Parity insertion with precoder feedback in a read channel

[0002] The present invention relates generally to write precoders for use in magnetic storage disk drives and more particularly to a method and apparatus for detecting and controlling errors within a data stream through a write precoder.

[0003] Conventional magnetic storage devices include a magnetic transducer or “head” suspended in close proximity to a recording medium, for example, a magnetic disk having a plurality of concentric tracks. The transducer is supported by an air-bearing slider mounted to a flexible suspension. The suspension in turn is attached to a positioning actuator. During normal operation, relative motion is provided between the head and the recording medium as the positioning actuator dynamically positions the head over the desired track. The information recorded on the magnetic disk is transmitted to a preamplifier which is in turn transmitted to a read channel. One example of read channels in use in today's technology is a PRML read channel.

[0004] The magnetic recording channel can be characterized as a channel with significant intersymbol interference, particularly at high recording densities. Partial response maximum likelihood (PRML) detection systems based on shaping the channel response to a suitable partial response have become a popular detection method for such channels. Partial responses such as class IV partial response (PR4) and enhanced PR4 (EPR4) are common due to their good performance on moderate density and high density channels. At higher densities, higher order polynomials such as EEPR4 have been proposed. These partial responses are of the form (1−D)(1+D)ⁿ, with n determining the order of the polynomial. As n increases, the high frequency response is attenuated, hence better matching the high frequency attenuation of the magnetic recording channel at high recording densities.

[0005] As recording densities increase, the use of trellis-based coding schemes have also been proposed. These include matched spectral null coding schemes based on the matched spectral null theorem. These have been used to increase the minimum distance on the PR4 based target from 2{square root over (2)} to 4 and have achieved efficient implementations with practical code rates of 8/10 through the use of time varying trellises.

[0006] At higher recording densities with higher order partial responses, run length constrained codes demonstrate improved distance properties. For example, the use of an EEPR4 target with a 2/3(1,7) code increases the minimum distance from 2{square root over (6)} to 2{square root over (10)}. Codes achieving the same increase in minimum distance but without the “d=1” constraint such as maximum transition run length (MTR) codes have been proposed for the EEPR4 partial response and finite delay tree search type detectors. These run length constrained codes help simplify the target trellis by eliminating states. Even higher rate codes to achieve the same increase in minimum distance have also been proposed. These include a family of codes and the rate 8/9 code based on a time varying MTR (TMTR) constraint.

[0007] Coding to detect and eliminate certain error events on the PR4 channel was considered. The eliminated error events were the ones most likely due to noise correlation from the equalization to the PR4 response. This achieved an increase in detection SNR of ≈1.25 dB with a rate 8/9 code at recording densities around 2 bits per PW₅₀.

[0008] A single bit parity code is utilized to detect the presence of the identified dominant error events. This coding constraint can achieve a moderate coding gain but with a high code rate which is desirable for high density magnetic recording. For the detection of the coded data, a postprocessor is possible based on correlating the received signal to identify the likely locations of the error events. The most likely event is then corrected.

[0009] The basic recording and detection system model is shown in FIG. 5 with the channel response based on the Lorentzian step response. The channel frequency response is

[0010] H_chan(𝑓)=jπPW₅₀sin (π𝑓T)e^−|πPW

[0011] where PW₅₀is the half amplitude pulse width and T is the recorded bit period.

[0012] The recording channel is often shaped to the required target frequency response G(𝑓) through the use of a continuous time and discrete time filter. For the purpose of analysis, the continuous time filter is assumed to band limit the signal and equalize it to the desired response before sampling at the baud rate 1/T. The equalizer is assumed to minimize the mean square error between the equalizer output and the desired target. This requires an equalizer response of $E\left(f\right)=\frac{S_x\left(f\right)G\left(f\right)H_{\mathrm{chan}}^{*}\left(f\right)}{N\left(f\right)+{\left|H_{\mathrm{chan}}\left(f\right)\right|}^2{S}_x\left(f\right)}$

[0013] where S_x(𝑓) is the power spectral density of the input data and N(𝑓) is the noise power spectral density at the channel output. At the detector input, the signal consists of the input signal shaped to the desired partial response plus correlated noise with a power spectral density of $N_d\left(f\right)=\frac{1}{T}\left(S_x\left(f\right){\left|G\left(f\right)-H_{\mathrm{chan}\left(f\right)}E\left(f\right)\right|}^2+N\left(f\right){\left|E\left(f\right)\right|}^2\right).$

[0014] While this includes distortion, it is considered as Gaussian noise for the purpose of analysis and the noise autocorrelation is assumed to be $R\left(k\right)=T{\int }_{-1/2T}^{1/2T}{N}_d\left(f\right)e^{\mathrm{j2\pi }\mathrm{fkT}}df.$

[0015] With maximum likelihood detection, the error rate performance is determined by the distance between any two allowable data sequences and the noise correlation. The probability of an error event occurring in the presence of correlated noise can be calculated as $P\left(\mathrm{ErrorEvent}\right)=Q\left(\frac{\sum _{k=0}^J\frac{e_k^2}{2}}{\sqrt{\sum _{k=0}^J{e}_k^2{R}_n\left(0\right)+\sum _{i=0}^J\sum _{j=0,j\ne i}^J{e}_i{e}_j{R}_n\left(i-j\right)}}\right)$

[0016] where the error event {e₀,e₁,. . . , ej} is the difference between any two possible noiseless sequences at the detector input and R(k) is the noise autocorrelation at the detector input. The corresponding error event in terms of channel input symbols will be denoted a_kwith

[0017] e_k=a_kg_k

[0018] where * denotes convolution and the sequence g_kis the inverse D transform of the desired target response G(D).

[0019] The error rate performance of the system depends on the likelihood of error events occurring and the noise correlation. As the recording density increases, the optimum target response changes and the likelihood of particular error events change relative to each other. Using the system model to calculate the noise autocorrelation and enumerating the possible error events, the relative likelihood of possible error events can be ranked. Tables I and II list the most likely error events for a channel response target of (1−D²)(2+2D+D²), taking into account noise correlation for channel recording densities of 3.0 and 3.5 bits per PW₅₀. The tables are based on a calculated error rate of 1×10⁻⁶, and the likelihoods are expressed in terms of effective SNR above the most likely event. It can be seen that the events a_k={+2, −2, +2} and a_k={+2, −2, +2, −2, +2} are the most likely at these densities. If the effect of these two events can be eliminated through coding, then a coding gain can be achieved.

[0020] As the dominant error events are a_k={+2, −2, +2} and a_k={+2, −2, +2, −2, +2}, a code to detect the occurrence of these error events is required. It can readily be seen that a single bit parity check block code can be used to detect these error events. Consider a parity code of length N. Whenever one of the error events occurs within a code word, three or five bits are inverted causing a parity violation. If the error event spans the boundary of two code words, then there will be an odd number of inverted bits in one of the code words causing its parity check to be violated. Hence, the use of a single bit parity code allows the dominant error events on the high density recording channel to be detected when equalized to the proposed target response. The decoder can then pick the most likely data pattern which does not violate the parity constraint.

[0021] While an event length parity code with odd parity can provide some run length constraints with a rate (N−1)/N, stricter constraints may be required to ensure sufficient timing and gain recovery information. An interleaved run length constraint is also required to ensure Viterbi path merging on a target with a Nyquist and DC null.

[0022] While a time varying trellis incorporating the target response and the parity constraint could be constructed, it would require twice the number of states than the target response on its own. This would require a considerably more complex detector. However, decoding may be achieved through the use of a post processor. The basic detector structure is shown in FIG. 6 and is based on a Viterbi detector matched to the channel response G(D)=(1−D²)(2+2D+D²). The Viterbi outputs {tilde over (x)}_kare used to reconstruct an estimate of the equalized samples {tilde over (y)}_k. This is used to calculate an estimate of the noise on the equalized samples

[0023] ñ_k=y_k−{tilde over (y)}_k.

[0024] These noise estimates are correlated with the two likely error events to produce a noise correlation for each event at each bit time. The correlation filter is the error event convolved with the channel response all reversed in time. For example, the a_k={+2, −2, +2} error event requires a correlation filter response of

[0025] H₊₂₋₂₊₂(D)=(2−2D+2D²)G(D⁻¹) =−2D⁻⁴−2D⁻³+2D⁻¹−2+4D².

[0026] A similar filter is used for the a_k={+2, −2, +2, −2, +2} event. The noise correlation values are only considered valid if the estimated bits {tilde over (x)}_ksupport the error event.

[0027] At each bit time the maximum of the valid noise correlation values and the corresponding type of error event is stored. At each code word boundary, the parity constraint on the estimated bits is checked. If the parity constraint is violated, the maximum valid noise correlation value over the length of the code words and across its boundaries is identified. The estimated bits {tilde over (x)}_kcorresponding to the error event associated with this maximum value are complemented under the assumption that the largest noise correlation value is the most likely position and error event to have occurred.

[0028] The use of such a postprocessor avoids increasing the complexity of the Viterbi detector, particularly when only a small number of error events need to be detected.

[0029] Modulation code on user data for use with recording channels is also known. Binary user data is mapped into constrained sequences, called (D,K/I) sequences, where D represents the minimum and K represents the maximum number of 0's between any pair of consecutive 1's. The parameter I represents the maximum run length of zeroes in the particular all-even and or all-odd subsequences. In a PRML system, such as EPR4, a small value of K is desirable for accurate timing and gain control, and a small value of I value reduces the length of survival registers required in the Viterbi detector due to the reducing length of the Quasi-catastrophic sequences. Using a rate 16/17 base code with constraint (0,6/8), the resulting parity code with have a 16/18 code rate. An even higher rate code can be constructed to meet run length requirements and the parity constraint. Consider a rate 16/17(0,6/8) code which consists of freely concatenateable code words of length 17. If at the end of each pair of code words (34 bits) an additional parity bit is appended, the result is a 32/35 (0,7/9) code. Likewise, if a parity bit is appended to each 3 code words (51 bits), the resulting system will attain a overall 51152 (0,7/9) code.

[0030] However, the above illustration does not take into consideration the effect of the precoder. FIG. 4A shows a system diagram with the parity bit being inserted before the write precoder, and the parity check after the postcoder during the read process. Inserting the parity bit upstream in the data before the precoder can cause considerable adverse effects. When an error occurs at the boundary of these parity-coded data blocks, the introduced parity bit cannot detect the error if the error event sequence spans over the boundaries of the parity-code data blocks. Therefore, dominant error events with long length could result in higher probability of causing a non-detectable error and reduces the effectiveness of the parity bit post-processing scheme. In an EPR4 channel, the most dominant error events are +/−(1) and +/−(1−1 1) at the output of Viterbi detector. After the postcoding, these two major errors become (1 0 1) and (1 1 0 1 1) assuming a 1/(1xor D²) precoder is being used. In both cases, length of the error events are increased by 2 bits. The invention described in this patent deals with the problems of introducing parity bit by using a write precoder with parity insertion feedback.

[0031] The present invention inserts a parity bit into the data stream after the data stream has been precoded by a precoder circuit. Furthermore, the present invention maintains constraints on an encoded word by not breaking the constraints. More particularly, the present invention inserts a parity bit in the RLL code by using feedback in the write precoder which maintains the (D,K/I) constraints. The present invention does not require the need of clock gapping on the precoder side of the parity insertion circuit. The present invention reduces the length of the error event and solves the uncorrectable data problem at the codeword boundaries by inserting the parity bit after the precoder and removing it correspondingly before the postcoder.

[0032] FIG. 1 illustrates a write precoder and parity insertion circuit with feedback.

[0033] FIG. 2 illustrates a write precoder and parity insertion circuit without feedback.

[0034] FIG. 3 illustrates a system of the present invention.

[0035] FIG. 4 illustrates an example of parity insertion after the precoder with feedback.

[0036] FIG. 4A illustrates an example of parity insertion before the precoder.

[0037] FIG. 5 illustrates a detection system model.

[0038] FIG. 6 illustrates detector structure.

[0039] In an EPR4 channel, the most dominant error events are +/−(1) and +/−(1−1 1) at the output of Viterbi detector. The EPR4 postprocessor with the parity check circuitry identifies and corrects the above two major error events. After the postcoding, these two major errors become (1 0 1) and (1 1 0 1 1) assuming a 1/(1 xor D²) precoder is being used. In both cases, the length of the error events are increased by 2 bits. Therefore, there is an advantage of placing the above circuitry before the postcoder. For the case of using one parity bit for 3 coded data words (51 bits), the probabilities of dominant error events being detected when the parity bit is introduced before and after the precoder are listed in Table III. As shown in Table II, there is a clear advantage of inserting parity bit after the precoder. This is because the error event to be detected had short length and therefore the probability of having an error event across the parity boundary is low.

[0040] FIG. 2 illustrates a write precoder circuit 210 with parity insertion after preceding without feedback. This write precoder circuit 210 is typically positioned between the data encoder circuit and the precompensation circuit and preamp. The encoded data from the encoder circuit of the read channel is input to precoder circuit 210. The precoder circuit is shown as an exclusive OR circuit. The input of the precoder circuit 210 is connected to D flip-flop 212 and the output of the precoder circuit 210 is connected to the D flip-flop 214. Additionally, the output of precoder circuit 210 is connected to MUX circuit 200. The output of D flip-flop 214 is connected to D flip-flop 212. The clocking of D flip-flop 214 and D flip-flop 212 is controlled by AND gate 216. The output of precoder circuit 210 is input to exclusive OR gate 208. Additionally, input to exclusive OR circuit 208 is the output of D flip-flop 206. The output of exclusive OR gate 208 is input into D flip-flop 206. The combination of exclusive OR circuit 208 and D flip-flop 206 is a parity check circuit. The output of exclusive OR circuit 208, which is the parity bit, is input to MUX circuit 200. The output of MUX 200 is input to D flip-flop 202. The output of D flip-flop 202 is the write precompensation circuit. The MUX circuit 200 multiplexes the output of precoder circuit 210 and the parity check circuit to input a parity check bit. The function of D flip-flop 202 is to buffer and delay the output of the MUX circuit 200. The AND circuit 216 is to provide timing for the D flip-flops 212 and 214 by providing clock pulses at T=0 through T=50. At T=51, no clock pulse is provided to D flip-flops 212 and 214. This allows the encoded data to be precoded and prevents the data from the precoder circuit 210 from being input to parity check circuit 208. The output from precoder circuit 210 is delayed by D flip-flop 214. At a clock pulse, the contents of D flip-flop 214 is input to the D flip-flop 212. At the clock pulse, the output of D flip-flop 212 is input to precoder circuit 210. In such a way, the user encoded data input to the precoder circuit 210 is precoded.

[0041] Additionally, the output from the precoder circuit is input to the exclusive OR circuit 208. This input is exclusively ORed with the output from the D flip-flop 206. The D flip-flop 206 delays the output from exclusive OR circuit 208 based upon clock T=51. At T=51, the output from the exclusive OR gate 208 contains the parity bit of the input data to the precoder 210. At T=51, the MUX selects input S₂which is the output from the parity circuit 208 to D flip-flop 202. At T=0 through T=50, the MUX circuit selects the input Si to output to the D flip-flop 208.

[0042] The parity bit inserted using the method in FIG. 2 will disturb the precoded data stream and the runlength constraint of the data stream will be increased. For a general base RLL of constraint (0,K/I), the resulting RLL constraint of a system with direct parity insertion after the precoder in FIG. 2 will be (0,K+K/2/I+I/2).

[0043] FIG. 3 illustrates a write precoder circuit with parity insertion and feedback. This circuit inserts a parity bit into the encoded data at predetermined position and the resulting runlength constraint will only be increased to (0,K+1/I+1) for a base cod with RLL constraint (0,K/I).

[0044] Turning now to FIG. 1, a precoder receives the input data. The output of D flip-flop 112 is connected to an input of precoder circuit 110. The output of the precoder circuit 110 is connected to the parity check circuit 108. Parity check circuit 108 is shown as a XOR circuit. An output of the parity check circuit 108 is connected to an input of D flip-flop 106, and an output of the D flip-flop 106 is connected to an input of the parity check circuit 108. Additionally, the output of the parity check circuit 108 is connected to the MUX circuit 100. The output of the MUX 100 is connected to the D flip-flop 102. The output of the D flip-flop 102 includes a feedback loop to feed back from the output of D flip-flop 102 to the input to D flip-flop 112. The feedback circuit keeps the clock running without interrupting the precoder and allows the data stream to be precoded continuously and maintains the (D,K/I) constraints. Clock gapping by the precoder circuit 110 is not required. The parity checking circuit includes parity check circuit 108 and D flip-flop 106. The D flip-flop 112 does not need clock gapping or in this specific example does not need to have the clock interrupted at T=51. The output of D flip-flop 102 is input to D flip-flop 112. The D flip-flop 112 delays the output of D flip-flop 102 from input to precoder circuit 110. At every clock pulse, the contents of D flip-flop 112 is input to precoder circuit 102. The contents of flip-flop 112 is provided by flip-flop 102. This feedback allows operation of inserting a parity bit without clock gapping. Furthermore, the present invention has been described with a 16/17 code which allows 51 bits of information and a parity bit to be placed in the 52nd bit. The present invention could be used with 24/25 code which allows 50 bits of information plus a parity bit to be placed in the 51st bit of information.

[0045] FIG. 4 illustrates a system diagram of the present invention. An I/F controller 400 sends user data to the read channel 410. The read channel includes an encoder 412. The encoder 412 outputs encoded information to a write precoder 414 which outputs data to the preamp 416. The write precoder 414 includes the write precoder and parity insertion circuit 130 with feedback or the write precoder and parity insertion circuit 230 without feedback. The output of the preamp is written to a medium. The data output from the write precoder circuit is an encoded stream of bit, for example, a 24/25 code with a parity bit. During a read cycle, the data is read from the medium and input to a preamp 416. The preamp 416 inputs data to the read channel 410. The read channel includes an AFE(Analog Front End) circuit 425 which filter and partially equalizes the signals and output to an AND converter 419. The A/D converter circuit 419 converts the analog signal to a digital signal. The digital signal is output from the A/D converter circuit 419 and input to the finite impulse response (FIR) filter 421. The FIR filter 421 shapes the digital signal to produce an equalized signal which outputs to aViterbi detector 415. The Viterbi detector detects the precoded data and outputs to a parity check circuit 423 which performs the parity check. . The output of the FIR filter 421,the Viterbi detector 415 and the parity check circuit 423 are input to a turbo post-processor 420 which outputs the information to a postcoder 417. The postcoder 417 outputs to a 24/25 decoder 422. The output of the 24/25 decoder 422 is input to an I/F controller 400.

[0046] FIG. 3 shows user data with a 16/17 code, three groups of 17 bits of user data combined to form 51 bits, leaving the 52nd bit free for a parity bit. Likewise, with a 24/25 code, two groups of 25 bits form 50 bits, leaving a 51st bit for a parity bit.