Abstract: This invention relates to methods for obtaining a bin number of path metrics. When performing such methods, a histogram is provided, which composes a bin number of values, a maximum value and a tail region left or right of the maximum value. A bin number of path metrics is obtained from said values. According to an embodiment a local extremum is removed from said tail region. According to another embodiment the tail region is forced to be convex. According to a further embodiment a maximum metric difference between neighboring metrics is ensured.

Abstract: Two decoding algorithms are introduced for the decoding of multi-level coded modulation and other types of coded modulation involving component codes and interleaving operations. An improved hard iterative decoding (IHID) algorithm is presented that improves upon a hard iteration decoding technique by adding a stopping criterion. Also, a list Viterbi hard iteration decoding (LV-IHID) algorithm is presented that employs list decoding in conjunction with the IHID algorithm. Both of these decoding algorithms improve upon conventional multi-stage decoding by reducing the effective error multiplicity that is observed at the lowest coding level. It is demonstrated that the LV-IHID algorithm performs close to soft iterative decoding. The computational and delay complexity of the proposed decoding algorithms compare favorably with soft iterative decoding strategies. Also, a novel labeling strategy for MLC design is presented.

Abstract: According to one embodiment, a data detection system includes a coefficient-and-variance engine for selecting which infinite impulse response (IIR) filter and prediction error variance to process and store at any time, and a maximum-likelihood sequence detector. The coefficient-and-variance engine comprises a filter bank storing a plurality of IIR filters that represent a plurality of data-dependent noise whitening or noise prediction filters; a least-mean square (LMS) engine for adapting each IIR filter to actual noise conditions: a variance hank storing a plurality of prediction error variance values; and a data-dependent prediction error variance computation unit which updates the plurality of prediction error variance values. The maximum-likelihood sequence detector includes a metric computation unit that employs the plurality of IIR filters in the filter bank and the plurality of prediction error variances in the variance bank to adaptively compute detector branch metrics.

Abstract: Techniques for generating soft values for parity bits in a convolutional decoding process are disclosed. An exemplary method comprises, for each of at least one iteration in at least one soft-input soft-output decoder, calculating intermediate probability values for each possible transition between a first plurality of candidate decoder states at a first time and a second plurality of candidate decoder states at a second time. Two or more partial sums are then computed from the intermediate probability values, wherein the partial sums correspond to possible combinations of two or more systematic bits, two or more parity bits, or at least one systematic bit and at least one parity bit. Soft values, such as log-likelihood values, are then estimated for each of at least one systematic bit and at least one parity bit of the received communications data corresponding to the interval between the first and second times, based on the partial sums.

Abstract: A channel decoder including an amplifier configured to amplify a signal; a first summer configured to generate an output signal based on the signal amplified by the amplifier; and a Viterbi detector module configured to, based on the output signal, generate a first estimate signal and a second estimate signal, wherein the first estimate signal and the second estimate signal respectively indicate an estimate of data in the signal. The channel decoder further includes a second summer configured to generate a first error signal indicating a first gradient based on the first estimate signal; and a third summer configured to generate a second error signal indicating a second error gradient based on the second estimate signal. The first summer is configured to generate the output signal based on (i) the first error signal and (ii) the second error signal.

Abstract: A method for calculating backward state metrics of a trellis, the method includes: performing a radix-K calculation of backward state matrices of multiple states of at least one time instance of a trellis; and performing a radix-J calculation of backward state matrices of multiple states of at least one other time instance of the trellis; wherein K differs from J.

Abstract: A receiver for a mobile communication device comprises an primary detector for generating an initial sequence estimate comprising a plurality of initial symbol estimates from a received symbol sequence corrupted by intersymbol interference, and a secondary detector to receive said initial sequence estimate and to output a final sequence estimate comprising a plurality of final symbol estimates. The secondary detector comprises a sequence generator configured to generate one or more revised sequence estimates by replacing at least one initial symbol estimate in said initial sequence estimate with a corresponding nearest neighbor symbol in each of said revised symbol estimates; an error calculator to compute error metrics for said revised sequence estimates; and a selection circuit to compare error metrics for said initial and revised sequence estimates and to output one of said initial or revised sequence estimates as said final sequence estimate based on said error metrics.

Abstract: A Viterbi decoder includes a survival memory unit, for storing a plurality of survivor metric into a writing column of a writing bank of a plurality of banks in alternating intervals of a clock according to a writing bank order and a writing column order, and a trace back unit, for reading a reading column of each bank not performing storing operations according to a reading bank order and a reading column order in every interval of the clock.

Abstract: Provided is a method and apparatus for receiving a signal for a MIMO system. The receiving apparatus includes: a QR decomposer for calculating a unitary matrix Q, an upper triangle matrix R, and a vector size for a received signal; a multiple dimension detector for calculating a first LLR for an output of the QR decomposer through multiple dimension detection; an inverse matrix and weight calculator for calculating an inverse matrix for the upper triangle matrix R and a weight; an interference remover for regenerating a symbol for a demodulated data stream using the fist LLR and removing interference from an output vector of the QR decomposer using the regenerated symbol; and a weight zero forcing unit for performing zero forcing on the interference removed output vector from the interference remover using the inverse matrix of the upper triangle matrix R and the weight and calculating a second LLR.

Abstract: This invention relates to methods for obtaining a bin number of path metrics. When performing such methods, a histogram is provided, which comprises a bin number of values, a maximum value and a tail region left or right of the maximum value. A bin number of path metrics is obtained from said values. According to an embodiment a local extremum is removed from said tail region. According to another embodiment the tail region is forced to be convex. According to a further embodiment a maximum metric difference between neighboring metrics is ensured.

Abstract: A decoding method and apparatus of a retransmission communication system are provided. In the decoding method and apparatus, weights are applied to error data and retransmitted data, and the resulting error data and the resulting retransmitted data are chase-combined. Therefore, it is possible to reduce the coding rate of combined data and enhance the reliability of decoding.

Abstract: A chunk of branch metric computation bits is generated including bits that correspond to transition bits of a possible chunk of transition bits that could have been generated by a state transition of a convolutional encoder of a transmitter. The bits of the chunk of branch metric computation bits are scrambled. A branch metric for the received chunk of soft scrambled code bits is calculated as a function of the scrambled bits of the chunk of branch metric computation bits and the soft scrambled code bits of the received chunk of soft scrambled code bits. The branch metric is indicative of the probability that the received chunk of soft scrambled code bits was originally generated by the convolutional encoder as the chunk of transition bits corresponding to the generated chunk of branch metric computation bits.

Abstract: Aspects of a method and system for UMTS HSDPA Shared Control Channel processing may include calculating at a receiver, for each one of a plurality of control channels, a quality metric based at least one Viterbi Decoder state metric. A control channel may be selected on the basis of the quality metrics, where the quality metric is selected that provides maximum confidence. The selected control channel may be chosen if its corresponding 3GPP metric is greater than a specified threshold, where the threshold is a design parameter. A validity of a selected control channel may be determined based on consistency and a CRC, where the CRC may be derived from decoding a sub-frame. The calculating and selecting may be done for a first slot of a sub-frame for High-Speed Shared Control Channels.

Abstract: A receiving apparatus and method of a Maximum Likelihood (ML) scheme in a Single-Carrier (SC) system are provided. The apparatus includes at least two antennas, at least two Orthogonal Frequency Division Multiplexing (OFDM) demodulators, at least two subcarrier mappers, at least two OFDM modulators, and a detector. The antennas receive signals. The OFDM demodulators convert the signals into frequency domain signals. The subcarrier mappers confirm signals mapped to frequency domain subcarriers. The OFDM modulators convert the signals into time domain signals. The detector constructs at least one set for candidate transmission symbols and detects receive signals through ML detection using the set.

Abstract: A detector recovers servo data from a servo signal generated by a read-write head, and determines the head-connection polarity from the recovered servo data. Such a detector allows a servo circuit to compensate for a reversed-connected read-write head, and thus allows a manufacturer to forego time-consuming and costly testing to determine whether the head is correctly connected to the servo circuit.

Abstract: Devices, systems, methods, and other embodiments associated with generating a moving average are described. In one example method an average value of a sliding window of M sequential data values is calculated on a per clock basis, where M is an integer. A data value is detected that has an error. The data value is in the sliding window of M sequential data values. The method corrects the average value of the sliding window as a function of the error.

Abstract: The invention which relates to a method and to an arrangement for generating soft bit information in a receiver of a multiple antenna system is based on the object of reducing the calculation complexity for generating the soft bit information.

Abstract: A survivor path memory is provided for a Viterbi detector. The survivor path memory comprises a plurality of columns, each associated with a different time step, and an input processor. Each column comprises a flip flop for storing one bit or portion of a bit sequence associated with a Viterbi state; and a multiplexer for each state controlled by a case signal indicating a time step, the multiplexer selecting a state from a previous time step, wherein an output of the multiplexer of a given state is connected to at least one data input of a flip flop of the given state. The input processor generates a control signal that exchanges one or more pointers based on a trellis structure, wherein each of the pointers points to one of the flip flops.

Abstract: A method for reconstructing a signal from incomplete data in a signal processing device includes acquiring incomplete signal data. An initial reconstruction of the incomplete signal data is generated. A reconstruction is generated starting from the initial reconstruction by repeating the steps of: calculating a sparsity transform of the reconstruction, measuring an approximation of sparsity of the reconstruction by applying an m-estimator to the calculated sparsity transform, and iteratively optimizing the reconstruction to minimize output of the m-estimator thereby maximizing the approximation of sparsity for the reconstruction. The optimized reconstruction is provided as a representation of the incomplete data.

Abstract: Systems and methods for processing and decoding TCM/BCM-coded signal vectors. A multi-dimensional signal vector is received by, for example, a TCM or BCM decoder. The TCM/BCM decoder identifies the closest signal points in the signal constellation set, or “nearest neighbors,” for each dimension of the received signal vector. The TCM/BCM decoder then forms a test set that includes a plurality of multi-dimensional test vectors, where each dimension of each test vector is based on an identified nearest neighbor. In particular, each test point in the test set is based on a different combination of the nearest neighbors. The TCM/BCM decoder can compute branch metrics based on only the test points in the test set, and can make detection decisions using the computed branch metrics.

Abstract: A path comparison unit is disclosed for determining paths in a trellis that compete with a survivor path. The disclosed path comparison unit comprises a first type functional unit comprising a multiplexer and a register to store one or more survivor bits associated with the survivor path; and at least two second type functional units, wherein each second type functional unit comprises a multiplexer and a logical circuit to compute at least one equivalence bit indicating whether the bit for a respective path and the bit for the survivor path are equivalent. Generally, the respective path is one or more of a win-lose path and a lose-win path.

Abstract: A vestigial sideband (VSB) modulation transmission system and a method for encoding an input signal in the system are disclosed. According to the present invention, the VSB transmission system includes a convolutional encoder for encoding an input signal, a trellis-coded modulation (TCM) encoder for encoding the convolutionally encoded signal, and a signal mapper mapping the trellis-coded signal to generate a corresponding output signal. Different types of the convolutional encoders are explored, and the experimental results showing the performances of the VSB systems incorporating each type of encoders reveals that a reliable data transmission can be achieved even at a lower input signal to noise ratio when a convolutional encoder is used as an error-correcting encoder in a VSB system.

Abstract: A channel adaptive iterative turbo decoder for computing with MAP decoders a set of branch metrics for a window of received data, computing the forward and reverse recursive path state metrics and computing from the forward and reverse recursive path state metrics the log likelihood ratio for 1 and 0 and interleaving the decision bits; and identifying those MAP decoder decision bits which are non-convergent, computing a set of branch metrics for the received data, computing from the forward and reverse recursive path state metrics the log likelihood ratio (LLR) for 1 and 0 for each non-converged decision bit and interleaving the non-convergent decision bits.

Abstract: A digital broadcast transmitting system and a signal processing method thereof that improves the receiving performance of the system. A digital broadcast transmitter includes a randomizer to receive and randomize a transport stream into a specified position of which stuff bytes are inserted, a replacement sequence generator to generate known data including a predefined sequence, a stuff-byte exchange unit to insert the known data into the specified position of the transport stream into which stuff bytes are inserted, an encoder to encode the transport stream output from the stuff-byte exchange unit for an error correction, and a transmission unit to modulate the encoded transport stream, RF-convert the modulated transport stream and transmit the RF-converted data. The digital broadcast receiving performance is improved even in an inferior multi-path channel by detecting the known data from the received transmission and using the known data for synchronization and equalization.

Abstract: A tail-biting decoding method and device are provided, so as to improve accuracy of backtracking state determination and decrease decoding delay. The method includes the following steps. Survivor paths of a training system are acquired. The training system is formed of a first transport block and a second transport block connected in series. The number of the survivor paths passing through each first state of the second transport block is counted. A first state having a maximum number of the survivor paths may be selected as a backtracking state of the second transport block. Backtracking decoding is performed on the second transport block by using the survivor paths on the backtracking state, so as to obtain a decoding result.

Abstract: In one embodiment, a signal processing receiver has a branch-metric calibration (BMC) unit that receives (i) sets of four hard-decision bits from a channel detector and (ii) a noise estimate. The BMC unit has two or more update blocks (e.g., tap-weight update and/or bias-compensation blocks) that generate updated parameters used by a branch-metric unit of the channel detector to improve channel detection. The two or more update blocks generate the updated parameters based on (i) the sets of four hard-decision bits, (ii) the noise estimate, and (iii) bandwidth values. The bandwidth values for at least two of the two or more update blocks are selected such that they are different from one another. Selecting different bandwidth values may reduce the bit-error rate for the receiver over the bit-error rate that may be achieved by selecting the bandwidth values to be the same as one another.

Abstract: A method for communication includes receiving at a receiver a signal from a transmitter embodying data encoded with an error correction code. The signal is processed in order to extract a sequence of samples in a complex signal space. Scalar values are extracted from the samples and the scalar values are processed so as to define one or more clusters of scalar data points. Gain and noise of the signal are estimated responsively to the defined clusters. Bit value metrics for the signal are computed based on the samples and the estimated gain and noise of the signal. The error correction code is decoded using the bit value metrics.

Abstract: A Viterbi detector includes a plurality of possible bit patterns that correspond to branches of a detector trellis and a plurality of data dependent noise prediction filters, with multiple filters of different orders being associated with a given bit pattern. A method of decoding includes applying observables to a Viterbi detector that associates a plurality of data dependent noise filters with a given possible bit pattern that corresponds to a branch of the detector trellis, calculating the composite maximum likelihood branch metric by incorporating the results of filtering the observables through the associated plurality of filters, calculating the composite maximum likelihood branch metrics in the same manner for other possible bit patterns, and so forth, and associating soft output values with detected bits in the observables based on the calculated branch metrics.

Abstract: A receiving method and apparatus for combining Hybrid Automatic Repeat Request (HARQ) data in a wireless communication system are provided. More particularly, a method and apparatus for increasing HARQ combining capability while effectively using a limited-sized memory are provided. The receiving method for combining the HARQ data includes predicting a maximum size of currently receivable data, converting HARQ data received from a transmitting end into Log Likelihood Ratio (LLR) information, determining whether the received HARQ data is retransmitted data, if the determination result shows that the HARQ data is not the retransmitted data, determining whether the converted LLR information is compressed according to the predicted maximum data size, and storing the converted LLR information in a memory according to the determination result on whether compression is necessary.

Abstract: Method and apparatus for decoding code words received over a communication channel are disclosed. A radius-adaptive sphere decoding methodology reduces the number of operations in sphere-constrained search. Imposing probabilistic noise constraint on top of sphere constraint, particularly at an early stage, provides a more stringent necessary condition. Hence, many branches that are unlikely to be selected are removed in the early stage of sphere search. The trade-off between computational complexity and performance can be controlled by adjusting the pruning probability.

Abstract: Methods and apparatus are described for reducing memory storage cells in a turbo decoder by storing only half the state metrics generated during a scan process. States associated with each bit transmission may be divided into couples and only one state from every state couple may be stored. In one example embodiment, only the state metric for a losing state of every state couple is saved, along with a single bit, e.g., 1 or 0, indicating whether the upper state or lower state of the state couple was the winner. The winning state may be reconstituted at a later stage. In this manner, for a code rate 1/3 and constraint length 3 turbo code, instead of storing 8*10=80 bits of state metrics for each systematic bit, only (4*10)+(4*1)=44 bits of scan state metrics data need be stored, a savings of nearly 50% regardless of the transistor technology used.

Abstract: Certain embodiments of the present disclosure provide a method for frequency-domain gain control in system utilizing orthogonal frequency division multiplexing (OFDM) multiple input multiple output (MIMO). The proposed method reduces the complexity of the system while maximizing the internal accuracy of the OFDM MIMO decoder and preserving the performance of the system.

Abstract: Provided are: plural circuit components including a circuit component which constitutes a receiving unit receiving a signal sequence which is arranged so that a desired signal and a signal different from the desired signal are lined up in time series, the desired signal indicating desired data which includes at least one of text data, sound data, image data, and a computer program product; and an operating parameter changing unit which changes an operating parameter of at least one of the plural circuit components, during a period in which the receiving unit receives the signal different from the desired signal.

Abstract: A method for estimating the speed of a mobile device in a network is provided that includes selecting a correlation length from a plurality of possible correlation lengths. A correlation result is generated based on the selected correlation length. A speed estimate is generated for the mobile device based on the correlation result.

Abstract: A system and method implement low complexity maximum likelihood sequence detection. A decision feedback algorithm computes x(M+D+L?1). Optimality examination is performed for x(M), and state values and values of Markov states along paths from states in x(M) to xl(M+L) are computed.

Abstract: Techniques for generating soft values for parity bits in a convolutional decoding process are disclosed. An exemplary method comprises, for each of at least one iteration in at least one soft-input soft-output decoder, calculating intermediate probability values for each possible transition between a first plurality of candidate decoder states at a first time and a second plurality of candidate decoder states at a second time. Two or more partial sums are then computed from the intermediate probability values, wherein the partial sums correspond to possible combinations of two or more systematic bits, two or more parity bits, or at least one systematic bit and at least one parity bit. Soft values, such as log-likelihood values, are then estimated for each of at least one systematic bit and at least one parity bit of the received communications data corresponding to the interval between the first and second times, based on the partial sums.

Abstract: Techniques are provided for transmitting and receiving a mother code in an incremental redundancy hybrid automatic repeat-request protocol. A set of information bits corresponding to a message is encoded and interleaved to produce the mother code. Each bit position of the mother code is mapped to an output symbol, and each output symbol is mapped to an antenna for transmission. One or more transmissions are performed, where each transmission includes puncturing the mother code by selecting one or more symbols from the output symbols, and transmitting each symbol in the one or more symbols on an antenna corresponding to that symbol. The mother code is decoded, in part, by determining combinable bits contained within a set of received symbols and computing one or more log-likelihood ratio values corresponding to each symbol in the set of received symbols.

Abstract: According to one aspect of the present invention, an apparatus is provided to enable weather band radio signals to be received and processed using a digital signal processor (DSP). The DSP can include functionality to implement both frequency modulation (FM) demodulation and weather band data demodulation, i.e., specific area encoding (SAME) demodulation. In one such embodiment, soft decision samples of a SAME message can be combined, and based on a combined result, a hard decision unit can generate a bit value of weather band data.

Abstract: A system, apparatus, and method are provided for a nonlinear Viterbi detector that may be used in an iterative decoding system or any other system with multiple, interconnected detectors. At least one of the Viterbi detectors may estimate the digital information sequence in a received signal based on the signal itself and an estimate of the signal from another of the Viterbi detectors. The at least one Viterbi detector may calculate branch metrics for a subset of the branches in an associated trellis diagram by selecting branches that correspond to the output of the other Viterbi detector.

Abstract: A decoding device includes a BM calculator calculating a branch metric in a Log-MAP algorithm from received data and extrinsic information, an ACS operator calculating a maximum value of a path metric based on the branch metric, a correction term calculator calculating a Jacobian correction value of the path metric, and a correction operator correcting the path metric by adjusting a value of the Jacobian correction value based on a size of the received data and adding the adjusted correction value to the maximum value.

Abstract: Certain embodiments provide methods and apparatus for decoding a string of data bits, encoded with a turbo encoding scheme, in a wireless communication system. One or more a-priori bit values corresponding to expected bit values at one or more identified bit locations in the string of data bits may be identified. One or more branch metrics used in a turbo decoding scheme may be manipulated to effectively remove decoding paths, from a collection of possible decoding paths, based at least on the identified one or more a-priori bit values, resulting in one or more remaining decoding paths. The string of data bits may be decoded by selecting a decoding path from the one or more remaining decoding paths.

Abstract: One embodiment of the invention features a programmable gain stage in analog update circuitry to overcome the accuracy limitation of the circuit gain and the maintenance of small finite number of possible sequence estimates.

Abstract: Apparatus and methods are disclosed for decoding data stored on a data storage medium. A disclosed decoding method and decoder include a radial incoherence (RI) detector that increases the probability of detecting RI and improves the decoding performance in terms of the bit error rate of the decoded signal. RI is detected by comparing an input signal to the decoder against a RI threshold value and generating a RI-type signal. The RI detector may include a filter for filtering out noise and error in the RI-type signal, an adaptive threshold unit that adjusts the RI threshold value based upon the RI-type signal, a transition-based threshold unit that adjusts the RI threshold value based upon each transition in the input signal, or a path-based threshold unit that adjusts the RI threshold value based upon a best surviving path corresponding to the input signal, in combination or alone.

Abstract: An application specific processor to implement a Viterbi decode algorithm for channel decoding functions of received symbols. The Viterbi decode algorithm is at least one of a Bit Serial decode algorithm, and block based decode algorithm. The application specific processor includes a Load-Store, Logical and De-puncturing (LLD) slot that performs a Load-Store function, a Logical function, a De-puncturing function, and a Trace-back Address generation function, a Branch Metric Compute (BMU) slot that performs Radix-2 branch metric computations, Radix-4 branch metric computations, and Squared Euclidean Branch Metric computations, and an Add-Compare-Select (ACS) slot that performs Radix-2 Path metric computations, Radix-4 Path metric computations, best state computations, and a decision bit generation. The LLD slot, the BMU slot and the ACS slot perform in a software pipelined manner to enable high speed Viterbi decoding functions.

Abstract: The present patent application discloses a method and apparatus for decoding, comprising decoding signals iteratively, mutually exchanging extrinsic information, calculating APP LLRs for both systematic and parity bits and making a hard decision after a plurality of iterations is completed based on accumulated soft information. The present patent application also discloses a method and apparatus for post decoding soft interference canceling, comprising generating updated a posteriori probabilities for systematic and parity bits from a turbo decoder, mapping the posteriori probabilities to soft symbols, quantizing the soft symbols, re-encoding a data packet, filtering a chip sequence, reconstructing an interference waveform, and scaling reconstruction filter coefficients using the symbols.

Abstract: In one embodiment, an apparatus includes a receiver configured to receive a transmission from a wireless communication device, the transmission associated with resource units, a detector configured to generate log-likelihood ratio data from the received transmission, and a controller configured to calculate noise and interference for each of the resource units and modify the generated log-likelihood ratio data based on the calculated noise and interference.

Abstract: Embodiments of a broadcast receiver and method for optimizing a scale factor in a log-likelihood ratio (LLR) mapper are generally described herein. In some embodiments, the broadcast receiver includes an LLR mapper to generate LLRs from demodulated data samples, a low-density parity-check (LDPC) decoder to generate decoded data from the LLRs, and an LLR optimizer to dynamically select a scale factor for the LLR mapper based on a number of iterations for convergence of the LDPC decoder. In some embodiments, the LLR optimizer iteratively revises the scale factor during receipt of broadcast signals until the number of iterations of the iterative decoder is either minimized for convergence or minimized for convergence failures.

Abstract: According to one aspect of the teachings presented in this document, a wireless communication receiver implements a form of joint detection that is referred to as “fast joint detection” (FJD). A receiver that is specially adapted to carry out FJD processing provides an advantageous approach to joint detection processing wherein the number of computations needed to produce reliable soft bits, for subsequent turbo decoding and/or other processing, is significantly reduced. Further, the algorithms used in the implementation of FJD processing are particularly well suited for parallelization in dedicated signal processing hardware. Thus, while FJD processing is well implemented via programmable digital processors, it also suits applications where high-speed, dedicated signal processing hardware is needed or desired.

Abstract: A method of calculating backward computations branch metrics for a butterfly in a trellis of a MAP-genre decoding algorithm includes providing initialized branch metrics for the transitions in the butterfly and incrementing the branch metrics with a group of data values corresponding to the transitions in accordance with control signals derived from the butterfly index and one or more polynomials describing tap positions of the encoding equipment to whose operation the trellis relates, wherein the group comprises systematic bit and parity bit values.

Abstract: A feedforward receiver and method are described herein that address inter-symbol interference in received symbols by using an enhanced equalizer to generate joint soft values (joint information of a previous modem bit x? and a modem bit x) and an enhanced decoder which uses the joint soft values and side information (bias about the previous modem bit x?) to output a more reliable information bit x.