By Hesse J.
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Additional resources for A p-extremal length and p-capacity equality
26 Hongwei Song and B. V. K. Vijaya Kumar SNR SNRinC Channel Detector C SNRout π SNRinL −1 Decoder L SNRout π Fig. 9. Dynamical model for a turbo equalization system. Assuming that the incoming messages to the bit nodes and check nodes involved in sum product algorithm have Gaussian densities and are independent, it is statistically suﬃcient to track their means at each iteration. 8) where j and k denote column weight and row weight of the LDPC code mb , mu , and mu0 are the means of the density of message passed from bit to check, from check to bit and from channel detector to LDPC decoder, respectively.
Full Turbo Eq. 6dB −5 10 −6 10 4 5 6 7 8 SNR (dB) 9 10 11 Fig. 10. BER vs. SNR for the EPR4 channel concatenated with a rate 8/9 turbo code, a rate 8/9 single convolutional code (SCC), and no outer code. −1 10 Uncoded EPR4 N = 108 N = 1125 N = 4608 N = 11250 −2 10 −3 BER 10 −4 10 −5 10 −6 10 −7 10 3 4 5 6 7 SNR (dB) 8 9 10 11 1 Fig. 11. BER versus SNR for the 1⊕D 2 precoded EPR4 channel concatenated with a rate 8/9 single convolutional code of various block length N . 2 Iterative Codes in Magnetic Storage Systems 31 −1 10 −2 10 −3 BER 10 −4 10 Uncoded EPR4 Turbo, 1/10 iterations Turbo, 10/1 iterations LDPC, 1/15 iterations LDPC, 5/3 iterations SCC, 15/1 iterations −5 10 −6 10 −7 10 4 5 6 7 SNR (dB) 8 9 10 Fig.
The plotted BER and BLER performance correspond to 50 LDPC decoder iterations with the 50th iteration results highlighted. For this 42 Hongwei Song and B. V. K. 4Gbps per iteration with 100 MHz system clock. 5 Conclusions Coding and signal processing are increasingly being recognized as a costeﬃcient approach to achieving substantial areal density growth while preserving the high integrity of magnetic storage systems. While it is well understood that the data dependent noise prediction technique  employed in current read channel achieves near maximum likelihood detection, the recent advances in iterative codes hold the promise to push the areal density to the ultimate coding limit for recording channels.