System and method for a message passing algorithm

The complexity of sparse code multiple access (SCMA) decoding can be reduced by pruning codebooks to remove unlikely codewords prior to, or while, performing an iterative message passing algorithm (MPA). The pruned codebook is then used by to perform one or more iterations of MPA processing, thereby reducing the number codeword probabilities that are calculated for the corresponding SCMA layer. The pruned codebook also reduces the computational complexity of calculating codeword probabilities associated with other SCMA layers. The pruned codebook may be “reset” by reinserting the pruned codewords into the codebook after a final hard-decision for a given set of received samples is made, so that the pruning does not affect evaluation of the next set of samples.

TECHNICAL FIELD

The present invention relates to a system and method for network and wireless communications, and, in particular, to a system and method for a message passing algorithm.

BACKGROUND

Frequency domain non-orthogonal multiple-access techniques may achieve better spectral efficiency than comparable orthogonal multiple-access techniques by virtue of using the same resource to carry portions of two or more different data streams. However, this enhanced throughput generally comes at the expense of increased signal processing complexity at the receiver. In particular, a receiver may need to iteratively process a received signal to compensate for interference between non-orthogonal transmissions in the received signal, which may consume significant amounts of processing resources, as well as introduce latency into the decoding process. Accordingly, techniques for reducing the processing complexity of iterative non-orthogonal signal processing techniques are desired to improve decoding performance.

SUMMARY OF THE INVENTION

Technical advantages are generally achieved, by embodiments of this disclosure which describe system and method for a message passing algorithm.

In accordance with an embodiment, a method for decoding wireless signals is provided. In this example, the method includes receiving, at a Message Passing Algorithm (WA) processor, a sequence of samples representative of a received signal from a device, receiving, or otherwise generating, one or more probabilities associated codewords of a codebook assigned to a data stream in the received signal, and removing, in accordance with the probabilities, at least one of the codewords from the codebook to obtain a pruned codebook. The pruned codebooks exclude the at least one codeword. The method further includes processing the received sequence of samples according to the pruned codebook to generate soft decision values corresponding to the received signal, and sending the soft decision values to a forward error correction (FEC) decoder. An apparatus and computer program product for performing this method are also provided.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Sparse code multiple access (SCMA) is a non-orthogonal multiple-access technique that transmits multiple data streams over a set of sub-carrier frequencies using non-orthogonal spreading sequences. In particular, the data streams are communicated over different SCMA layers by mapping the data streams to the set of sub-carriers using SCMA codewords (e.g., a spreading sequence) selected from codebooks assigned to the respective SCMA layers. Each SCMA layer is mapped to a different combination of sub-carrier frequencies in the set of sub-carrier frequencies over which the data streams are collectively transmitted. SCMA codewords in a given codebook specify that different combinations of symbols are communicated over the combination of sub-carrier frequencies mapped to the corresponding SCMA layer. Thus, the codeword is selected based on the bit-encoding of the data stream.

The relative sparsity of SCMA codewords allow the data streams in a received signal to be distinguished from one another, and ultimately decoded, using an iterative message passing algorithm (MPA). In particular, an MPA processor evaluates the received signal carrying data streams over a series of iterations. During each iteration, the MPA processor computes codeword probabilities for all codewords in each codebook assigned to the SCMA layers. Each of the codeword probabilities corresponds to a likelihood that a particular codeword in the codebook was transmitted over the corresponding SCMA layer. The codeword probabilities associated with one SCMA layer are calculated, in part, based on the codeword probabilities for other SCMA layers. As a result, improving the accuracy of codeword probabilities for one layer during a given iteration improves the accuracy of codeword probabilities for other layers during a subsequent iteration. In this way, the MPA processor is able to iteratively refine the probabilities during each successive iteration until a stop condition is reached, at which point the MPA processor uses the codeword probabilities to calculate log likelihood ratios (LLRs) for bits mapped to the most-probable codeword. The LLRs are then sent to a forward error correction (FEC) decoder, which uses the LLRs to make hard decisions during bit-level decoding.

Because codeword probabilities are generally computed for all codewords in a codebook during each iteration of MPA processing, the computational complexity associated with SCMA decoding is heavily influenced by the number of codewords in the corresponding codebooks. The number of codewords in a codebook is largely determined by size of the constellation used to modulate the symbols. As a result, SCMA decoding complexity may be significantly increased when larger constellation sizes are used to achieve higher data rates. Accordingly, techniques for reducing the complexity of SCMA decoding are desired.

Aspects of this disclosure reduce the complexity of SCMA decoding by pruning codebooks to remove unlikely codewords. The pruned codebook is then used by the MPA processor to perform one or more iterations of MPA processing, thereby reducing the number codeword probabilities that are calculated for the corresponding SCMA layer. The pruned codebook also reduces the computational complexity of calculating codeword probabilities associated with other SCMA layers. In particular, an MPA processor may typically use codeword probabilities of SCMA layers that are non-orthogonal to a given SCMA layer as an input parameter when computing codeword probabilities for the given SCMA layer. Hence, pruning codewords from codebooks associated with one SCMA layer may reduce the number of interfering codeword probabilities that are taken into consideration when computing codeword probabilities for another SCMA layer. It should be appreciated that the pruned codebook may be “reset” (e.g., the pruned codewords may be re-inserted) after a final hard-decision for a given set of received samples is made, so that the pruning does not affect evaluation of the next set of samples (e.g., the next set of symbols in a subsequent time-slot).

Various techniques are provided for determining which codewords to prune from a given codebook. For example, codebooks may be pruned based on codeword probabilities or a priori probability (APP) values corresponding to codewords in the codebook. In one embodiment, an MPA processor prunes a codeword from a codebook when a codeword probability or an APP value associated with the codeword is less than a threshold. APP values are computed based on LLRs to further improve the decoding accuracy. In particular, LLRs are generated during an initial set of iterative computations by an MPA processor. The LLRs from an MPA processor are an input to a FEC decoder that produces a second set of LLRs. The FEC decoder's LLRs are then fed-back to an APP processor via an outer feedback loop, where they are used to compute APP values. The APP values specify likelihoods that SCMA codewords were communicated over a given layer, and are themselves fed-back to the MPA processor, where they are effectively used by the MPA processor as a starting point for computing codeword probabilities during a subsequent round of MPA iterations. In this way, codeword probabilities are iteratively computed based on received signal samples and, during later iterations, APP values in an inner feedback loop. When an inner feedback loop stop condition occurs, the codeword probabilities are used to compute LLRs, which are used to compute APP values in an outer feedback loop. Similar to the inner feedback loop, the APP values become further refined (e.g., more accurate) during each successive iteration of the outer feedback loop, thereby increasing the accuracy and/or convergence times of both the codeword probabilities generated during the inner feedback loop and the LLRs computed from the more accurate codeword probabilities.

As another example, codebooks may be pruned based on LLRs corresponding to bit values mapped to codewords in the codebooks. A set of LLRs for a given bit typically include a sign bit indicating a binary value of the bit (e.g., a one or a zero) and a set of magnitude bits indicating a confidence level of the sign bit. In an embodiment, an MPA processor removes a codeword from a codebook when an LLR indicates a different binary value than that mapped to the codeword and has a magnitude that exceeds a threshold. The LLR sign bit indicates a different binary value than the codeword when the LLR sign bit indicates a 1 and the codeword maps to 0, or vice versa. When LLR sign bit indicates a different binary value than the codeword, and the LLR magnitude exceeds the threshold, it may logically follow that the codeword itself is unlikely to have been transmitted at the corresponding layer. The threshold used to determine whether a codeword probability, an APP value, or an LLR magnitude warrants pruning may be predefined. For example, a codeword may be removed from a codebook once it is determined that there is at least a certain probability (e.g., ninety percent chance) that the codeword was transmitted in the data stream for a given period. The threshold may also be dynamically defined based on the values of other codeword probabilities, APP values, or LLRs associated with the codeword, codebook, layer, or received signal. These and other aspects are discussed in greater detail below. It should be noted that although reference is made here to decoding and pruning operations on binary values, in a transmission scheme that makes use of higher order representations of number (e.g. ternary or higher systems) may be used. Where reference is made to halving the number of codewords by fixing a bit value based on an LLR, it should be understood that in a non-binary system the reduction in codewords in the codebook will be less than 50%.

Codeword probabilities, APP values, and LLRs are referred to collectively as “probabilities” throughout this disclosure. Although codeword probabilities and the APP values both correspond to likelihoods that a given codeword was transmitted over a given layer, it should be appreciated that codeword probabilities are generated by the MPA processor during an inner-feedback loop based on, amongst other things, samples of the received signal, while APP values are computed by the MPA processor based on LLRs. Hence, codeword probabilities and APP values are computed by different entities using different techniques (e.g., different objective functions) based on different input information

FIG. 1illustrates a schematic representation of a network100for communicating data. Network100includes communications controller102having a coverage area106, a plurality of user equipments (UEs), including UE104and UE105, and backhaul network108. Two UEs are depicted, but many more may be present. Communications controller102may be any component (or collection of components) capable of providing wireless access by establishing uplink (dashed line) and/or downlink (dotted line) connections with UE104and UE105, such as a base station, a NodeB, an enhanced nodeB (eNB), an access point, a picocell, a femtocell, relay node, and other wirelessly enabled devices. It will be understood that in some embodiments, a first controller102may be responsible for uplink communication with a UE, while a second controller is responsible for downlink communication with the same UE. UE104and UE105may be any component capable of establishing a wireless connection with communications controller102, such as cell phones, smart phones, tablets, sensors, etc. UE104and UE105are representative of a mobile device that can connect to the mobile network that controller102belongs to. The term mobile device will be understood to refer to a device that connects to a mobile network, and is not restricted to devices that are themselves mobile. Backhaul network108may be any component or collection of components that allow data to be exchanged between communications controller102and a remote end. In some embodiments, the network100may include various other wireless devices, such as relays, etc. Network100may use encoding and decoding, for example using turbo codes such as turbo codes, or polar codes.

SCMA decoders may include MPA processors to perform symbol level decoding, and an FEC decoder to perform bit-level decoding. Some SCMA decoders may further include an APP processor to improve the accuracy of the symbol level decoding.FIG. 2illustrates an embodiment SCMA decoder200for decoding received signals carrying SCMA data streams. As shown, the embodiment SCMA decoder200includes an MPA processor222, an APP processor224, and an FEC decoder226. The MPA processor222may include any component, or collection of components, configured to perform iterative MPA processing on samples of a received signal to compute LLRs. The FEC decoder226may include any component, or collection of components, configured to perform bit-level decoding on the LLRs to obtain decoded bits. The APP processor224may include any component, or collection of components, configured to predict APP values based on the LLRs.

As mentioned above, the MPA processor222performs an initial round of iterative MPA processing on the received signal samples to generate codeword probabilities. Once a condition is reached, the MPA processor222computes LLRs based on the codeword probabilities, and then sends the LLRs to the FEC decoder226. The FEC decoder may receive input from a plurality of different MPA processors assigned different related sequences. The FEC decoder226uses the received LLRs as an input and may perform further processing. The FEC decoder226outputs a set of LLRs that are then fed back to the APP processor224, which computes APP values based on the LLRs. The APP values are then fed-back to the MPA processor222, which uses the APP values as an input parameter during a subsequent round of iterative MPA processing.

The iterative generation of the codeword probabilities by the MPA processor222generally entails exchanging messages that include the codewords probabilities between different nodes of the MPA processor. In this way, the exchanging of messages between nodes of the MPA processor222forms an inner-feedback loop, while the exchanging of LLRs and APP values between the MPA processor222, the FEC decoder226, and the APP processor224forms the outer feedback loop.

The exchanging of messages between nodes of an MPA processor can be modeled using a Tanner graph.FIG. 3illustrates a diagram of a multi-layer SCMA transmission scheme300, andFIG. 4illustrates a Tanner graph400of an iterative MPA processing technique to decode a signal carrying data streams transmitted according to the multi-layer SCMA transmission scheme300. As shown inFIG. 3, the multi-layered SCMA transmission scheme300assigns the codebooks350,351,352,353,354,355to the SCMA layers320,321,322,323,324,325, respectively. Each of the SCMA layers320,321,322,323,324,325are mapped to a different combination of sub-carrier frequencies in the set of subcarrier frequencies310,311,312,313over which the data streams are communicated. In particular, the SCMA layer320maps to the subcarrier frequencies311,313, the SCMA layer321maps to the subcarrier frequencies310,312, the SCMA layer322maps to the subcarrier frequencies310,311, the SCMA layer323maps to the subcarrier frequencies312,313, the SCMA layer324maps to the subcarrier frequencies310,313, and the SCMA layer325maps to the subcarrier frequencies311,312. Those skilled in the art will appreciate that if two devices (e.g. two different UEs) transmit using the same codebooks, a receiver may still be able to decode the two messages.

Based on the codebook or codebooks from the multi-layer SCMA transmission scheme assigned to a given data stream, samples from that data stream are encoded into codewords using the appropriate codebook. In the case of multiple codebooks, i.e., layers, being assigned to a given data stream, the codewords may be summed together prior to transmission. Each codeword within a respective codebook maps a different combination of symbols to the respective combination of sub-carrier frequencies. The data streams are then transmitted over a wireless network to a receiver.

As shown inFIG. 4, function nodes (FNs)410,411,412,413of an SCMA decoder exchange messages with variable nodes (VNs)420,421,422,423,424,425of the SCMA decoder in order to iteratively decode data streams of the received signal. The FNs410,411,412,413are interconnected to the VNs420,421,422,423,424,425via edges, which are represented by the lines inFIG. 4. The FNs410,411,412,413calculate codeword probabilities based on information corresponding the respective sub-carrier frequencies during a first iteration of MPA signal processing. This information corresponding to the respective sub-carrier frequencies may include signal samples (y0, y1, y2, y3), channel estimation information (h0, h1, h2, h3), and noise information (N0, N1, N2, N3). The FNs410,411,412,413then send the codeword probabilities in messages to the respective VNs420,421,422,423,424,425over the respective edges.

The VNs420,421,422,423,424,425may then compute codeword probabilities based on the messages received from FNs410,411,412,413as well as APP values (ap0, ap1, ap2, ap3, ap4, ap5). During the first round of iterations in the inner feedback loop (e.g., prior to APP values being computed by the APP processor), the APP values used by the VNs420,421,422,423,424,425indicate an equal probability for all of the codewords. During subsequent rounds of iterations in the inner feedback loop, the VNs420,421,422,423,424,425may use the APP values provided by the APP processor. After computing the codeword probabilities, the VNs420,421,422,423,424,425send the codeword probabilities in messages to the respective FNs410,411,412,413over the respective edges. The FNs410,411,412,413then use the codeword probabilities in the messages received from the VNs420,421,422,423,424,425in addition to the information related to their corresponding sub-carrier frequency to compute/update their codeword probabilities. This iterative process continues until a stop condition is reached on the inner feedback loop. The codebooks maintained by the VNs420,421,422,425425may initially include an entire set of the codewords in the codebooks350,351,352,353,354,355(respectively) used to transmit the data streams over the SCMA layers350,351,352,353,354,355. As the VNs420,422,425prune their codebooks in accordance with embodiments provided herein, the pruned codebooks maintained by the VNs420,422,425may contain a sub-set of the codewords (e.g., fewer than all codewords) in the codebooks350,352, and355(respectively) used to transmit the data streams.

Pruning codebooks maintained by VNs reduces the computational complexity at FNs.FIG. 5illustrates an example of an iteration of a message exchange from the point of view of the FN411. In this example, the initial messages from the FNs to the VNs are not depicted. As shown, the FN411first receives messages510,512,515from the VNs420,422,425(respectively). The messages510,512,515include codeword probabilities computed by the VNs420,422,425. In particular, the message510includes a set of codeword probabilities for codewords in a codebook maintained by the VN420, the message522includes a set of codeword probabilities for codewords in a codebook maintained by the VN422, and the message515includes a set of codeword probabilities for codewords in a codebook maintained by the VN425. The FN411then generates the messages520,522,525, and sends the messages520,522,525to the VNs420,422,425. The message520includes codeword probabilities for the set of codeword probabilities for codewords in the codebook maintained by the VN420. Codeword probabilities in the message520are generated as a function of the codeword probabilities in the messages512,515as well as signal samples (y1), channel estimation information (h1), and noise information (N1) corresponding to the sub-carrier frequency311assigned to the FN411. Likewise, the message522includes codeword probabilities for the set of codeword probabilities for codewords in the codebook maintained by the VN422, and the message525includes codeword probabilities for the set of codeword probabilities for codewords in the codebook maintained by the VN425. Codeword probabilities in the message522are calculated as a function of the codeword probabilities in the messages510,515and the signal samples (y1), channel estimation information (h1), and noise information (N1) corresponding to the sub-carrier frequency311assigned to the FN411. Codeword probabilities in the message525are calculated as a function of the codeword probabilities in the messages510,512and the signal samples (y1), channel estimation information (h1), and noise information (N1) corresponding to the sub-carrier frequency311assigned to the FN411.

In this example, the number of codewords in the codebooks maintained by the VNs420,422, and425is directly related to the number of codeword probabilities that are calculated by the FN411. It should also be appreciated that the number of codewords in the codebook maintained by the VN420directly affects the number of interfering codewords that are taken into consideration when generating the messages522,525. Likewise, the number of codewords in the codebook maintained by the VN422directly affects the number of interfering codewords that are taken into consideration when generating the messages520,525, and the number of codewords in the codebook maintained by the VN425directly affects the number of interfering codewords that are taken into consideration when generating the messages520,522. Thus, pruning the codebooks maintained by the VNs420,422, and425may reduce the computational complexity at the FN411.

Pruning codebooks maintained by VNs also reduces the computational complexity at VNs.FIG. 6illustrates an example of iterative message exchange from the point of view of the VN422. As shown, the VN422receives messages610,611from the FNs410,411respectively. The messages610,611include codebook probabilities for codewords in a codebook maintained by the VN422. The codebook probabilities in the message610are computed as a function of the signal samples (y0), channel estimation information (h0), and noise information (N0) corresponding to the sub-carrier frequency310assigned to the FN410. If the depicted iteration is a subsequent iteration (e.g., not the first iteration of the current inner feedback loop), then the codebook probabilities in the message610may also be computed as a function of codebook probabilities in messages communicated from the VNs420,421to the FN410during a previous iteration.

The codebook probabilities in the message611are computed as a function of the signal samples (y1), channel estimation information (h1), and noise information (N1) corresponding to the sub-carrier frequency311assigned to the FN411. If the depicted iteration is a subsequent iteration (e.g., not the first iteration of the current inner feedback loop), then the codebook probabilities in the message611may also be computed as a function of codebook probabilities in messages communicated from the VNs424,425to the FN411during a previous iteration.

Upon reception of the messages610,611, the VN422computes codebook probabilities for codewords in the codebook maintained by the VN422, and then sends the codebook probabilities to the FNs410,411via the messages620,621. The set of codebook probabilities communicated in the message620are calculating as a function of information in the message611and APP values (ap2) associated with the codebook maintained by the VN422. The set of codebook probabilities communicated in the message621are calculating as a function of information in the message610and the APP values (ap2) associated with the codebook maintained by the VN422.

In this example, the number of codewords in the codebook maintained by the VN422is directly related to the number of codeword probabilities that are calculated by the VN422. Thus, pruning the codebook maintained by the VN422may reduce the computational complexity at the VN422.

There are a variety of encoding schemes which may be used for transmitting data. A message passing algorithm (MPA) may be used for decoding the transmitted data. One example of an encoding scheme is a convolutional code. Convolutional codes operate on streams of bits or symbols having an arbitrary length. Convolutional codes may be soft decoded, for example using the Viterbi algorithm or another soft decoding algorithm. A convolutional code which is terminated is also a block code. Terminated convolutional codes include tail-biting and bit-flushing codes. Block codes operate on fixed size blocks, or packets, of bits or symbols having a predetermined size. Block codes may be hard-determined in polynomial time to their block length. Block codes include classical block codes and modern block codes. Classical block codes include Reed-Solomon coding, Golay coding, Bose Chauduri Hocquengham (BCH) coding, multi-dimensional parity coding, and Hamming coding. Modern block codes include low-density parity check (LDPC) coding. LDPC codes are highly efficient linear block codes made from many single parity check (SPC) codes. Concatenated codes incorporate both a classical block coding and a convolutional coding.

Turbo coding is an iterated soft-decoding scheme which combines two or more convolutional codes and an interleaver to produce a block code. Rateless Fountain Codes include Luby Transform (LT) codes. The code words of an LT code are generated based on k information symbols based on a probability distribution on the numbers 1, . . . , k. Each codeword symbol is obtained independently, by first sampling the distribution to obtain a number d, and adding the values of d randomly chosen information symbols. Raptor codes are a modified version of LT codes, where the information sequence of k symbols is pre-coded by a high rate block code, and n symbols are used to generate the Raptor codeword symbols as in LT codes. Another encoding method involves polar codes. A polar code is a linear block error correcting code. Polar codes can be systematic or non-systematic.

As discussed above, SCMA is a non-orthogonal multiple access scheme, using sparse codebooks to convey user data symbols. SCMA typically requires an advanced receiver that can be implemented with reasonable complexity that is made possible by the sparsity of SCMA codebooks

Where encoding methods or access schemes are used, iterative decoding methods are often applied. An embodiment method of decoding involves an inner MPA which uses feedback information from a soft decoding outer iterative decoder. A priori knowledge of the received encoded data fed back by the outer decoder to the inner MPA can be used to reduce the MPA decoding schedule by eliminating highly unlikely possibilities from computations. The feedback information may take the form of a priori probabilities or log-likelihood ratios (LLRs). When the feedback data indicates that a codeword is unlikely, it can be pruned from the codebook (also referred to as an alphabet). This allows for a simplified set of inner loop iterations due to a simplification of the scheduling of the function nodes and variable nodes. When an alphabet is used, the decoding process considers every alphabet entry in the initial set of inner loop iterations. In the next outer loop iteration, the alphabet may be reduced to include only a subset of the alphabet entries, or only one alphabet entry, when the feedback indicates that alphabet entries outside the subset are highly unlikely. In one example, a subset of an alphabet is determined to be unlikely, leaving another subset, which is evaluated. When only one alphabet entry is considered, an extreme value is assigned to the likelihood value of that alphabet entry, which is used within a function node update, and another LLR corresponding to the extreme value is assigned to the MPA output for that variable node. Those skilled in the art will appreciate that although the above description is based on starting with a complete alphabet and pruning out alphabet entries to reduce the alphabet size, it may be possible to create the reduced alphabet in reverse by having a list of possible alphabet entries and then building the alphabet based on the entries in the list that have sufficiently high likelihoods/probabilities.

The complexity of an MPA based decoder for coding schemes such as SCMA, low density signature-orthogonal frequency-division multiplexing (LDS-OFDM), LDPC codes, or another forward error correction (FEC) code, may be used with a priori knowledge of bits being decoded. During the decoding of a received block or symbol, the MPA may use the soft output of the outer decoder. Knowing a priori that certain encoded bits are highly likely to be the correct bits may facilitate assigning a high likelihood value to the known values, and reducing the MPA update schedules to avoid considering unlikely bit values. An embodiment reduces the complexity of an inner MPA decoding function using a priori knowledge feedback from a soft decision outer decoder.

SCMA decoders typically make use of an MPA processor for recovery of the transmitted SCMA codewords. The relationship between SCMA codebooks, which spread their codewords across the same resource elements (REs) and subcarriers, along with the MPA used to decode these codewords, may be visualized using a Tanner graph. Each Tanner graph node works in isolation, only accessing the messages on its connected edges. An edge is the link in the Tanner graph that connects two nodes. For an SCMA decoder, the messages that are exchanged between FNs and VNs are probabilities that represent a level of belief regarding the possible received codewords.

In one MPA iteration of an SCMA decoder, the FNs compute messages to send across the edges to their connected VNs. Upon receiving the messages from the FNs, each VN computes messages to send across the edges to the connected FNs. The FNs receive extrinsic information as input. For example, FN410receives y0, h0, and N0,0, FN411receives y1, h1, and N0,1, FN116receives y2, h2, and N0,2, and FN118receives y3, h3, and N0,3, where ynis the received signal vector on subcarrier n, hnis the channel estimation for subcarrier n, and N0,nis the noise estimate for subcarrier n. The FNs perform calculations, and send messages to their connected VNs. The VNs receive information from the connected FNs and use these messages, along with the input ap values to generate messages for the FNs as discussed above. This process can be repeated until a stopping criterion is reached.

The kth variable node, VNk, represents the transmitted SCMA codeword using the codebook ckbeing recovered in the node. VNkis connected to dvFNs. Following the final iteration of the MPA decoder, the VNs output a vector, where each element represents the LLR of that bit having been 0 when encoded by the transmission SCMA encoder based on ck.

Messages are passed between two FNs and VNk. The messages include the probabilities that the transmitted SCMA codeword from ckbeing decoded is each of the M possible codewords from ck. That is:
Pr{=Ck(2)}, . . .Pr{=Ck(M)},
based on the messages arriving at the node. The messages are refined in each iteration, with information flowing from the different nodes in the MPA. The messages passed to FNnare based on the messages from the previous decoder iteration from all other FNs connected to VNk, using the notation:
Iqk→cn.

The messages passed to VNkare based on the messages from the previous decoder iteration from all other VNs connected to FNn, using the notation:
Icn→qk.

The messages contain extrinsic information, because the sending node computes the messages with information from all connected nodes besides the destination node.

There are some relevant MPA parameters which are used in the SCMA decoder and for developing the SCMA codebooks. There are df=3 VNs connected to each FN. Also, there are dv=2 FNs connected to each VN. Each codeword spreads across K=4 subcarriers or REs, so there are K FNs. Also, there are J=6 codebooks which may transmit at the same time, so there are J VNs. Additionally, there are M=SCMA codewords within an SCM codebook M={4, 8, 16}. There are M messages in:
Iqk→cn
and
Icn→qk.

The MPA decoder stops after Ni=15 iterations.

Standard MPA implementations are computationally expensive. The computation of values at the FNs is particularly computationally expensive due to the computationally intensive nature of determining values for each edge.

In SCMA, four values correspond to possible codewords within the codebook. When a bit is fixed, half of the possible codewords, or alphabets, may be discarded. By discarding codewords, a new codebook is obtained. The decoding schedule in MPA processor222is adjusted based on the fixed bits (i.e. based on the new codebook). A new cycle with a set of MPA iterations is performed, to obtain a new set of LLRs, which are sent to the FEC. This is repeated until the codeword is decoded.

FIG. 7illustrates flowchart740for an embodiment method of decoding using an MPA. Initially, in step742, a signal is received by a system. The received signal corresponds to an encoded that has been transmitted and received by a receiver. Next, in step744, the received signal is sampled to obtain a sequence of samples.

Then, in step745, a fast Fourier transform (FFT) is performed on the sequence of samples. The FFT (which may be implemented as a discrete Fourier transform (DFT)) is used convert the sequence of samples from the time domain to the frequency domain. An FFT may be used to rapidly compute the transform by factorizing the DFT matrix into a product of sparse factors.

In step746, decoding is performed using an MPA on the sampled received signal. The MPA is done based on the received samples and a decoder codebook, and may take into account other information including channel and noise models. In the first iteration of the MPA, the MPA is performed without the use of APP feedback values (as during the first iteration, there have been no APPs generated so all codewords in active the codebooks/layers are considered to be equally likely to have been transmitted). The iterative process is repeated until a stopping criterion is met. In some embodiments, a set of stopping criteria may be reached if either a set number of iterations have occurred or until the results sufficiently converge.

In step748, the LLRs may optionally be converted from parallel to serial. When the MPA completes the inner iterations, it has a set of LLRs available as output. These LLRs are typically provided to a FEC processor in series. Those skilled in the art will appreciate that the serialization of the LLRs may not be necessary depending on the design of a FEC processor.

Then, in step750, soft-in soft-out (SISO) outer FEC decoding is performed on the LLRs. A SISO decoder is a type of soft-decision decoder commonly used with error correcting codes. Soft-in refers to the fact that the incoming data may have values between 0 and 1 to indicate reliability. Similarly, soft-out refers to the fact that each bit in the decoded output also takes on a value indicating reliability.

In step750a decision on the decoding is made. If the results are found to have sufficient confidence, the decoding process can stop and the decoded bit values are output in step752. The decoded bit values may be transmitted for use. If the decoding process has not concluded in step750, a set of LLRs is provided as the input for an a priori probability generation in step754. The a priori probability values are fed back to the MPA. This is the conclusion of a single outer loop iteration. A subsequent inner loop set of iterations of the MPA is performed in step746. In subsequent inner loop iterations, codewords may be removed from the alphabet based on the feedback values. By pruning the overall decoding alphabet based on very high or very low likelihood values (or the corresponding APP values) it is possible to reduce the number of operations required in the inner loop iterative process. In some embodiments, the alphabet is reduced when some, but not all, of the a priori probability values are extreme. When all of the a priori probability values are extreme, MPA operations related to this VN are not performed, and the LLR values corresponding to the extreme a priori probability values are automatically output. The values for other VNs (which do not have extreme APP or LRR values) are still computed.

It should be understood that in subsequent executions of step746, the APP values from step154are used as an initial condition in step746. An APP value indicates the likelihood of a codeword in the alphabet. This information can be used in the iterations, and can also be used to determine that codewords (or groups of codewords) can be removed from the alphabet. In other embodiments, the pruning of the codebook can be based on the LLR output by the FEC.

FIG. 8illustrates flowchart860for an embodiment method of MPA calculation using alphabet reduction. This method may be performed for MPA iterations after the initial iteration. Initially, in step861, the feedback values, such as a priori probability values or LLR values, are received. The probability values received in step861, indicate the likelihood of the different bits being either a 0 or a 1. An extreme likelihood value (in comparison to either a threshold or to the other probability values, indicates a very strong likelihood of a particular value.

Next, in step862, the system determines whether at least one LLR value is extreme. When an LLR value is extreme it indicates a very high level of certainty for a bit value. In one example, the a priori probability values are four bits and range from zero to fifteen, where zero indicates that the LLR value is 0 and a fifteen indicates that the LLR value is 1. In one example, values of 1, 2, 13, and 14 are considered to be extreme values. In another example, only values of 1 and 14 are considered to be extreme values. In another example, eight bits are used, and the a priori probability values range from zero to 127. In one example, the feedback values are identified as being extreme by comparing them to a predefined threshold. In another example, the feedback value is compared one or more dynamic threshold based on some rule set. In an additional example, the feedback value is compared to other feedback values to determine if it is extreme. For example, when the MPA is initialized, the a priori values are set to the same value. This avoids pruning of the alphabet in the first set of iterations. At the end of the first outer iteration, the LLRs from the FEC can be used as feedback values. If there is an identified extreme value, pruning of the alphabet can occur. In another example, if all feedback values are similar, it can be concluded that the feedback does not provide sufficient information to justify prune the alphabet

When none of the LLR values are extreme, the system proceeds to step870to run the MPA without reducing the alphabet. When at least one a LLR value is extreme, the system proceeds to step864.

In step864, the system determines whether all of the LLR values are extreme. When some, but not all, of the LLR values are extreme, the system proceeds to step866to perform alphabet reduction. When all of the feedback values are extreme, the system proceeds to step872.

If, in step864, all LLRs are extreme and are indicative of the same result, the MPA process can be skipped in step872and the inner loop ends in step874. Alternatively, if only some LLR values are extreme, the alphabet can be reduced to a subset alphabet based on the extreme feedback values in step866. Bit values associated with the extreme feedback values are fixed, and only the codewords having bits corresponding to the fixed bits are considered.

Then, in step868, an updated computation schedule is calculated based on the pruned subset of the alphabet that forms the new alphabet. Only the calculations which use the reduced alphabet are used. Then, the system proceeds to step870

In step870, the MPA is performed. If the alphabet has been pruned, only the reduced alphabet is used during the MPA. The MPA is performed iteratively until a stopping point is reached.

In an FN, the message from the FN to the VN may be given by:
Icn→qk(i)=Σα=1|Ca|Σβ=1|Cb|φn(yn,α,β,i,N0,n,hn)(Iqa→cn(α)Iqb→cn(β)),
for i=1, . . . , |ck|, where n indicates the FN and k indicates the VN. Also:
Icn→qk
indicates the ith message from FN n along the edge to VN k, and
Iqk→cn
indicates the ith message from VN k along the edge to FN n.

When the a priori probabilities corresponding to VN k are sufficiently extreme to eliminate all but one likely codeword at that node, the updating of all messages from an FN to VN k may be removed from the schedule. This means that the values of:
φn(yn,α,β,i,No,n,hn)
and
Icn→qk(i)
are not computed for any value of n or i.

When a subset of the a priori probabilities corresponding to VN k are sufficiently extreme to eliminate a subset of the likely codewords at that node:
φn(yn,α,β,i,No,n,hn)
and:
Icn→qk(i)
are only computed for values of i corresponding to the remaining likely codewords. When a subset of codewords is evaluated, a bias or scaling may be applied to:
φn(yn,α,β,i,No,n,hn),
and/or to:
Icn→qk(i)

When the a priori probabilities corresponding to VN a and/or to VN b are sufficiently extreme to eliminate some or all but one likely codeword for that node, the set of combinations over which:
φn(yn,α,β,i,No,n,hn),
and:
Icn→qk(i)
are computed is reduced by only using the subsets of α=1, . . . , |Ca| and β=1, . . . , |Cb| corresponding to the remaining likely codewords for VNs a and b.

In another example, a log-MAP max-log-MAP variant is used for the MPA where the messages are comprised of log-likelihood value representations instead of probabilities or likelihoods. In this example, the message from the FN to the VN may look more like the following:
Icn→qk(i)=max(φn(yn,α,β,i,N0,n,hn))(Iqa→cn(α)+Iqb→cn(β)).
Regardless of the numerical representation, so long as the underlying MPA algorithm is being used in the decoder, the above complexity reductions due to the present invention may be realized.

In an example, a code such as an LDPC code, is used. The sampled sequence representing the received signal is provided to the variable nodes as input.FIG. 9illustrates flowchart980for an embodiment method of variable node message updating, for example using an LDPC code. Initially, in step982, the variable node determines whether there is only one remaining codeword in the pruned codebook. If there is only one codeword, the method proceeds to step986. In step986, the variable node sets the edge message to an appropriate extreme value. When the feedback value is not extreme, the variable node proceeds to step984. In step984, the variable node sets updates the edge messages for the parity check nodes normally.

FIG. 10illustrates flowchart1090for a method at either a parity check node or a function node. In step1092, the node determines whether the pruned codebook associated with the target VN has only 1 codeword. When this condition is satisfied, the process continues to step1096, an in the alternate proceeds to step1094. In step1096, the node does not perform an update for the edge associated with the VN with a 1 entry codebook. In step1094where the node updates the edge messages normally.

FIG. 11illustrates flowchart1100for an embodiment method of decoding using an MPA. Initially, in step1102, the method starts with the receipt of LLR values as the feedback values. If these values are received in series an optional step1104is performed to ensure that the LLR values are provided to the MPA processor in parallel.

In step1106, the system performs an MPA decoding process. In the first iteration, the MPA decoding is performed assuming that all codewords are equally likely. In subsequent iterations, APP values are received that provide different initial conditions for the MPA based on the likelihood of different codewords.

In step1108, LLR values from the MPA decoding are optionally converted from a parallel set of LLRs to serial set LLRs so that they can be transmitted to an FEC processor designed for receipt of a series of LLR values. Those skilled in the art will appreciate that if the FEC processor is capable of receiving a set of LLR values in parallel, this step can be bypassed.

Next, in step1110, the system performs FEC decoding (e.g. SISO outer FEC decoding) on the LLRs. If stopping conditions for the outer iterative loop have been met, then the system can output the decoded bits in step1112. If the stopping conditions are not met, then the FEC decoder provides a set of LLRs as output. These LLRs are used both as feedback to the MPA, and in the generation of APP values.

Also, in step1114, the system generates a priori probability values. The a priori probability values are fed back to the MPA decoding in step1106. The LLRs from step210are also used to prune the codebook based on bit level confidence as described above. This allows some codewords to be removed from the alphabet which reduces the number of calculations in subsequent iterations. When in step1112it is determined that outer loop stopping criteria have been met, the decoding process can terminate with step1112in which the decoded bits are output.

FIG. 12illustrates flowchart1220for an embodiment method of performing a turbo MPA. Initially, in step1228, the method starts. Then, in step1230, the system receives new signal information. In one example, the new signal information is a new signal. In step1232, the system runs an iterative MPA. The MPA iterations are performed until stopping conditions are met. In step1236, the iterative MPA generates a set of LLRs as its output which is provided as the input to a FEC process. Then, in step1238, FEC is performed using the LLR values determined in step1236.

In step1240, the system determines whether stopping conditions for the iterative outer loop have been met. When stopping conditions have been met, the system proceeds to step1242where the decoded bits are output and the process ends at step1244When stopping conditions have not been met, the method continues to step1222.

In step1222, the LLR values output by the FEC are used to generate a priori probability values. The APP values are provided to the MPA in step1224where they replace the APP values used in the previous inner loop iterations.

Next, in step1226, the MPA decoding schedule is updated to prune codewords from the available codebook. Then, the system proceeds to step1232to again run the MPA with the reduced alphabet.

FIG. 13illustrates flowchart1350for an embodiment method of a priori probability processing. Initially, in step1352, the method starts. In step1354, the system sets the first VN to be the current VN. Then, in step1356, the system determines new a priori probabilities (APPs) for the current VN. The system cycles through the APPs. In step1358, the system determines whether an APP indicates an extremely low likelihood. When the APP does not indicate an extremely low likelihood, the system proceeds to step1362. On the other hand, when the APP indicates an extremely low likelihood, the system proceeds to step1360. In step1360, the APP is flagged as unlikely. Then, the system proceeds to step1362. In step1362, the system determines whether the last APP examined is the last APP for the current APP. When the APP is the last APP for the current VN, the system proceeds to step1364. On the other hand, when the APP is not the last APP for the current VN, the system proceeds to step1356to examine the next APP for the current VN. In step1364, the system determines whether all APPs in the VN have been flagged. When all APPs in the VN have been flagged, the system proceeds to step1366. When not all of the APPs in the VN have been flagged, the system proceeds to step1368.

In step1366, the system removes all flags. When all of the APPs in the VN are flagged, the flagging of the APPs is not useful, because it is not desirable to prune all of the APPs. Then, the system proceeds to step1372.

In step1368, the system prunes unlikely codewords from the alphabet.

Next, in step1370, the system prunes the MPA schedule of operations to reflect the pruned alphabet of the current VN. In step1372, the system initializes VN to FN messages from the current VN.

Then, in step1374, the system determines whether the current VN is the last VN. When the current VN is not the last VN, the system proceeds to step1376. On the other hand, when the current VN is the last VN, the system proceeds to step1378.

In step1376, the system proceeds to the next VN, and assigns the next VN to be the current VN. Then, the system proceeds to step1356do determine the APPs for the next VN.

In step1378, the system determines whether there is only one remaining codeword per VN. When there is only one remaining codeword per VN, the system proceeds to step1380. When there is more than one remaining codeword for at least one VN, the system proceeds to step1382.

In step1380, the system generates extreme LLR values based on the remaining codewords for each VN output. Then, the system proceeds to step1384, and the method ends.

In step1382, the system runs the MPA. Also, the system proceeds to step1384, and the method ends.

The MPA may be performed serially or in parallel. Parallel processing is faster. However, alphabet reduction may have a greater impact on speed in a serial implementation. In parallel implementations, the hardware not in use may be powered down to same energy. In some embodiments, the computational complexity is reduced. The reduction in computational complexity may be an exponential reduction in computation, and may lead to a reduction in the time spent and power consumed by the decoding process. Also, an embodiment may strengthen the decoding capabilities, leading to quicker convergence. In an embodiment, the decoder hardware requirements are reduced, along with the decoding latency.

FIG. 14illustrates a block diagram of an embodiment processing system1400for performing methods described herein, which may be installed in a host device. As shown, the processing system1400includes a processor1404, a memory1406, and interfaces1410-1414, which may (or may not) be arranged as shown inFIG. 14. The processor1404may be any component or collection of components adapted to perform computations and/or other processing related tasks, and the memory1406may be any component or collection of components adapted to store programming and/or instructions for execution by the processor1404. In an embodiment, the memory1406includes a non-transitory computer readable medium. The interfaces1410,1412,1414may be any component or collection of components that allow the processing system1400to communicate with other devices/components and/or a user. For example, one or more of the interfaces1410,1412,1414may be adapted to communicate data, control, or management messages from the processor1404to applications installed on the host device and/or a remote device. As another example, one or more of the interfaces1410,1412,1414may be adapted to allow a user or user device (e.g., personal computer (PC), etc.) to interact/communicate with the processing system1400. The processing system1400may include additional components not depicted inFIG. 14, such as long term storage (e.g., non-volatile memory, etc.).

In some embodiments, one or more of the interfaces1410,1412,1414connects the processing system1400to a transceiver adapted to transmit and receive signaling over the telecommunications network.FIG. 15illustrates a block diagram of a transceiver1500adapted to transmit and receive signaling over a telecommunications network. The transceiver1500may be installed in a host device. As shown, the transceiver1500comprises a network-side interface1502, a coupler1504, a transmitter1506, a receiver1508, a signal processor1510, and a device-side interface1512. The network-side interface1502may include any component or collection of components adapted to transmit or receive signaling over a wireless or wireline telecommunications network. The coupler1504may include any component or collection of components adapted to facilitate bi-directional communication over the network-side interface1502. The transmitter1506may include any component or collection of components (e.g., up-converter, power amplifier, etc.) adapted to convert a baseband signal into a modulated carrier signal suitable for transmission over the network-side interface1502. The receiver1508may include any component or collection of components (e.g., down-converter, low noise amplifier, etc.) adapted to convert a carrier signal received over the network-side interface1502into a baseband signal. The signal processor1510may include any component or collection of components adapted to convert a baseband signal into a data signal suitable for communication over the device-side interface(s)1512, or vice-versa. The device-side interface(s)1512may include any component or collection of components adapted to communicate data-signals between the signal processor1510and components within the host device (e.g., the processing system1400, local area network (LAN) ports, etc.).

Those skilled in the art will appreciate that although the above description has been addressed to a mechanism for reducing the complexity of a decoding making use of a belief propagating message passing algorithm, it should be appreciate that an expectation propagating message passing algorithm can be similarly implemented. The ability to prune an alphabet based on likelihoods and APP values can also be used to reduce the complexity of an MPA processor that is relying upon expectation propagation. Extreme expectation values can be identified and used to prune the codewords in an possible decoding alphabet to allow for a complexity reduction.