Windowed level detector for partial response channels
View Patent ↗An estimator of the noiseless output of a noisy partial response channel is described. The estimator operates recursively. In each iteration, the estimator processes a window of the N most recently received noisy channel outputs to compare output level metrics for all possible channel output level, and selects a noiseless output level with maximal posterior probability.
1. A method comprising:
receiving a synchronously sampled output of a partial response channel, said output corrupted by noise; and
processing, at the [i]th received output of the partial response channel, by:
using
(a) a window of N most recent noisy outputs of the partial response channel,
(b) all distinct sequences of N most recent noiseless outputs possible at the output of the partial response channel,
(c) the prior probability of each distinct sequence of N most recent noiseless outputs, and
(d) an index j of a noiseless sampled output in the window to be estimated,
determining a set of quantities, each said quantity related to the conditional probability of a noiseless sequence given the window of noisy channel outputs;
determining a metric, for each possible noiseless sampled output level in the [j]th sample in the window, by adding a subset of the quantities;
comparing the determined metrics to find the noiseless sampled output level with largest conditional probability; and
generating the noiseless sampled output level with largest conditional probability as an estimate of the [i−N+j]th noiseless output of the partial response channel.
2. The method of claim 1 wherein a quantity associated with a window of noisy samples,
y[i−N+1], y[i−N+2], . . . , y[i]
and a possible noiseless sequence
v[1], v[2], . . . , v[N]
with a prior sequence probability is proportional to the product of an exponential term and the prior sequence probability.
3. The method of claim 2 wherein the exponential term is the transcendental number e (˜2.718281828459) raised to a power equal to a numerator term divided by a denominator term.
4. The method of claim 3 wherein the numerator term is a negative distance term, denoted d, reflecting the Euclidean distance between a noisy sequence {y[i−N+1], y[i−N+2], . . . , y[i]} and a possible noiseless sequence {v[1], v[2], . . . , v[N]} of the form
d =−{( y[i−N+ 1]− v[ 1])2+( y[i−N+ 2]− v[ 2])2+ . . . +( y[i]−v[N]) 2}.
5. The method of claim 3 , wherein the denominator term is two times an estimated noise variance.
6. The method of claim 1 , wherein a metric for a [j]th noiseless sample value, w[j], is determined by adding the quantity for each possible distinct noiseless sequence with the property that the [j]th noiseless sample value is equal to w[j].
7. The method of claim 1 , wherein the partial response channel is an extended class-IV partial response (EPR4) channel.
8. A method comprising:
receiving a synchronously sampled output of a partial response channel, said output corrupted by noise; and
processing, at the [i]th received output of the partial response channel, by:
using
(a) a window of N most recent noisy outputs of the partial response channel,
(b) all distinct sequences of N most recent noiseless outputs possible at the output of the partial response channel,
(c) the prior probability of each distinct sequence of N most recent noiseless outputs, and
(d) an index j of a noiseless sampled output in the window to be estimated;
determining a set of quantities, each said quantity related to the conditional probability of a noiseless sequence given the window of noisy channel outputs;
determining, for each possible noiseless sampled output level in the [j]th sample in the window, a sub-metric by adding a subset of the quantities;
processing the determined sub-metrics to determine a set of thresholds;
comparing the [i−N+j]th noisy channel output with the determined thresholds;
logically combining the comparison outputs to determine the noiseless sampled output level with largest conditional probability;
generating the noiseless sampled output level with largest conditional probability as an estimate of the [i−N+j]th noiseless output of the partial response channel.
9. The method of claim 8 wherein a quantity associated with a window of noisy samples,
y[i−N+1], y[i−N+2], . . . , y[i]
and a possible noiseless sequence
v[1], v[2], . . . , v[N]
with a prior sequence probability is proportional to the product of an exponential term and the prior sequence probability.
10. The method of claim 9 wherein the exponential term is the transcendental number e (˜2.718281828459) raised to a power equal to a numerator term divided by a denominator term.
11. The method of claim 10 wherein the numerator term is equal to the sum of a negative distance term, denoted d, and a square term, denoted f, of the form
d =−{( y[i−N+ 1]− v[ 1])2+( y[i−N+ 2]− v[ 2])2+ . . . +( y[i]−v[N]) 2} and
f =( y[i−N+j]−v[j ]) 2.
12. The method of claim 10 wherein the denominator term is two times an estimated noise variance.
13. The method of claim 8 wherein a sub-metric for a [j]th noiseless sample value, w[j], is determined by adding the quantity for each possible distinct noiseless sequence with the property that the [j]th noiseless sample value is equal to w[j].
14. The method of claim 8 wherein, denoting the sub-metric for a noiseless output level L as SM[L], the sub-metric for a successive output level L+1 as SM[L+1], and an estimated noise variance as v, the threshold between levels L and L+1 is
v*ln{SM[L]−SM[L+1]}+L+½, where
ln{x} is the base e or natural logarithm of x.
15. The method of claim 14 wherein the result of a comparison of a first threshold between levels L and L+1 and a second threshold between levels L+1 and L+2 determines a detection error when the first threshold is greater than the second threshold.
16. An apparatus to sequentially estimate a noiseless output of a noisy partial response channel, the apparatus comprising:
a memory operative to store noisy outputs of a partial response channel and
a logic circuit operative to:
access the memory to obtain the N most recent samples of noisy channel output;
use a set of all possible sequences of the N most recent noiseless outputs of the noisy partial response channel and a prior probability of each such possible sequence;
process the set of all possible sequences of the N most recent noiseless outputs of the noisy partial response channel by using circuitry operative to:
determine a sequence metric to associate with each member of the set of all possible sequences;
determine a level metric to associate with each possible noiseless sample level with a summation unit to add the determined sequence metric for each sequence which takes on said level in a select sample in the window of the N most recent noiseless output samples:
compare the level metric; and
determine a maximal level metric in the set of the level metrics; and
output an estimate for a select sample in the window of N most recent samples equal to the level associated with the maximal level metric.
17. The apparatus of claim 16 further comprising:
A circuit containing a serial cascade of an adder unit, an exponentiator unit, and a multiplier unit; and
circuitry to modify the inputs and multiplication constant of said circuit to serially determine a plurality of sequence metrics.
18. An apparatus to sequentially estimate a noiseless output of a noisy partial response channel, the apparatus comprising:
a memory operative to store noisy outputs of a partial response channel and
a logic circuit operative to:
access a window of N most recent samples of a noisy channel output, wherein N is greater than one;
use
(a) all distinct sequences of N most recent noiseless outputs possible at the output of the partial response channel,
(b) the prior probability of each distinct sequence of N most recent noiseless outputs, and
(c) an index j of a noiseless sampled output in the window to be estimated;
determine a set of quantities, each said quantity related to the conditional probability of a noiseless sequence given the window of noisy channel outputs;
determine, for each possible noiseless sampled output level in the [j]th sample in the window, a sub-metric by adding a subset of the quantities;
process the determined sub-metrics to determine a set of thresholds;
compare the [i−N+j]th noisy channel output with the determined thresholds;
logically combine the comparator outputs to determine the noiseless sampled output level with largest conditional probability;
generate the noiseless sampled output level with largest conditional probability as an estimate of the [i−N+j]th noiseless output of the partial response channel.
19. The apparatus of claim 18 wherein the partial response channel is an extended class-IV partial response (EPR4) channel.
20. The apparatus of claim 18 further comprising:
A circuit containing a cascade of an adder unit, an exponentiator unit, and a multiplier; and
circuitry to modify the inputs and multiplication constant of said circuit to serially determine a plurality of sequence sub-metrics.