Algorithms and schedules for turbo equalization
Algorithms and schedules for turbo equalization of partial response channels, such as those encountered in magnetic recording are investigated. Aspects of decoding error-correcting codes transmitted over the erasure channel are also considered.
Ideas of message passing are applied to the problem of removing the effects of intersymbol interference from partial-response channels. Two new algorithms, a bit-based and a state-based message-passing algorithm, are proposed. For a fixed number of iterations less than the block length, the bit-error rate of the state-based algorithm approaches a non-zero constant as the signal-to-noise ratio approaches infinity. For a class of partial-response channels, necessary and sufficient conditions are shown for a precoder to unambiguously map input sequences to output sequences, so that the bit-error rate will approach zero.
Turbo equalization is the application of the turbo principle to joint decoding and detection of error-correcting codes transmitted over a partial-response channel. For low density parity check (LDPC) coded partial-response channels, the scheduling of LDPC iterations over the turbo iterations is considered. It is found that the best schedule depends upon the signal-to-noise ratio, and lower signal-to-noise ratios requires more turbo iterations than LDPC decoder iterations. It is also shown that asymmetric schedules can achieve minimum bit-error rates with the least complexity.
For decoding on the erasure channel, sequence maximum likelihood (ML), and the symbol maximum a posteriori (MAP) decisions are shown to have the same probability of symbol error. It is shown that the number of state metrics of the Viterbi and BUR algorithms are the same and finite. This finiteness leads to three results: exact expressions for the probability of decoder symbol error, exact expressions for the probability of decoder event error, and a lookup table-based decoder implementation, suitable for turbo decoding.
Efficient representation of the BCJR algorithm's state metrics is considered using vector quantization techniques, for detection of partial-response channels with AWGN. The recurrent region for two channel models is visualized, and its vector components are shown to be correlated. The codebook generated by vector quantization is used to propose a soft-output detection algorithm which implements the forward and backward recursions, and the generation of soft outputs, by table lookup.