity bits are now unprotected by the parity checks, resulting in some performance loss. However, simulation results show that in ISI channels like magnetic recording, the performance loss is small. Hardware implementation issues have also been investigated based on FPGA. For more information see
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