Pattern dependent thresholds for slicing a multi-level signal

Abstract

The present disclosure relates to slicing a multi-level signal and proposes a receiver for determining thresholds and / or for slicing an input signal. The receiver comprises: an equalizer configured to generate a reconstructed signal; a first slicer; a first optimization module configured to determine a set of second thresholds by using the reconstructed signal and a set of first quantization decisions from the first slicer; a second slicer configured to determine a set of second quantization decisions by using the set of first quantization decisions, the set of second thresholds, and the reconstructed signal; a second optimization module configured to determine a set of third thresholds by using the reconstructed signal and the set of second quantization decisions, wherein each second and third threshold delimits two adjacent signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal.

Description

[0001] PATTERN DEPENDENT THRESHOLDS FOR SLICING A MULTI-LEVEL SIGNAL

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to slicing a multi-level signal. The disclosure proposes a receiver for determining thresholds for slicing an input signal, a receiver for slicing the input signal, and corresponding methods for operating said receivers. Said receivers comprise a new kind of slicer.

[0004] BACKGROUND

[0005] Conventionally, a reconstructed signal is generated based on an input signal by using equalization techniques for signal reconstruction. The reconstructed signal is sliced by quantizers with fixed thresholds to obtain quantization decisions. The thresholds can be optimized based on optimization algorithms. However, conventionally optimized thresholds may display diminished effectiveness due to factors such as intrinsic electronic noise, interference, for example, inter-symbol interference, or fluctuating signal conditions, which can impair the overall performance of the signal reconstruction process.

[0006] SUMMARY

[0007] In view of the above, an objective of this disclosure is to determine improved thresholds for slicing a multi-level input signal. Another objective is to improve the slicing of a reconstructed signal based on the improved thresholds. For example, an objective is to reduce slicing errors related to inter-symbol interference.

[0008] These and other objectives are achieved by this disclosure as described in the enclosed independent claims. Advantageous implementations are further defined in the dependent claims.

[0009] The disclosure is based on the following considerations. Conventionally optimized thresholds may depend on past and future symbols and / or on symbol patterns. For example, if pulse amplitude modulation 4 (PAM4), with exemplary symbols (0, 1,2,3) is used, the optimum thresholds can be different for the case when both neighbors are 0 compared to the case when both neighbors are 3. Therefore, advanced algorithms are required to properly slice the reconstructed signal.

[0010] High-speed optical interconnects use equalizers followed by a slicer to detect the transmitted signal. The slicer uses fixed thresholds that may provide suboptimum performance if the signal levels depend on the transmitted symbol patterns. Exploiting pattern dependent thresholds and using cascaded slicers can improve quantization decisions.

[0011] An iterative approach can be used to improve decisions before the final decisions are made, which may be applied in many digital receivers relying on different signal reconstruction algorithms.

[0012] A first aspect of this disclosure provides a receiver for determining thresholds for slicing an input signal associated with a set of signal levels, the receiver comprising: an equalizer, a first slicer, a second slicer, a first optimization module, and a second optimization module, wherein the equalizer is configured to receive the input signal and generate a reconstructed signal based on the input signal; wherein the first slicer is configured to: obtain a set of first thresholds, and determine a set of first quantization decisions by using the set of first thresholds and the reconstructed signal, wherein each first quantization decision is based on a respective symbol of the reconstructed signal and / or one or more respective neighboring symbols of the respective symbol; wherein the first optimization module is configured to: generate a first set of histograms using the reconstructed signal and the set of first quantization decisions, and determine a set of second thresholds by using the first set of histograms, wherein each second threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal; wherein the second slicer is configured to: determine a set of second quantization decisions by using the set of first quantization decisions, the set of second thresholds, and the reconstructed signal; and wherein the second optimization module is configured to: generate a second set of histograms using the reconstructed signal and the set of second quantization decisions, and determine a set of third thresholds by using the second set of histograms, wherein each third threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal.

[0013] The receiver for determining thresholds for slicing an input signal may be referred to as a first receiver.

[0014] In the following description of the first aspect and the third aspect, the term “the receiver” may refer to “the first receiver”.

[0015] The receiver may comprise a processor. The processor may be configured to perform at least some of the steps of the receiver.

[0016] The first receiver may be associated with an acquisition phase for acquiring thresholds for slicing the input signal.

[0017] The reconstructed signal is based on the input signal. The term “slicing the input signal” may refer to “slicing a signal that is based on the input signal” or “slicing the reconstructed signal”.

[0018] The performance of the receiver may be improved compared to conventional receivers at the price of introducing more slicers and / or simple look-up-tables. Additional complexity may be much less than the complexity of some very complicated algorithms used to achieve similar performance.

[0019] The performance of modules with faulty / inaccurate components may be improved.

[0020] The first slicer and / or the second slicer may be a conventional slicer that for example, does not consider memory or neighboring symbols of any particular symbol.

[0021] The input signal and / or the reconstructed signal may be multi-level signals.

[0022] In an implementation form of the first aspect, for each respective symbol of the reconstructed signal, the second slicer is configured to: select, for each respective symbol of the reconstructed signal, one or more respective second thresholds of the set of second thresholds by using the set of first quantization decisions, and determine the set of second quantization decisions by using the one or more respective second thresholds for each respective symbol of the reconstructed signal.

[0023] In a further implementation form of the first aspect, for each respective symbol of the reconstructed signal, the second slicer is configured to: estimate one or more neighboring symbols of the respective symbol by using the set of first quantization decisions, obtain a set of first signal level centers for the respective symbol adjacent to, for example, surrounded by, the one or more estimated neighboring symbols, determine two or more respective most reliable intermediate second quantization decisions based on the set of first signal level centers, select the one or more respective second thresholds of the set of second thresholds by using the two or more respective most reliable intermediate second quantization decisions.

[0024] Obtaining the set of first signal level centers may be based on the set of second thresholds and / or the first set of histograms. The set of first signal level centers may be centers of the first set of histograms. For example, a subset of thresholds associated with a particular neighbor pattern of the set of second thresholds may be selected. The subset of thresholds may be converted into the signal level centers by, for example, determining a mean between adjacent thresholds.

[0025] In a further implementation form of the first aspect, each histogram of the first set of histograms is based on a respective symbol pattern of a first set of symbol patterns, wherein each symbol pattern of the first set of symbol patterns comprises a respective symbol associated with a respective quantization decision of the set of first quantization decisions, and one or more respective neighboring symbols associated with one or more neighboring quantization decisions of said respective quantization decision, wherein each histogram of the second set of histograms is based on a respective symbol pattern of a second set of symbol patterns, wherein each symbol pattern of the second set of symbol patterns comprises a respective symbol associated with a respective quantization decision of the set of second quantization decisions, and one or more respective neighboring symbols associated with one or more neighboring quantization decisions of said respective quantization decision.

[0026] In a further implementation form of the first aspect, wherein the receiver further comprises one or more additional slicers according to the second slicer of any one of the preceding claims and one or more additional optimization modules according to the second optimization module of any one of the preceding claims, wherein the one or more additional slicers and the one or more additional optimization modules are alternately electrically connected in series to the second optimization modules and configured to consecutively generate one or more sets of additional quantization decisions and one or more sets of additional thresholds starting with the set of third thresholds.

[0027] The term “alternately electrically connected” may refer to each additional slicer being sandwiched in terms of electrically connections between two optimization modules, and each additional optimization modules being directly electrically connected to a previous slicer. Thus, a chain of modules and slicers may be formed that comprises alternately slicers and optimization modules.

[0028] For example, the one or more additional slicers may be or comprise a fourth slicer, and / or the one or more additional optimization module may comprise a fourth optimization module.

[0029] For example, slicers and optimization modules may be electrically connected in series in the following order: the first slicer, the first optimization module, the second slicer, the second optimization module, the fourth slicer, the fourth optimization module.

[0030] Each additional slicer and additional optimization module may receive data, for example histograms and / or quantization decisions, from respectively a previous optimization module and a previous slicer. Thus, the receiver may provide an iterative procedure to determine a set of final thresholds by further improving the set of third thresholds and / or one or more sets of additional thresholds.

[0031] In a further implementation form of the first aspect, further comprising a third optimization module and a third slicer, wherein the third slicer is configured to: obtain a set of fourth thresholds, determine a set of third quantization decisions by using the set of fourth thresholds and the reconstructed signal, wherein each third quantization decision is based on a respective symbol of the reconstructed signal, and wherein the third optimization module is configured to: generate a third set of histograms using the reconstructed signal and the set of third quantization decisions, determine the set of first thresholds by using the third set of histograms, wherein each first threshold delimits two adjacent signal levels of the set of signal levels, and provide the set of first thresholds to the first slicer. Thus, there may be an additional optimization of thresholds that is not based on memory. The first set of thresholds may provide an improved starting set of thresholds for the other slicers and optimization modules of the receiver.

[0032] In a further implementation form of the first aspect, the receiver is configured to determine at least one of the set of first thresholds, the set of second thresholds, the set of third thresholds, and the one or more sets of additional thresholds by being configured to: determine at least one zero bin region of respectively at least one of the third set of histograms, the first set of histograms, the second set of histograms, and one or more additional sets of histograms, select a predetermined number of closest bins surrounding the at least one zero bin region, determine one or more respective fit parameters by fitting the selected bins using a function, and determine respectively at least one of the set of first thresholds, the set of second thresholds, the set of third thresholds, and the one or more sets of additional thresholds based on the one or more respective fit parameters. Thus, each set of thresholds can be efficiently and accurately determined.

[0033] In a further implementation form of the first aspect, the receiver comprises a microcontroller comprising at least one of the equalizer, the first slicer, the second slicer, the third slicer, the first optimization module, the second optimization module, the third optimization module, the one or more additional slicers, and the one or more additional optimization modules.

[0034] In a further implementation form of the first aspect, M is the number of neighboring symbols comprised in each respective pattern of one or more neighboring symbols, wherein L is the number of signal levels in the set of signal levels, and wherein at least one of the third set of histograms includes L histograms, the first set of histograms includes L(M+1)histograms, the second set of histograms includes L(M+1)histograms, and each set of additional of histograms of the one or more sets of additional histograms includes L(M+1)histograms.

[0035] In a further implementation form of the first aspect, the set of fourth thresholds is predetermined. The set of fourth thresholds may be default thresholds.

[0036] In a further implementation form of the first aspect, configured to store at least one of the set of second thresholds, the set of third thresholds, and the one or more sets of additional thresholds in a look-up-table. Thus, said thresholds may be efficiently stored. Said thresholds may then be efficiently used for slicing the input signal. A second aspect of this disclosure provides a receiver for slicing an input signal associated with a set of signal levels, the receiver comprising: an equalizer, a first slicer, and a second slicer, wherein the equalizer is configured to receive the input signal and generate a reconstructed signal based on the input signal; wherein the first slicer is configured to: obtain a set of first thresholds, determine a set of first quantization decisions by using the set of first thresholds and the reconstructed signal, wherein each first quantization decision is based on a respective symbol of the reconstructed signal and / or one or more respective neighboring symbols of the respective symbol, and provide the set of first quantization decisions to the second slicer; and wherein the second slicer is configured to: obtain a set of final thresholds, wherein each final threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal, and determine a set of fourth quantization decisions by using the set of final thresholds, the reconstructed signal, and the set of first quantization decisions.

[0037] The receiver for slicing an input signal may be referred to as a second receiver. The first receiver and the second receiver may be the same receiver or may be different receivers. The components comprised in the first receiver may be the same or different components that are comprised in the second receiver.

[0038] In the following description of the second aspect and the fourth aspect, the term “the receiver” may refer to “the second receiver”.

[0039] The receiver may comprise a processor. The processor may be configured to perform at least some of the steps of the receiver.

[0040] The reconstructed signal is based on the input signal. The term “slicing the input signal” may refer to “slicing a signal that is based on the input signal” or “slicing the reconstructed signal”.

[0041] The second receiver may be associated with a steady-state phase for slicing the input signal.

[0042] The set of fourth quantization decisions may be or be comprised in the one or more sets of additional quantization decisions. The set of fourth quantization decisions may be the sliced input signal or be used to determine the sliced input signal. In an implementation form of the second aspect, the receiver further comprises a fourth slicer configured to obtain the set of final thresholds, determine a set of fifth quantization decisions by using the set of final thresholds, the reconstructed signal, and the set of fourth quantization decisions.

[0043] The set of fifth quantization decisions may be the sliced input signal or be used to determine the sliced input signal.

[0044] In a further implementation form of the second aspect, the second slicer is configured to select, for each respective symbol of the reconstructed signal, one or more respective final thresholds of the set of final thresholds by using the set of first quantization decisions, and determine a set of fourth quantization decisions by using the one or more respective final thresholds for each respective symbol of the reconstructed signal, and / or wherein the fourth slicer is configured to select, for each respective symbol of the reconstructed signal, one or more respective final thresholds of the set of final thresholds by using the set of fourth quantization decisions, and determine a set of fifth quantization decisions by using the one or more respective final thresholds for each respective symbol of the reconstructed signal.

[0045] In a further implementation form of the second aspect, for each respective symbol of the reconstructed signal, the second slicer is configured to: estimate one or more neighboring symbols of the respective symbol by using the set of first quantization decisions, obtain a set of first signal level centers for the respective symbol adjacent to, for example, surrounded by, the one or more estimated neighboring symbols, determine two or more respective most reliable intermediate second quantization decisions based on the set of first signal level centers, select the one or more respective second thresholds of the set of second thresholds by using the two or more respective most reliable intermediate second quantization decisions.

[0046] Obtaining the set of first signal level centers may be based on the set of second thresholds. For example, a subset of thresholds associated with a particular neighbor pattern of the set of second thresholds may be selected. The subset of thresholds may be converted into the signal level centers by, for example, determining a mean between adjacent thresholds. In a further implementation form of the second aspect, for each respective symbol of the reconstructed signal, the fourth slicer is configured to: estimate one or more neighboring symbols of the respective symbol by using the set of second quantization decisions, obtain a set of second signal level centers for the respective symbol adjacent to, for example, surrounded by, the one or more estimated neighboring symbols, determine two or more respective most reliable intermediate fourth quantization decisions based on the set of second signal level centers, select the one or more respective final thresholds of the set of final thresholds by using the two or more respective most reliable intermediate fourth quantization decisions.

[0047] Obtaining the set of second signal level centers may be based on the set of third thresholds. For example, a subset of thresholds associated with a particular neighbor pattern of the set of second thresholds may be selected. The subset of thresholds may be converted into the signal level centers by, for example, determining a mean between adjacent thresholds.

[0048] In a further implementation form of the second aspect, the receiver comprises an application specific integrated circuit (ASIC) which comprises at least one of: the equalizer, the first slicer, the second slicer, and the fourth slicer. Thus, the slicing of the input single may be more efficient.

[0049] The first receiver and second receiver may comprise the same equalizer or different equalizers.

[0050] In a further implementation form of the second aspect, the receiver is configured to obtain from a look-up table at least one of: the set of first thresholds, the set of final thresholds, or wherein the receiver is configured to obtain from another device or another module in the receiver at least one of: the set of first thresholds, the set of final thresholds.

[0051] Obtaining data from a look-up table may be more efficient. For example, the respective thresholds may not need to be determined multiple times.

[0052] In a further implementation form of the second aspect, the receiver further is the receiver according to receiver according to the first aspect or any of its implantation forms.

[0053] The receiver according to the second aspect or any of its implementation forms may be or be comprised in the receiver according to the first aspect or any of its implantation forms. In a further implementation form of the second aspect, the set of final thresholds is the set of third thresholds or a set of additional thresholds of the one or more sets of additional thresholds.

[0054] In a further implementation form of the second aspect, the equalizer comprises a feed-forward equalizer, and / or wherein the equalizer is followed by a decision-feedback equalizer or a noise cancellation block for reducing noise amplification.

[0055] The receiver of the second aspect may have one or more implementation forms that correspond to the implementation forms of the receiver of the first aspect. The receiver of the second aspect and its implementation forms may achieve one or more advantages and effects described above for the receiver of the first aspect and its respective implementation forms.

[0056] The receiver of the first aspect may have one or more implementation forms that correspond to the implementation forms of the receiver of the second aspect. The receiver of the first aspect and its implementation forms may achieve one or more advantages and effects described above for the receiver of the second aspect and its respective implementation forms.

[0057] A third aspect of this disclosure provides a method of operating a receiver for determining thresholds for slicing an input signal associated with a set of signal levels, the receiver comprising: an equalizer, a first slicer, a second slicer, a first optimization module, and a second optimization module, wherein the method comprises: receiving, with the equalizer, the input signal and generate a reconstructed signal based on the input signal; obtaining, with the first slicer, a set of first thresholds; determining, with the first slicer, a set of first quantization decisions by using the set of first thresholds and the reconstructed signal, wherein each first quantization decision is based on a respective symbol of the reconstructed signal and / or one or more respective neighboring symbols of the respective symbol; generating, with the first optimization module, a first set of histograms using the reconstructed signal and the set of first quantization decisions; determining, with the first optimization module, a set of second thresholds by using the first set of histograms, wherein each second threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal; determining, with the second slicer, a set of second quantization decisions by using the set of first quantization decisions, the set of second thresholds, and the reconstructed signal; and generating, with the second optimization module, a second set of histograms using the reconstructed signal and the set of second quantization decisions; and determining, with the second optimization module, a set of third thresholds by using the second set of histograms, wherein each third threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal.

[0058] The method of the third aspect may have implementation forms that correspond to the implementation forms of the receiver of the first aspect. The method of the third aspect and its implementation forms achieve the advantages and effects described above for the receiver of the first aspect and its respective implementation forms.

[0059] A fourth aspect of this disclosure provides a method of operating a receiver for slicing an input signal associated with a set of signal levels, the receiver comprising: an equalizer, a first slicer, and a second slicer, wherein the method comprises: receiving, with the equalizer, the input signal; generating, with the equalizer, a reconstructed signal based on the input signal; obtaining, with the first slicer, a set of first thresholds; determining, with the first slicer, a set of first quantization decisions by using the set of first thresholds and the reconstructed signal, wherein each first quantization decision is based on a respective symbol of the reconstructed signal and / or one or more respective neighboring symbols of the respective symbol; providing, with the first slicer, the set of first quantization decisions to the second slicer; obtaining, with the second slicer, a set of final thresholds, wherein each final threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal; and determining, with the second slicer, a set of fourth quantization decisions by using the set of final thresholds, the reconstructed signal, and the set of first quantization decisions.

[0060] The method of the fourth aspect may have implementation forms that correspond to the implementation forms of the receiver of the second aspect. The method of the fourth aspect and its implementation forms achieve the advantages and effects described above for the receiver of the second aspect and its respective implementation forms.

[0061] A fifth aspect of this disclosure provides a computer program product comprising a program code for performing, when the program code is executed on a computer, the method according to the third aspect or the fourth aspect. In this disclosure, the term “most reliable” may, for example, refer to “closest”, “minimum error”, or “estimated minimum error”.

[0062] It has to be noted that all devices, elements, units and means described in the disclosure could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the disclosure as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities.

[0063] Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

[0064] BRIEF DESCRIPTION OF DRAWINGS

[0065] The above described aspects and implementation forms will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

[0066] FIG. 1 shows a receiver for determining thresholds for slicing an input signal according to this disclosure.

[0067] FIG. 2 shows a receiver for slicing an input signal according to this disclosure.

[0068] FIG. 3 shows an exemplary receiver according to this disclosure.

[0069] FIG. 4 shows a receiver for slicing an input signal according to this disclosure.

[0070] FIG. 5 shows an exemplary histogram for determining thresholds according to this disclosure. FIG. 6 shows selected bins of a histogram and interpolation function bins according to this disclosure.

[0071] FIG. 7 shows experimental results based on a receiver according to this disclosure.

[0072] FIG. 8 shows equalization schemes according to this disclosure including: MLSE (top), full-trellis MLSE (middle), and RS-MLSE (bottom).

[0073] FIG. 9 shows a method according to this disclosure.

[0074] FIG. 10 shows a method according to this disclosure.

[0075] DETAILED DESCRIPTION OF EMBODIMENTS

[0076] FIG. 1 shows a receiver 100 for determining thresholds for slicing an input signal 101 according to this disclosure. The input signal 101 is associated with a set of signal levels.

[0077] The receiver 100 comprises: an equalizer 103, a first slicer 104a, a second slicer 104b, a first optimization module 105a, and a second optimization module 105b.

[0078] The equalizer 103 is configured to receive the input signal 101 and generate a reconstructed signal 102 based on the input signal 101.

[0079] The first slicer 104a is configured to: obtain a set of first thresholds 106a, and determine a set of first quantization decisions 107a by using the set of first thresholds 106a and the reconstructed signal 102, wherein each first quantization decision 107a is based on a respective symbol of the reconstructed signal 102 and / or one or more respective neighboring symbols of the respective symbol.

[0080] The first optimization module 105a is configured to: generate a first set of histograms 108a using the reconstructed signal 102 and the set of first quantization decisions 107a, and determine a set of second thresholds 106b by using the first set of histograms 108a. Each second threshold 106b delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal 102. For example, a respective set of histograms, for example, the first set of histograms 108a, may be generated by dividing the reconstructed signal 102 into one or more subsets of data by using a respective set of quantization decisions, for example, the set of first quantization decisions 107a, wherein each subset of data is used to generate a respective histogram of the respective set of histograms, for example, the first set of histograms 108a.

[0081] The second slicer 104b is configured to: determine a set of second quantization decisions 107b by using the set of first quantization decisions 107a, the set of second thresholds 106b, and the reconstructed signal 102.

[0082] The second optimization module 105b is configured to: generate a second set of histograms 108b using the reconstructed signal 102 and the set of second quantization decisions 107b, and determine a set of third thresholds 106c by using the second set of histograms 108b, wherein each third threshold 106c delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal 102.

[0083] For example, one or more neighboring symbols of a first symbol of the reconstructed signal 102 may form a first neighbor pattern. Each neighbor pattern may be associated with a subset of thresholds, for example, third thresholds or final thresholds that delimit the set of signal levels for said neighbor pattern. For example, based on a particular neighbor pattern the subset of thresholds or one thresholds may be selected that can be used to determine a quantization decision associated with the neighbor pattern more efficiently.

[0084] The number of one or more neighboring symbols that form a neighbor pattern may be predetermined and referred to as “memory”.

[0085] FIG. 2 shows a receiver 200 for slicing an input signal 101 according to this disclosure. The input signal 101 is associated with a set of signal levels. The receiver 200 comprises an equalizer 103, a first slicer 104a, and a second slicer 104b.

[0086] The receiver 200 for slicing an input signal 101 may be or be comprised in the receiver 100 for determining thresholds. The components comprised in the second receiver 200 may be the components that are comprised in the first receiver 100. The equalizer 103 comprised in the receiver 200 may or may not be the equalizer 103 comprised in the receiver 100.

[0087] The equalizer 103 is configured to receive the input signal 101 and generate a reconstructed signal 102 based on the input signal 101.

[0088] The first slicer 104a is configured to: obtain a set of first thresholds 106a, determine a set of first quantization decisions 107a by using the set of first thresholds 106a and the reconstructed signal 102, wherein each first quantization decision is based on a respective symbol of the reconstructed signal 102 and / or one or more respective neighboring symbols of the respective symbol, and provide the set of first quantization decisions 107a to the second slicer 104b.

[0089] The second slicer 104b is configured to: obtain a set of final thresholds 106c, 106d, wherein each final threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal 102, and determine a set of fourth quantization decisions 107d by using the set of final thresholds 106c, 106d, the reconstructed signal 102, and the set of first quantization decisions 107a.

[0090] The set of third thresholds 106c may or may not be the set of final thresholds 106c, 106d. The one or more sets of additional thresholds 106d may or may not be the set of final thresholds 106c, 106d. The set of final thresholds 106c, 106d may refer to the thresholds that are determined last during an iterative procedure of improving a set of initial thresholds, for example, the set of first thresholds 106a or the set of fourth thresholds 106e.

[0091] The receiver 100, 200 may differ from conventional receivers by implementing at least one of:

[0092] 1. A specific blind procedure to find pattern dependencies.

[0093] 2. A multistep procedure to determine the final thresholds.

[0094] 3. An algorithm based on the fitting of selected histogram bins to calculate the final thresholds.

[0095] 4. More advanced equalizations schemes with reduced complexity to compensate for ASIC simplification penalties.

[0096] Performance in receivers 100, 200 may be improved using advanced equalization schemes. The performance of modules with faulty / inaccurate components may be improved. For example, if only a certain percentage of photo detectors generate strong pattern dependencies, said modules may be rejected after a final test due to certain performance requirements. However, a receiver 100, 200 according to this disclosure may enable acceptable performance. When components are good enough for certain performance requirements, the algorithm may not be necessary and the fourth slicer 104d with a set of third thresholds 106c PDT2 may be bypassed. Thus, for example, power consumption may be reduced.

[0097] The equalizer 103 may be based on a feed-forward equalizer (FFE) and may be followed by a decision-feedback equalizer (DFE). Complex DFEs may suffer from latency. Instead of a DFE much simpler feedforward block so-called noise cancellation (NC) can be used to reduce noise amplification after the FFE.

[0098] In an acquisition phase, two or more different slicers, for example, only one conventional slicer (memoryless) and one or more so-called M-slicer (slicer based on memory), may be used to find pattern-dependent thresholds (PDT). In a steady-state phase two or more different slicers, for example, only one conventional slicer (memoryless) and one or more so-called M-slicer (slicer based on memory), may be used.

[0099] The acquisition phase may be performed by the first receiver 100 and / or partially done in a micro-controller. When the pattern-dependent optimum thresholds are found only the one M- slicer, for example, the second slicer 104b, or an additional slicer 104d, including a look-up table (LUT) and the first slicer 104a may be used.

[0100] FIG. 3 shows an exemplary receiver 100 according to this disclosure. The receiver 100 includes several slicers engaged to find the set of third thresholds 106c. FIG. 3 shows an exemplary block diagram for pattern-dependent threshold learning. The pattern-dependent threshold learning may be done in a micro controller. The pattern-dependent threshold learning may be referred to as the acquisition phase.

[0101] In the acquisition phase several steps may be executed until the set of final thresholds 106c, 106d are derived, for example: 1. A set of fourth thresholds 106e, for example, default thresholds (DT) may be used by the third slicer 104c to get the set of fourth quantization decisions. For example, the set of fourth thresholds 106e may be at -2,0,2 in a conventional PAM4 slicer for target equalizer 103 output levels of -3,-1, 1,3.

[0102] 2. A third set of histograms may be generated and used by a third optimization module 105c to find the set of first thresholds 106a, for example, improved thresholds (IT).

[0103] 3. The set of first thresholds 106a may be used by the first slicer 104a to determine the set of first quantization decisions 107a, which may be improved decisions compared the set of third quantization decisions 107c.

[0104] 4. A memory parameter M (M=k means k neighboring symbols are considered) may be set. M-histograms may be generated by the second optimization module 105b. For example, for A / =l and PAM4, 4A(A / +1)=16 histograms may be generated. A neighboring symbol sequence of a particular symbol may be denoted by: ns. For A7=2, with a 3-symbol pattern s3=(s0,sl,s2) and ns=(s0,s2). For each ns three thresholds (for PAM4) nst=(nst0, nstl, nst2) may be defined to minimize the bit error rate (BER).

[0105] 5. The first slicer 104a may have determined the quantization decisions associated with the neighbors of a particularly symbol. Said neighboring quantization decisions may be used to select a subset of thresholds from the set of second thresholds 106b (PDT1). The subset of thresholds may be used determine the set of second quantization decisions 107b.

[0106] 6. The set of second quantization decisions 107b may be used by the second optimization module 105b to determine the set of third threshold 106c, for example, final thresholds 106c, 106d (PDT2) or further improved thresholds 106d.

[0107] 7. Optionally, in the steady state phase, the set of third threshold 106c may be stored in a look-up table and used by an additional slicer 104d, for example, fourth slicer 104d, for continuous thresholding in ASIC.

[0108] All of the steps to find the final thresholds may be done in a microcontroller.

[0109] An ASIC PDTA may be realized by two slicers. An optional fourth slicer 104d may be added to further improve the slicing. However, using only two slicers may cause only small degradations. The ASIC blocks may be combined with a micro controller. FIG. 4 shows a receiver 200 for slicing an input signal 101 according to this disclosure. FIG. 4 shows an exemplary block diagram of pattern-dependent slicing. The pattern dependent slicing may be performed in an ASIC.

[0110] The equalizer 103 may be configured to generate the reconstructed signal 102 based on the input signal 101.

[0111] The exemplary receiver comprises three slicers: the first slicer 104a, the second slicer 104b, and the fourth slicer 104d. The set of first thresholds 106a (IT), and the set of final thresholds 106c are predetermined and, for example, stored in a look up table.

[0112] The first slicer 104a, for example, a conventional slicer, may obtain the set of first thresholds 106a, which may not be pattern dependent, to generate a set of first quantization decisions 107a using the reconstructed signal.

[0113] The second slicer 104b and the fourth slicer 104d may both obtain the final set of thresholds 106c, 106d, which may be pattern dependent, to generate respectively one set of additional quantization decisions 107d, for example, the set of fourth quantization decisions, and one other set of additional quantization decisions 107d using both the reconstructed signal 102 and a previous set of quantization decisions. For example, the previous set of quantization decisions of the one set of additional quantization decisions 107d may be the set of first quantization decisions 107a, and the previous set of quantization decisions of the one other set of additional quantization decisions 107d may be the one set of additional quantization decisions 107d.

[0114] At least one of the second slicer 104b, the one or more additional slicers 104d, and the fourth slicer 104d may be pattern dependent slicers or M-slicers. The first slicer 104a and / or the third slicer 104c may not be pattern dependent slicers or may not be M-slicers.

[0115] At least one of the first slicer 104a, the second slicer 104b, the one or more additional slicers 104d, and the fourth slicer 104d may deliver data for pattern-dependent histograms and thresholds.

[0116] At least one of: the first optimization module 105a, the second optimization module 105b, and the one or more additional optimization modules 105d may be pattern dependent optimization modules. The third optimization module 105c may not be a pattern dependent optimization module.

[0117] At least one of: the set of second thresholds 106b, the set of third thresholds 106c, the one or more sets of additional thresholds 106d, the set of final thresholds 106c, 106d may be pattern dependent thresholds. The set of first thresholds 106a and / or the set of fourth thresholds 106e may not be pattern dependent thresholds.

[0118] At least one of the set of first quantization decision 107a, the set of second quantization decision 107b, and each set of additional quantization decisions of the one or more sets of additional quantization decisions 107d may comprise data suitable for pattern-dependent histograms and thresholds.

[0119] At least one of: the first set of histograms 108a, the second set of histograms 108b, and each set of histograms of the one or more additional sets of histograms may comprise pattern-dependent histograms. For example, each pattern of any particular symbol and neighboring symbols of said symbol may be associated with one histogram. The third set of histograms 108c may not comprise pattern-dependent histograms. For example, third set of histograms 108c may consist of N-l thresholds, wherein N may be the number of signal levels of the set of signal levels.

[0120] The second slicer 104b may further be configured to receive the centers of the first set of histograms 108a, for example, from the first optimization module 105a. The fourth slicer 104d may further be configured to receive the centers of the second set of histograms 108b, for example, from the second optimization module 105b. Each additional slicer of the one or more additional slicers 104d may further be configured to receive the centers of a previous set of histograms, for example, from a previous optimization module 105a, 105b, 105d.

[0121] In the following example, a PAM-N modulation format associated with the levels 0,1,2,. . ,,N- 1 and 2-symbol memory thresholds is considered. A set of decoded symbols may be a(0),a(l),a(2),...,a(k). A slicer, for example, the fourth slicer 104d or the second slicer 104b, may contain the centers of N3histograms or may determine the center of said histograms based on a set of pattern dependent thresholds, for example, the set of third thresholds 106c. The slicer may slice an input signal 101, e.g. x(l), by using N center values C (vector C) with neighbors a(0) and a(2). A vector b=abs(C-x) may be calculated and sorted to determine a vector c=sort(b) indicating sorting indices. The c(0) value indicates the most reliable decision while the c(l) value indicates a next reliable decision. If c(0)=k and c(l)=m (abs(k-m)=l) two competing histograms can be selected H(a(0),k,a(2)) and H(a(0),m,a(2)). These two histograms define the threshold T(a(0),k_m,a(2)), where k_m=m_k=0,l,2,...,N-2. The signal x(l) may be sliced by the threshold T(a(0),k_m,a(2)) and either symbol k or m may be decided.

[0122] FIG. 5 shows an exemplary histogram for determining thresholds according to this disclosure. FIG. 5 shows histograms before and after quantization.

[0123] FIG. 6 shows selected bins of a histogram and interpolation function bins according to this disclosure.

[0124] A particular set of thresholds, for example, the set of first, second, third, fourth, and / or additional thresholds, may be derived in a blind mode based on corresponding histograms.

[0125] The following steps may be applied in case of equally probably symbols:

[0126] 1. Derive histograms between two specific levels (shown as circles in FIG. 5). Different levels of the set of signal levels can be detected by finding histogram peaks based on the full histogram (shown as a line in FIG. 5).

[0127] 2. Find the location of the minimum histogram bin. In some cases, there may be multiple 0 bins. In this case, determine a “zero bin region” (ZBR).

[0128] 3. Select J bins on the left and J bins on the right side (shown as rhombuses in FIG. 6) of the ZBR to achieve the best symmetry.

[0129] 4. Use, for example, the second order polynomial (al+a2x+a3x) to fit the selected bins.

[0130] 5. Calculate the threshold T, for example, by T=a2 / a3 / 2.

[0131] FIG. 7 shows experimental results based on a receiver 100, 200 according to this disclosure.

[0132] FIG. 7 shows experimental data with and without digital predistortion (DPD). FFE, DFE, and NC are considered with and without a Volterra filter using 41 linear taps and 5 symbols in second and third order parts. Two and four neighboring symbols are considered (M=2,4).

[0133] • Case 1 - linear FFE and VF(41,0,0): It is impossible to cross pre-forward error correction (FEC) BER=4.85e-3 (PFEC). PDT helps to bring BER bellow PFEC. • Case 2 - NC and VF(41,0,0): PDT brings 0.8 and 1.3 dB gain without DPD depending on memory. With DPD, a smaller gain is observed.

[0134] • Case 3 - DFE and VF(41,0,0): PDT brings 0.4 and 0.6 dB gain without DPD depending on memory. With DPD, a smaller gain is observed.

[0135] • Case 4, 5, and 6 - When VF(41,5,5) is used a small gain is observed. In this case, nonlinear VF is very efficient but may be complex and / or not practical.

[0136] FIG. 8 shows equalization schemes according to this disclosure including: MLSE (top), fulltrellis MLSE (middle), and RS-MLSE (bottom).

[0137] If Maximum Likelihood Sequence Estimation (MLSE) is used to achieve the best performance, the full-trellis MLSE may be too complex and simplified versions may be used.

[0138] One simplified MLSE variant uses a pre-quantizer Q (middle variant of FIG. 8) to decrease the number of MLSE states (reduced- state MLSE, RS-MLSE). In this case, RS-MLSE may use default metrics to avoid large number of multiplications. However, when the Q thresholds are not optimized the performance degradation is almost 0.5 dB in experimental data.

[0139] RS-MLSE (bottom) includes a PDT2 quantizer (Q-PDT2). PDT2 refers to the set of final thresholds.

[0140] Using a procedure according to this disclosure to slice the FFE outputs with the set of third thresholds 106c with M=2 provides performance very similar to those of the full-state MLSE. Small degradation is also observed with the set of first thresholds (which is a simple implementation).

[0141] Unlike PDT used without MLSE, the number of MLSE PDT thresholds is equal to GA(Af+l), where G is number of decision regions. Instead of using the quantized FFE signal to map thresholds, the pre-decisions that require smaller LUT than in the case without MLSE may be used.

[0142] With some modifications, methods according this disclosure can be implemented in systems using the most advanced equalizer 103 schemes such as MLSE. This disclosure may be for coherent and non-coherent digital receivers 100, 200.

[0143] Generally, the processor may be configured to perform, conduct or initiate the various operations of the receiver 100, 200 described herein. The processor may comprise hardware and / or may be controlled by software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. The receiver 100, 200 may further comprise memory circuitry, which stores one or more instruction(s) that can be executed by the processor, in particular under control of the software. For instance, the memory circuitry may comprise a non-transitory storage medium storing executable software code which, when executed by the processor, causes the various operations of the receiver 100, 200 to be performed. In one embodiment, the receiver 100, 200 may comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the receiver 100, 200 to perform, conduct or initiate the operations or methods described herein.

[0144] FIG. 9 shows a method 300 according to this disclosure. The method 300 is a method of operating a receiver 100 for determining thresholds for slicing an input signal 101 associated with a set of signal levels. The receiver 100 comprises: an equalizer 103, a first slicer 104a, a second slicer 104b, a first optimization module 105a, and a second optimization module 105b.

[0145] The method 300 comprises a step 301 of receiving, with the equalizer 103, the input signal 101 and generate a reconstructed signal 102 based on the input signal 101. Further, the method 300 comprises a step 302 of obtaining, with the first slicer 104a, a set of first thresholds 106a. Further, the method 300 comprises a step 303 of determining, with the first slicer 104a, a set of first quantization decisions 107a by using the set of first thresholds 106a and the reconstructed signal 102, wherein each first quantization decision is based on a respective symbol of the reconstructed signal 102 and / or one or more respective neighboring symbols of the respective symbol. Further, the method 300 comprises a step 304 of generating, with the first optimization module 105a, a first set of histograms 108a using the reconstructed signal 102 and the set of first quantization decisions 107a. Further, the method 300 comprises a step 305 of determining, with the first optimization module 105a, a set of second thresholds 106b by using the first set of histograms 108a, wherein each second threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal 102. Further, the method 300 comprises a step 306 of determining, with the second slicer 104b, a set of second quantization decisions 107b by using the set of first quantization decisions 107a, the set of second thresholds 106b, and the reconstructed signal 102. Further, the method 300 comprises a step 307 of generating, with the second optimization module 105b, a second set of histograms 108b using the reconstructed signal 102 and the set of second quantization decisions 107b. Further, the method 300 comprises a step 308 of determining, with the second optimization module 105b, a set of third thresholds 106c by using the second set of histograms 108b, wherein each third threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal 102.

[0146] FIG. 10 shows a method 400 according to this disclosure. The method 400 is a method of operating a receiver 100 for slicing an input signal 101 associated with a set of signal levels. The receiver 100 comprises: an equalizer 103, a first slicer 104a, and a second slicer 104b.

[0147] The method 400 comprises a step 401 of receiving, with the equalizer 103, the input signal 101. Further, the method 400 comprises a step 402 of generating, with the equalizer 103, a reconstructed signal 102 based on the input signal 101. Further, the method 400 comprises a step 403 of obtaining, with the first slicer 104a, a set of first thresholds 106a. Further, the method 400 comprises a step 404 of determining, with the first slicer 104a, a set of first quantization decisions 107a by using the set of first thresholds 106a and the reconstructed signal 102, wherein each first quantization decision is based on a respective symbol of the reconstructed signal 102 and / or one or more respective neighboring symbols of the respective symbol. Further, the method 400 comprises a step 405 of providing, with the first slicer 104a, the set of first quantization decisions 107a to the second slicer 104b. Further, the method 400 comprises a step 406 of obtaining, with the second slicer 104b, a set of final thresholds 106c, 106d, wherein each final threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal 102. Further, the method 400 comprises a step 407 of determining, with the second slicer 104b, a set of fourth quantization decisions 107d by using the set of final thresholds 106c, 106d, the reconstructed signal 102, and the set of first quantization decisions 107a. The disclosure has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed matter, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

CLAIMS1. A receiver (100) for determining thresholds for slicing an input signal (101) associated with a set of signal levels, the receiver (100) comprising: an equalizer (103), a first slicer (104a), a second slicer (104b), a first optimization module (105a), and a second optimization module (105b), wherein the equalizer (103) is configured to receive the input signal (101) and generate a reconstructed signal (102) based on the input signal (101); wherein the first slicer (104a) is configured to: obtain a set of first thresholds (106a), and determine a set of first quantization decisions (107a) by using the set of first thresholds (106a) and the reconstructed signal (102), wherein each first quantization decision (107a) is based on a respective symbol of the reconstructed signal (102) and / or one or more respective neighboring symbols of the respective symbol; wherein the first optimization module (105a) is configured to: generate a first set of histograms (108a) using the reconstructed signal (102) and the set of first quantization decisions (107a), and determine a set of second thresholds (106b) by using the first set of histograms (108a), wherein each second threshold (106b) delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal (102); wherein the second slicer (104b) is configured to: determine a set of second quantization decisions (107b) by using the set of first quantization decisions (107a), the set of second thresholds (106b), and the reconstructed signal (102); and wherein the second optimization module (105b) is configured to: generate a second set of histograms (108b) using the reconstructed signal (102) and the set of second quantization decisions (107b), anddetermine a set of third thresholds (106c) by using the second set of histograms (108b), wherein each third threshold (106c) delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal (102).

2. The receiver (100) according to claim 1, wherein, for each respective symbol of the reconstructed signal (102), the second slicer (104b) is configured to: select, for each respective symbol of the reconstructed signal (102), one or more respective second thresholds of the set of second thresholds (106b) by using the set of first quantization decisions (107a), and determine the set of second quantization decisions (107b) by using the one or more respective second thresholds for each respective symbol of the reconstructed signal (102).

3. The receiver (100) according to claim 2, wherein, for each respective symbol of the reconstructed signal (102), the second slicer (104b) is configured to: estimate one or more neighboring symbols of the respective symbol by using the set of first quantization decisions (107a), obtain a set of first signal level centers for the respective symbol adjacent to the one or more estimated neighboring symbols, determine two or more respective most reliable intermediate second quantization decisions based on the set of first signal level centers, select the one or more respective second thresholds of the set of second thresholds (106b) by using the two or more respective most reliable intermediate second quantization decisions.

4. The receiver (100) according to any one of the preceding claims,wherein each histogram of the first set of histograms (108a) is based on a respective symbol pattern of a first set of symbol patterns, wherein each symbol pattern of the first set of symbol patterns comprises a respective symbol associated with a respective quantization decision of the set of first quantization decisions (107a), and one or more respective neighboring symbols associated with one or more neighboring quantization decisions of said respective quantization decision, wherein each histogram of the second set of histograms (108b) is based on a respective symbol pattern of a second set of symbol patterns, wherein each symbol pattern of the second set of symbol patterns comprises a respective symbol associated with a respective quantization decision of the set of second quantization decisions (107b), and one or more respective neighboring symbols associated with one or more neighboring quantization decisions of said respective quantization decision.

5. The receiver (100) according to any one of the preceding claims, wherein the receiver (100) further comprises one or more additional slicers (104d) according to the second slicer (104b) of any one of the preceding claims and one or more additional optimization modules (105d) according to the second optimization module (105b) of any one of the preceding claims, wherein the one or more additional slicers (104d) and the one or more additional optimization modules (105d) are alternately electrically connected in series to the second optimization modules (105b) and configured to consecutively generate one or more additional quantization decisions and one or more sets of additional thresholds (106d) starting with the set of third thresholds (106c).The one or more sets of additional quantization decisions may consist of or comprise a set of fourth quantization decisions (107d).

6. The device according to any one of the preceding claims, further comprising a third optimization module (105c) and a third slicer (104c), wherein the third slicer (104c) is configured to:obtain a set of fourth thresholds (106e), determine a set of third quantization decisions (107c) by using the set of fourth thresholds (106e) and the reconstructed signal (102), wherein each third quantization decision is based on a respective symbol of the reconstructed signal (102), and wherein the third optimization module (105c) is configured to: generate a third set of histograms using the reconstructed signal (102) and the set of third quantization decisions (107c), determine the set of first thresholds (106a) by using the third set of histograms, wherein each first threshold delimits two adjacent signal levels of the set of signal levels, and provide the set of first thresholds (106a) to the first slicer (104a).

7. The receiver (100) according to any one of the preceding claims, wherein the receiver (100) is configured to determine at least one of the set of first thresholds (106a), the set of second thresholds (106b), the set of third thresholds (106c), and the one or more sets of additional thresholds (106d) by being configured to: determine at least one zero bin region of respectively at least one of: the third set of histograms, the first set of histograms (108a), the second set of histograms (108b), and one or more additional sets of histograms, select a predetermined number of closest bins surrounding the at least one zero bin region, determine one or more respective fit parameters by fitting the selected bins using a function, and determine respectively at least one of: the set of first thresholds (106a), the set of second thresholds (106b), the set of third thresholds (106c), and the one or more sets of additional thresholds ( 106d) based on the one or more respective fit parameters.

8. The receiver (100) according to any one of the preceding claims, wherein the receiver (100) comprises a microcontroller comprising at least one of:the equalizer (103), the first slicer (104a), the second slicer (104b), the third slicer (104c), the first optimization module (105a), the second optimization module (105b), the third optimization module (105c), the one or more additional slicers (104d), and the one or more additional optimization modules (105d).

9. The receiver (100) according to any one of the preceding claims, wherein M is the number of neighboring symbols comprised in each respective pattern of one or more neighboring symbols, wherein L is the number of signal levels in the set of signal levels, and wherein at least one of: the third set of histograms includes L histograms, the first set of histograms (108a) includes L(M+1)histograms, the second set of histograms (108b) includes L(M+1)histograms, and each set of additional of histograms of the one or more sets of additional histograms includes L(M+1)histograms.

10. The receiver (100) according to any one of the preceding claims, wherein the set of fourth thresholds (106e) is predetermined.

11. The receiver (100) according to any one of the preceding claims, configured to store at least one of the set of second thresholds (106b), the set of third thresholds (106c), and the one or more sets of additional thresholds (106d) in a look-up-table.

12. A receiver (200) for slicing an input signal (101) associated with a set of signal levels, the receiver (100) comprising: an equalizer (103), a first slicer (104a), and a second slicer (104b), wherein the equalizer (103) is configured to receive the input signal (101) and generate a reconstructed signal (102) based on the input signal (101); wherein the first slicer (104a) is configured to: obtain a set of first thresholds (106a),determine a set of first quantization decisions (107a) by using the set of first thresholds (106a) and the reconstructed signal (102), wherein each first quantization decision is based on a respective symbol of the reconstructed signal (102) and / or one or more respective neighboring symbols of the respective symbol, and provide the set of first quantization decisions (107a) to the second slicer (104b); and wherein the second slicer (104b) is configured to: obtain a set of final thresholds (106c, 106d), wherein each final threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal (102), and determine a set of fourth quantization decisions (107d) by using the set of final thresholds (106c, 106d), the reconstructed signal (102), and the set of first quantization decisions (107a).

13. The receiver (200) according to claim 12, the receiver (100) further comprises a fourth slicer ( 104d) configured to obtain the set of final thresholds (106c, 106d), determine a set of fifth quantization decisions by using the set of final thresholds (106c, 106d), the reconstructed signal (102), and the set of fourth quantization decisions ( 107d).

14. The receiver (200) according to claim 12 or 13, wherein the second slicer (104b) is configured to select, for each respective symbol of the reconstructed signal (102), one or more respective final thresholds of the set of final thresholds (106c, 106d) by using the set of first quantization decisions (107a), and determine a set of fourth quantization decisions (107d) by using the one or more respective final thresholds for each respective symbol of the reconstructed signal (102), and / or wherein the fourth slicer ( 104d) is configured toselect, for each respective symbol of the reconstructed signal (102), one or more respective final thresholds of the set of final thresholds (106c, 106d) by using the set of fourth quantization decisions (107d), and determine a set of fifth quantization decisions by using the one or more respective final thresholds for each respective symbol of the reconstructed signal (102).

15. The receiver (200) according to any one of the claims 12 to 14, wherein the receiver (200) comprises an application specific integrated circuit, ASIC, which comprises at least one of: the equalizer (103), the first slicer (104a), the second slicer (104b), and the fourth slicer (104d).

16. The receiver (200) according to any one of the claims 12 to 15, wherein the receiver (200) is configured to obtain from a look-up table at least one of the set of first thresholds (106a), the set of final thresholds (106c, 106d), or wherein the receiver (200) is configured to obtain from another device or another module in the receiver (200) at least one of the set of first thresholds (106a), the set of final thresholds (106c, 106d).

17. The receiver (200) according to any one of the claims 12 to 16, wherein the receiver (200) further is the receiver (100) according to any one of the claims 1 to 11.

18. The receiver (200) according to any one of the claims 12 to 17, wherein the set of final thresholds (106c, 106d) is the set of third thresholds (106c) or a set of additional thresholds of the one or more sets of additional thresholds (106d).

19. The receiver (200) according to any one of the preceding claims,wherein the equalizer (103) comprises a feed-forward equalizer, and / or wherein the equalizer (103) is followed by a decision-feedback equalizer or a noise cancellation block for reducing noise amplification.

20. A method of operating a receiver (100) for determining thresholds for slicing an input signal (101) associated with a set of signal levels, the receiver (100) comprising: an equalizer (103), a first slicer (104a), a second slicer (104b), a first optimization module (105a), and a second optimization module (105b), wherein the method comprises: receiving, with the equalizer (103), the input signal (101) and generate a reconstructed signal (102) based on the input signal (101); obtaining, with the first slicer (104a), a set of first thresholds (106a); determining, with the first slicer (104a), a set of first quantization decisions (107a) by using the set of first thresholds (106a) and the reconstructed signal (102), wherein each first quantization decision is based on a respective symbol of the reconstructed signal (102) and / or one or more respective neighboring symbols of the respective symbol; generating, with the first optimization module (105a), a first set of histograms (108a) using the reconstructed signal (102) and the set of first quantization decisions (107a); determining, with the first optimization module (105a), a set of second thresholds (106b) by using the first set of histograms (108a), wherein each second threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal (102); determining, with the second slicer (104b), a set of second quantization decisions (107b) by using the set of first quantization decisions (107a), the set of second thresholds (106b), and the reconstructed signal (102); and generating, with the second optimization module (105b), a second set of histograms (108b) using the reconstructed signal (102) and the set of second quantization decisions (107b); anddetermining, with the second optimization module (105b), a set of third thresholds (106c) by using the second set of histograms (108b), wherein each third threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal (102).

21. A method of operating a receiver (200) for slicing an input signal (101) associated with a set of signal levels, the receiver (200) comprising: an equalizer (103), a first slicer (104a), and a second slicer (104b), wherein the method comprises: receiving, with the equalizer (103), the input signal (101); generating, with the equalizer (103), a reconstructed signal (102) based on the input signal (101); obtaining, with the first slicer (104a), a set of first thresholds (106a); determining, with the first slicer (104a), a set of first quantization decisions (107a) by using the set of first thresholds (106a) and the reconstructed signal (102), wherein each first quantization decision is based on a respective symbol of the reconstructed signal (102) and / or one or more respective neighboring symbols of the respective symbol; providing, with the first slicer (104a), the set of first quantization decisions (107a) to the second slicer (104b); obtaining, with the second slicer (104b), a set of final thresholds (106c, 106d), wherein each final threshold delimits two adjacent signal levels of the set of signal levels for a respective pattern of one or more neighboring symbols of any particular symbol of the reconstructed signal (102); and determining, with the second slicer (104b), a set of fourth quantization decisions ( 107d) by using the set of final thresholds (106c, 106d), the reconstructed signal (102), and the set of first quantization decisions (107a).

22. A computer program product comprising a program code for performing, when the program code is executed on a computer, the method according to claim 20 or 21.

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