Communication systems are described that use signal constellations, which have unequally spaced (i.e. geometrically shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes d.sub.min, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.

A hybrid voltage mode (VM) and current mode (CM) four-level pulse amplitude modulation (PAM-4) transmitter circuits (a.k.a. drivers) is calibrated using a configurable replica circuit and calibration control circuitry. The replica circuit includes an on-chip termination impedance to mimic a receiver's termination impedance. The amount of level enhancement provided by the current mode circuitry is calibrated by adjusting the current provided to the output node and sunk from the output node by the replica current mode circuitry while the replica voltage mode circuitry is driving an intermediate PAM-4 level. After the level enhancement has been set, the non-linearity between levels is calibrated by adjusting the amount of current provided to the output node by the replica current mode circuitry while the replica voltage mode circuitry is driving a maximum output voltage level.

A method for data transmission includes receiving a data stream from a host device, the data stream as received from the host device including encoded data, separating the encoded data in the data stream into first data blocks and second data blocks, and generating a first forward error correction (FEC) block. The first FEC block includes a first parity section and a first data section, the first parity section includes a first parity bit corresponding to the first data blocks and a second parity bit corresponding to the second data blocks, and the first data section includes the first data blocks and the second data blocks. The method further includes transmitting the first FEC block.

Methods, systems, and devices related to a memory system or scheme that includes a first memory device configured for low-energy access operations and a second memory device configured for storing high-density information and operations of the same are described. The memory system may include an array configured for high-density information and may interface with a host via a controller and a cache or another array of a relatively fast memory type. The memory system may support signals communicated according to one or several modulation schemes, including a modulation scheme or schemes that employ two, three, or more voltage levels (e.g., NRZ, PAM4). The memory system may include, e.g., separate channels configured to communicate using different modulation schemes between a host and between memory arrays or memory types within the memory system.

Communication systems are described that use signal constellations, which have unequally spaced (i.e. geometrically shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes d.sub.min, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.

Communication systems are described that use signal constellations, which have unequally spaced (i.e. geometrically shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes d.sub.min, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.

A PAM reception circuit includes a first comparison circuit that outputs a first bit value in two-bit values based on a result of a comparison between a reception signal of pulse amplitude modulation 4 in which the two-bit values are associated with four potential levels divided by three threshold values by gray codes and a first threshold value which is a center of the three threshold values, an absolute value circuit that outputs an absolute value of a difference between the reception signal and the first threshold value or a negative value obtained by inverting a sign of the absolute value from a positive sign to a negative sign, and a second comparison circuit that outputs a second bit value in the two-bit values based on a result of a comparison between a second threshold value which is larger than the first threshold value in the three threshold values.

Precompensator-based quantization techniques offer a way to reduce the complexity and power requirements of clock recovery modules while offering improved timing recovery performance relative to a bang-bang scheme operating in a lossy channel. One illustrative method embodiment includes: (a) obtaining a receive signal having a sequence of symbols from a symbol set, the receive signal exhibiting trailing intersymbol interference; (b) operating on the receive signal with a precompensation unit having a set of comparators to produce, for each sampling instant, a set of comparator results representing a quantized receive signal value, the set of comparators applying a set of threshold values that at least partly compensate for the trailing intersymbol interference; (c) deriving a symbol decision from each set of comparator results; (d) combining the symbol decisions with said quantized receive signal values to determine an estimated timing error for each sampling instant; and (e) filtering the estimated timing errors to generate a sampling clock.

Methods of operating a serial data bus divide series of data bits into sequences of one or more bits and encode the sequences as N-level symbols, which are then transmitted at multiple discrete voltage levels. These methods may be utilized to communicate over serial data lines to improve bandwidth and reduce crosstalk and other sources of noise.

Mechanisms to reduce noise and/or energy consumption in PAM communication systems, utilizing conditional symbol substitution in each burst interval of a multi-data lane serial data bus.