Abstract: Various embodiments of the present invention provide systems and methods for data processing. For example, some embodiments of the present invention provide data processing circuits including a pattern detection circuit having at least two data detector circuits each operable to receive the same series of data samples and to provide a first detected data output and a second detected data output, respectively. In addition, the data pattern detection circuit includes a result combining circuit that is operable to assert a pattern found output based at least in part on the first detected data output and the second detected data output.

Abstract: Signal transmitting and decoding methods considering repeatedly transmitted information in transmitting informations in various types are disclosed. Both a first type information varying with a long period and a second type information varying with a short period are simultaneously transmitted by a same period. A receiving side receiving these informations is able to perform fast decoding by unmasking the corresponding information prior to decoding of a next received signal after obtaining the first type information in a manner of considering a fact that the first type information is repeatedly transmitted for a prescribed period of time.

Abstract: A method and apparatus for decoding encoded data bits of a wireless communication transmission are provided. A set of a-priori bit values corresponding to known bit values of the encoded data bits may be generated. Decoding paths that correspond to decoded data bits that are inconsistent with the a-priori bit values may be removed from the possible decoding paths to consider, and decoding the encoded data bits by selecting a decoding path from remaining decoding paths of the possible decoding paths that were not removed.

Abstract: An equalizing structure and method for a wireless communication system receiving device. Two or more transmit signals transmitted in parallel from one or more transmitters are received in received signal vectors representing two or more received data streams, the signals including information modulated onto carrier signals according to a modulation scheme, all possible transmit signals being represented by candidate constellation values in the signal constellation of the modulation scheme. A processor calculates an estimate for a constellation value of a received signal and determines a number of candidate constellation values in the vicinity of the estimated constellation value in the signal constellation. A metric value calculator calculates metric values based on the received signal vectors and the product of channel estimation values with candidate signal vectors.

Abstract: Systems, devices and techniques for soft-in, soft-out (SISO) decoding can include accessing initial soft information on a series of data units received over a communication channel, using a cyclic graphical model to represent a coding scheme associated with the received data units, obtaining cycle-free graphical models for a plurality of second conditions allowable by the coding scheme, and generating soft-out decision information by using information that includes the obtained cycle-free graphical models and the initial soft information. The number of obtained cycle-free graphical models can be less than a total number of conditions associated with the cyclic graphical model. Soft decision information can include confidence levels for each data unit.

Abstract: In a receiver, a channel estimation unit estimates channel characteristics of each channel, and a weight generation unit generates a weight matrix used in equalization processing by an equalizer in accordance with the estimated values of channel characteristics for each channel as estimated by the channel estimation unit. Furthermore, a likelihood calculation unit calculates a likelihood indicating a degree of certainty for each transmission stream using the weight matrix generated by the weight generation unit, and an adaptive control unit determines a transmission rate appropriate for transmission of a signal from a transmitter to the receiver in accordance with the likelihood of each transmission stream calculated by the likelihood calculation unit, notifying the transmitter of the determined transmission rate.

Abstract: An apparatus for decoding a received plurality of multi-path signals to recover the data content of transmitted signals may include an integrated circuit. The integrated circuit may be configured to generate a logarithm likelihood ratio based on a received plurality of multi-path signals, where the received plurality of multi-path signals is representative of transmitted data content. The integrated circuit may be further configured to arrange coefficients of an expression generated based on the received plurality of multi-path signals and integrate the expression. The integrated circuit may be further configured to divide the integrated expression by prior information. As a result, the integrated circuit may be configured to receive the plurality of multi-path signals and decode the signals via integration. Associated methods and computer program products may also be provided.

Abstract: Certain aspects of the present disclosure relate to a technique for two-step joint demapping based on sphere decoding for log-likelihood ratio (LLR) computation related to a received multiple-input multiple-output (MIMO) signal. The first step of the proposed algorithm comprises a linear minimum mean square error (LMMSE) based detection to form soft symbol estimates of symbols being transmitted. Then, the LMMSE-based soft symbol estimates can be utilized to form a set of constellation points of a stream interfering to a stream of interest. These candidate constellation points can be then subtracted (canceled) from the received signal to improve the LLR computations of the stream of interest. After the cancellation, the maximum ratio combining (MRC) can be applied to each individual stream to form more refined soft symbol estimates as well as an effective signal-to-noise ratio (SNR) estimate.

Abstract: Method and arrangement for use in a receiving node, for determining whether received data is encoded with a certain channel code candidate. The method involves obtaining baseband data encoded with an unknown channel code and calculating the respective posterior probabilities that a set of syndrome checks are satisfied, given the obtained data, which syndrome checks are associated with the channel code candidate. The method further involves combining the posterior probabilities and determining whether the channel code candidate was used for encoding the obtained data, based on the combined posterior probabilities.

Abstract: The present invention relates a system and method for mitigating impairment in a communication system. In one embodiment, the system comprises a transmitter adapted to transmit at least one signal and a receiver adapted to receive the at least one signal and mitigate inter code interference in the signal using at least one inter code interference coefficient.

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: The present invention discloses a candidate list augmentation apparatus with dynamic compensation in the coded MIMO systems. The proposed path augmentation technique in the present invention can expand the candidate paths derived from the detector to a distinct and larger list before computing the soft value of each bit. Consequently, the detector is allowed to deliver a smaller list, leading to reduction in computation complexity. Moreover, an additive correction term is introduced to dynamically compensate the approximation inaccuracy in the soft value generation, which improves the efficiency and performance of the coded MIMO systems.

Abstract: Techniques are provided to improve receive beamforming at a wireless communication device that receives energy in a frequency band at M plurality of antennas, where the received energy includes desired signals and interference signals. The wireless communication device has no knowledge of the spatial signatures of the desired signals and interference signals. A weighted sum signal vector is computed from the received signals and a covariance matrix is computed from the receive signals. Eigenvalue decomposition of the covariance matrix is computed to obtain M eigenvalues of corresponding M eigenvectors of the covariance matrix. A correlation rate is computed between the M eigenvectors and the weighted sum signal vector. A combined receive beamforming and nulling weight vector is computed from the M eigenvectors and the weighted sum signal vector and based further on the correlation rate.

Abstract: An equalizing structure and method for a wireless communication system receiving device, in which two or more transmit signals transmitted in parallel from one or more transmitters are received in received signal vectors representing two or more received data streams, the signals including information modulated onto carrier signals according to a modulation scheme, all possible transmit signals being represented by candidate constellation values in the signal constellation of the modulation scheme. A metric value calculator calculates metric values based on the received signal vectors and the product of channel estimation values with candidate signal vectors, each candidate signal vector including a candidate constellation value for each of the two or more transmit signals. A maximum likelihood detector detects one of the candidate signal vectors having a minimum Euclidean distance to a respective receive signal vector as a most likely transmit signal vector based on the metric values.

Abstract: A method and an apparatus are provided for binarizing an input signal, which is capable of reliably correcting an offset of the input signal even when the input signal does not reach a reference level or has a single frequency, a disc driver and a recording medium. The binarizing method includes viterbi-decoding the input signal to obtain a viterbi-decoded signal; slicing the input signal based on a predetermined reference level to obtain a sliced signal; obtaining an offset of the input signal by low-pass filtering the viterbi-decoded signal or the sliced signal; and correcting the offset of the input signal based on the obtained offset. The viterbi-decoded signal is a binary signal of the input signal.

Abstract: Various embodiments of the present invention provide systems and methods for data processing. For example, a data processing circuit is disclosed that includes a first data detection circuit that applies a phase dependent data detection algorithm to a data set such that a first output of the first data detection circuit varies depending upon a phase of the data set presented to the first data detection circuit. A first phase of the data set is presented to the first data detection circuit. The circuits further include a decoder circuit that applies a decoding algorithm to the first output to yield a decoded output, and a phase shift circuit that phase shifts the decoded output such that a second phase of the data set is provided as a phase shifted output.

Abstract: An iterative, blind, frequency-offset estimation process that does not require any training signal or demodulated information symbols is disclosed. Receivers embodying the disclosed processes can produce periodic frequency-offset estimates, without running computationally intensive equalization or demodulation algorithms, by exploiting the temporal correlation of the received signal in the time domain, as well as the received signal's correlation across in-phase and quadrature dimensions, in some embodiments, to find a frequency-offset estimate that best fits the received signal in a maximum-likelihood sense. In an exemplary method of estimating receiver frequency offset, a spatially stacked signal block is formed from multi-branch signal samples corresponding to each of two or more time-separated samples of the received signal.

Abstract: A method for building a look-up table for a receiver in a multiple-input multiple-output (MIMO) detection system simulates a MIMO detector over many channel realizations, tracks channel metric and parameter values used for each channel realization resulting from such simulating, and stores, in a look-up table, best values of the tracked values used for a particular channel metric.

Abstract: A signal separating device the computational complexity of which is reduced and the communication quality of which is improved. A channel matrix interchanging section (110) creates matrices defined by interchanging the elements of channel estimation matrices multiplied by symbol candidates relevant to the final stage. A QR separating/QH multiplying sections (121, 122) each perform QR separation by using the created matrices and perform multiplication of the transposed matrix of the Q matrix of each created matrix by the received signal.

Abstract: Provided is a decoding apparatus capable of reducing the error rate of the decoding results and also the circuit scale. A computing unit computes a plurality of distances only for a number of code word candidates of code words from demodulated data, the number being smaller than a number of values the code words can express, the code words having a possibility of being transmitted. A decoding unit decodes the code words from the plurality of computed distances. This invention is applicable to a decoding apparatus for Long Term Evolution (LTE).

Abstract: In a sphere decoding process, P PPM symbols emitted simultaneously are represented by a point of the modulation product constellation in a space of signals transmitted of dimension MP decomposed into P layers, each layer representing M modulation positions. The signal received is transformed into a representative point. The point of the product constellation closest to the received point within a sphere of given quadratic radius is determined. For each layer of rank p, ZF-DFE equalization is carried out; sorting in a list of the M PPM symbols as a function of the contributions that they would make to the quadratic distance to the received point is then carried out, followed by selection of the PPM symbol making the lowest contribution. The contribution is added to those from previous layers to obtain a sum of contributions. These steps are repeated until the lowest layer is attained.

Abstract: A digital broadcasting transmission/reception system having improved receiving performance and signal processing method thereof. A digital broadcasting transmitter according to the present invention includes a data pre-processor which processed robust data and generates robust data packet of predetermined format, a TS stream generator which combines robust data packet with a normal data packet to generate a TS stream of a predetermined format, a randomizer which randomizes the TS stream output from the TS stream generator, a convolution encoder which performs convolution encoding with respect to the robust data of the data output from the randomizer, and a RS encoder which performs RS encoding with respect to the data output from the convolution g encoder. Accordingly, digital broadcasting receiving performance can be improved in a poor multipath channel, while maintaining compatibility with existing transmission/reception system.

Abstract: A decoding device that decodes demodulated data obtained by demodulating a quadrature modulated signal arising from digital modulation of a carrier and detects synchronization, the decoding device includes, a decoder configured to decode first demodulated data that is the demodulated data obtained by demodulating the quadrature modulated signal and is composed of in-phase axis data and quadrature axis data. The decoding device decodes second demodulated data obtained by interchanging the in-phase axis data and the quadrature axis data of the first demodulated data. A synchronization detector is configured to detect a boundary between predetermined information symbol sequences from first decoded data obtained by decoding the first demodulated data and detect the boundary from second decoded data obtained by decoding the second demodulated data. The synchronization detector selects and outputs one of the first decoded data and the second decoded data based on a result of the detection of the boundary.

Abstract: The present invention provides a system, apparatus and method to improve the signal-to-noise ratio performance in receivers configured to receive differential data signals. According to various embodiments of the invention, a received differential signal is processed to consider both forward-looking and backward-looking error components to improve SNR performance, and ultimately the reach of the optical line system. Additional processing is provided to further enhance noise tolerance related to chromatic dispersion.

Abstract: A dynamic voltage scaling system for a packet-based data communication transceiver includes a constant voltage supply, a variable voltage supply, and a voltage control unit. The constant voltage supply is configured to supply a constant voltage to at least one parameter-independent function of the transceiver, and the variable voltage supply is configured to supply a variable voltage in accordance with a control signal to at least one parameter-dependent function of the transceiver. Parameter-independent transceiver functions perform operations independent of a predetermined parameter and parameter-dependent transceiver functions perform operations dependent on the predetermined parameter The voltage control unit is configured to generate the control signal based on information provided by at least one parameter-independent transceiver function about the predetermined parameter.

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: A system including a differential demodulation module, a first summing module, and a second summing module. The differential demodulation module generates differentially demodulated signals based on having differentially demodulated received signals. The first summing module generates a combined signal by adding the differentially demodulated signals, wherein the combined signal includes a plurality of symbols. The second summing module generates a plurality of sums for each of a plurality of derived preamble sequences, wherein the derived preamble sequences are derived from preamble sequences, and wherein each of the derived preamble sequences includes a plurality of derived symbols. The second summing module further generates cross-correlation values for the derived preamble sequences based on the plurality of sums, wherein one of the cross-correlation values generated for one of the derived preamble sequences is a sum of the plurality of sums generated for the one of the derived preamble sequences.

Abstract: A method of decoding a signal includes receiving multiple data symbols corresponding to multiple transmitted data symbols. The method further includes selecting one candidate data symbol from multiple candidate data symbols corresponding to the multiple transmitted data symbols. The method further includes determining a global optimum candidate value for the selected one candidate data symbol. The method further includes grouping all possible values of the selected one candidate data symbol into two or more bit groups. The method further includes selecting a bit group from the two or more bit groups that does not include the global optimum value. The method further includes determining a local optimum candidate value from values in the selected bit group. The method further includes calculating a likelihood value for a bit in the selected one candidate data symbol based at least in part on the determined global and local optimum candidate values.

Abstract: An apparatus and a method for Low-density parity-check (LDPC) decoding are provided. The apparatus for LDPC decoding comprises a post effective noise variance estimation unit for estimating a post effective noise variance based on a preamble in a received signal, an LLR calculation unit for calculating an LLR based on the estimated post effective noise variance, and a decoding unit for performing LDPC decoding based on the calculated LLR. The post effective noise variance estimation unit comprises a channel frequency response estimation unit for estimating a channel frequency response based on the preamble in the received signal, a noise variance estimation unit for estimating a noise variance based on the preamble in the received signal, and a post effective noise variance calculation unit for calculating the post effective noise variance based on the channel frequency response and the noise variance.

Abstract: A reception device includes reception antennas and an address generation unit that converts a write-in or read-out order of channel estimation values according to a rearrangement rule. A storage unit writes in or reads out channel estimation values in the converted order, and an address generation unit converts a data sequence write-in or read-out order according to the rearrangement rule. A signal storage unit writes in or reads out data sequences in the converted order, and a replica generation unit generates a replica signal by re-modulating the data sequence according to the channel estimation value. A cancel unit successively generates a stream signal in which a data sequence interference signal is cancelled, by using the channel estimation value, the data sequence, and the replica signal.

Abstract: In a pulse-based communication system a transmitting device may generate a series of pulses to convey information via a communication medium to a receiving device. In some situations, interference from one or more interfering devices may alter the pulse energy as it is transmitted through the communication medium. To mitigate the effect of such interference, a receiving device may mark certain received pulses as erasures. In this way, such pulses may be ignored during the decoding operation of the receiver.

Abstract: A soft-decision forward error correction scheme for received optical signals is described. Differential decoding may be performed, for example, in each polarization after coherent QPSK detection. Hard decisions may be made based on judging the most likely transition between each pair of received input symbols. Soft-input generation is also described, representing the reliability of the hard decisions. The soft-input information may be generated through simplified algorithms that utilize the most likely transitions to determine a reliability assignment.

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.

Abstract: A “post-squaring” detection algorithm, and related devices, that may reduce the complexity of maximum likelihood detection (MLD) schemes while preserving their performance is provided. Rather than search for optimum metrics (such as minimum distance metrics) based on squared norm values, a search may be based on un-squared norm metrics, and the squaring may be postponed, for example, until subsequent log-likelihood ratio (LLR) computation. For certain embodiments, approximations of un-squared norm values may significantly reduce computation complexity.

Abstract: In at least some disclosed embodiments, a system includes a Viterbi decoder and predecoding logic coupled to the Viterbi decoder. The predecoding logic decodes encoded data. The system further includes detection logic coupled to the predecoding logic. The detection logic tests decoded data, and the detection logic produces a binary result. The Viterbi decoder is enabled if the binary result is a first value, and the Viterbi decoder is disabled if the binary result is a second value.

Abstract: An FFT processor for an OFDM receiver includes multiple interrelated operational blocks. The FFT processor is configured to perform data demodulation, channel estimation, and fine timing acquisition on received OFDM symbols. The FFT processor incorporates a pipelined FFT engine using a memory architecture shared with channel estimation and demodulation blocks. The combination of the shared memory structure and the pipelined FFT operation enable the channel estimation and demodulation processing to be completed during the time used to capture the next received symbol.

Abstract: The impairment processor described herein uses a look-up table operation to reduce the computational complexity associated with determining an impairment correlation between first and second sample streams for an interference rejection receiver. One exemplary impairment processor iteratively computes multiple partial impairment correlations based on values selected from look-up table(s), and combines the partial impairment correlations to obtain a final impairment correlation between the first and second sample streams.

Abstract: The present invention maps coded bits that have been output from a low density parity check coder 11 onto specific bit positions on a 16 QAM constellation diagram in accordance with a column weighting of the coded bits.

Abstract: A transceiver apparatus, a receiver and a power saving method thereof are provided. The receiver includes an analog-to-digital converter, an equalizer, a slicer, a delay unit, a decoder, a select unit and a control unit. The analog-to-digital converter transforms a received signal into a digital signal. The equalizer adjusts the digital signal to generate an equalized signal. The slicer receives and slices the equalized signal and generates a sliced signal. The delay unit delays the sliced signal. The decoder determines whether to decode the equalized signal or not according the control signal. The select unit selects one of the output of the delayed sliced signal and the output of the decoder to be an output signal according to a second control signal. The control unit determines whether to enable the control signal and the second control signal according to the state of the sliced signal and the output signal.

Abstract: Flexible rate matching. No constraints or restrictions are placed on a sending communication device when effectuating rate matching. The receiving communication device is able to accommodate received transmissions of essentially any size (e.g., up to an entire turbo codeword that includes all systematic bits and all parity bits). The receiving communication device employs a relatively small-sized memory to ensure a lower cost, smaller sized communication device (e.g., handset or user equipment such as a personal wireless communication device). Moreover, incremental redundancy is achieved in which successive transmissions need not include repeated information therein (e.g., a second transmission need not include any repeated information from a first transmission). Only when reaching an end of a block of bits or codeword to be transmitted, and when wrap around at the end of such block of bits or codeword occurs, would any repeat of bits be incurred within a later transmission.

Abstract: Teachings presented herein offer reduced computational complexity for symbol sequence estimation, and also provide for the generation of soft bit values representing the reliability of that estimation. A demodulator is configured to generate these soft bit values by identifying a candidate value for each symbol in the sequence which is more likely than at least one other in a defined set of candidate values. Based on the candidate value identified for each symbol, the demodulator forms a reduced set of candidate values for the symbol by selecting as many additional candidate values from the defined set as are needed to have complementary bit values for each bit value in that identified candidate value. The demodulator calculates soft bit values for the symbol sequence based on a sequence estimation process whose state space for each symbol is constrained to the corresponding reduced set.

Abstract: Compact pulse shape partial response (CPS PR) signaling is developed for trellis based signals like QM-MSK, and for PAM/QAM type signals to improve the performance to bandwidth tradeoff. Compact pulse shaped signals are partial response signals that employ a very short pulse shaping filter and use Viterbi decoding to optimally detect the CPS signal in presence of its inherent inter-symbol interference. The CPS filters considered herein have much shorter impulse response than the well-known raised cosine (RC) filter. There is no need to equalize the received signal to eliminate ISI or to allow a fixed amount of ISI between received signal samples as sampled at the symbol rate as is common in partial response maximum likelihood (PRML) systems. Numerical results indicate that CPS QM-MSK and CPS QAM provides between several dB of gain, depending on constellation size, over PR-CPM and RC QAM, when compared at a given value of bandwidth, i.e., B99Tb.

Abstract: Embodiments achieve favorable performance-complexity trade-offs in MIMO detection for three or more channel inputs. Some embodiments describe systems and methods comprising a leaf node predictor for receiving a processed communications stream, determining at least one channel metric corresponding to the communications stream for a given channel realization, and generating at least three instructions to output, which at least one instruction corresponds to at least one predicted best leaf node candidate for the given channel realization. Further embodiments alternatively describe systems and methods which enumerate N1 best values of a first symbol, enumerate N2(i) best values of a second symbol for an i-th best value of the first symbol, enumerate N3(i, j) best values of a third symbol for an i-th best value of the first symbol and j-th best value of the second symbol, combine enumerated best values of each symbol into a leaf-node value, and compute the cost of each leaf-node value enumerated.

Abstract: A decoder for a layered modulation system can be configured to independently and concurrently decode each of a base and enhancement layer. The base layer decoder and enhancement layer decoder can be configured substantially in parallel and can each operate concurrently on the same received layered modulation symbol. Each of the base and enhancement layer decoders can be configured with a bit metric module that is configured to determine a signal quality metric based on the received symbol. In systems having turbo encoded data, the bit metric module can be configured to determine a log likelihood ratio. The ratio is based in part on a channel estimate and an energy ratio used in the layered modulation constellation.

Abstract: A method for data transmission in a multiple input multiple output (MIMO) system. The method for data transmission includes receiving multiple input data streams and performing low density parity check (LDPC) encoding of the input data streams utilizing a parity check matrix. The parity check matrix comprises a plurality of sub-parity check matrices for encoding respective associated ones of the input data streams and performing space time encoding for transmitting the LDPC encoded input data streams over a plurality of antennas. The performing of the LDPC encoding of the input data streams includes generating one or more connection matrices, each connection matrix for injecting information of one of the input data streams into the encoding of another one of the input data streams.

Abstract: A method for identifying the modulation scheme of a software defined radio in real-time without pilot symbols between transmitters and receivers, includes providing a predetermined look-up table (LUT) in the software-defined radio wherein the LUT is prepared by pre-calculating discrete likelihood ratio test (DLRT) function values; storing the pre-calculated DLRT values in said LUT; and indexing the pre-calculated DLRT values by addresses.

Abstract: Provided is a signal separating device capable of reducing the calculation amount and improving the communication quality. The signal separating device performs signal separation by the MLD method using the QR decomposition.

Abstract: A method and device is provided for the detection of data symbols contained in a received radio signal, whereby each data symbol is allocated transmit-side a symbol value-specific PN sequence of successive PN chips in the chip clock and the PN sequences allocated to the data symbols are offset QPSK modulated. The method of the invention for incoherent detection provides for converting the received radio signal into a complex baseband signal sampled in the chip clock, generating a demodulated signal by differential demodulation of the complex baseband signal sampled in the chip clock, providing the derived sequences, calculating correlation results by correlating the demodulated signal with the derived sequences, and deriving, i.e., detecting, the values of the data symbols by evaluating the correlation results.

Abstract: A method of determining a variable quantization step size is disclosed. In the method of determining a variable quantization step size, a channel characteristic parameter is obtained in order to calculate a quantization step size (?) used in channel decoding. The quantization step size (?) is variably determined based on the channel characteristic parameter. Therefore, the method of determining a variable quantization step size may improve channel decoding.

Abstract: Systems, methods, and other embodiments associated with iterative decoders are described. According to one embodiment, an apparatus includes a set of decoders that are configured to receive data to be decoded. The apparatus may also include a controller configured to separately control each decoder to initiate a decoding sequence based on an occurrence of a transition point. The transition point is a global transition that occurs iteratively for the set of decoders and is based on iterations in a decoding sequence.