DE102010044458A1 - Method for estimating original information sequence from faulted receipt sequence by channel equalizer and decoder of digital transmission system, involves identifying correct and incorrect blocks of coded information sequence - Google Patents

Abstract

The method involves setting the probabilities of bits of coded information sequence. An estimation signal of all bits of information sequence is transmitted as an output from a decoder, when termination condition occurs in an iteration loop with iteration probabilities of all coded bits from decoder to back-coupled channel equalizer. A syndrome sequence associated with estimation signal is computed. Correct and incorrect blocks of estimated coded information sequence are identified based on syndrome sequence, for decoding the incorrect blocks by the decoder. An independent claim is included for reception system for receiving particular faulted receipt sequence.

Description

The invention relates to a method and a receiving system for estimating a transmitted original information sequence from a particular faulty receive sequence by means of a channel equalizer and a subsequent decoder, wherein the decoder forms probabilities to the bits of a coded information sequence and in an iteration loop with each iteration the probabilities to all Bits are fed back from the decoder to the channel equalizer until an abort condition occurs and the decoder issues the estimate of all bits of the information sequence.

Such a method is known in the art and is referred to as turbo equalization or turbo equalizer and z. B. in the EP 0 808 538 B1 described.

Digital transmission systems are characterized in that both the information itself is displayed digitally, and the signal processing in the transmitter and receiver is mostly digital.

When transmitting over a channel (eg wireless, wired or optical), a distortion of the signal z. B. occur as a result of multipath propagation or for other reasons. Furthermore, the signal is disturbed by superimposed noise. The task of the receiver in a digital transmission system is to calculate an as accurate as possible estimate of the transmitted original information sequence from the sampled and quantized reception sequences.

To eliminate the distortion of the signal caused by multipath propagation or other reasons, the digital receive data or receive sequences are fed to a channel equalizer or equalizer prior to the estimation. This achieves a significant improvement in the estimation quality.

The robustness of a transmission system can be further increased by encoding the data to be transmitted in an original information sequence (sequence of bits) before transmission. The error correction codes used, so-called channel codes, allow the correction of a limited number of transmission errors in the receiver. For this purpose, certain algorithms are used for channel decoding. The invention relates to the common iterative channel equalization and channel decoding, in particular the decoding of convolutional codes, in a digital transmission system with the least possible number of arithmetic operations and the best possible quality of the estimated data.

Convolutional codes, which still distinguish between recursive and non-recursive convolutional codes, are known and customary in digital transmission technology. Folding encoders form state machines, whereby an encoder with p memory cells can assume 2 ^p states. In this case, a convolutional encoder successively can not assume any states, but rather, subsequent states are dependent on previous states. It is known to represent the possible successive states of a convolutional encoder in a so-called trellis diagram.

A sequence of data bits represents a path in such a diagram. Such a trellis diagram can then also contribute to the decoding of received coded information sequences since it is possible to check whether a reception sequence can form a possible path in the trellis diagram or not. If this is not the case, then the receive sequence contains errors. It is thus possible to calculate probabilities for the correctness of the individual bits of the reception sequence.

Decoders used for channel decoding can thus resort to a trellis suitable for the channel coder used.

Channel equalization and channel decoding are central tasks of a receiver in a digital transmission system. In simple concepts, channel equalization and channel decoding are considered separately, i. H. the received data is first equalized and then decoded. It is also possible to perform channel equalization and channel decoding together, i. H. All possible send sequences are compared with the receive data. However, this approach is largely irrelevant because of its complexity for practical systems.

A very powerful and at the same time practically feasible method is the channel equalization or decoding according to the aforementioned turbo method (Turbo Equalizer). This is an iterative method in which information between channel equalizer and channel decoder in both Directions are exchanged. This feedback and the iterative approach can significantly increase the quality of the data estimate.

The channel equalization according to the turbo method describes the feedback and iterative information transfer, in particular of probability information between the two components Kanalentzerrer and channel decoder. At first it is irrelevant which concepts and algorithms are used.

Correspondingly simple linear algorithms such as zero-forcing or MMSE can be used for the channel equalizer, but also more complex estimation methods such as log-MAP or max-log-MAP. The channel decoder can be realized, for example, by the soft output Viterbi decoder (SOVA), log-MAP or max-log-MAP.

Depending on the required error rate and implementation complexity, different combinations of these methods can be used. Decisive for both components is the ability to generate probability information or reliability information of the output values (so-called soft outputs).

In general, the error rate decreases as the number of iterations increases, with the improvement from iteration to iteration becoming smaller and smaller. An abort criterion to be specified or a defined maximum number of iterations terminates the iteration process.

However, the reduction of the error rate with increasing number of iterations remains unconsidered in today's methods. Thus, the number of arithmetic operations of commonly used channel decoders (SOVA, MAP) is constant over all iterations, i. H. even if there are only a few or no errors after a few iterations, the computational effort remains at a high level. This is particularly disadvantageous for energy-critical applications (eg mobile devices with limited battery capacity).

The object of the invention is to provide a method for estimating an original information sequence from a particular faulty receive sequence and thereby save energy and computing resources.

In this case, it is preferable to transform an original information sequence with a convolutional encoder into an encoded information sequence, interleave the bits of the encoded information sequence with an interleaver and convert it into so-called symbols by means of a mapper, which are then transported over the channel.

The inventive method starts in the receiver at the point at which a receive sequence formed from the received symbols is fed to the channel equalizer, corresponding to the transmission between channel equalizer and decoder, which performs the unfolding, a device for demapping (to form bits in so-called "Hard decisions" or probabilities in so-called "soft decisions" from the symbols) and a device for deinterleaving (deinterleaver) is provided.

The object is achieved in that with each iteration an estimate is formed as a so-called "hard decision" for all bits of the encoded information sequence estimated by the channel equalizer, in particular as a "soft decision", and the syndrome sequence (b) associated with the estimation is calculated with a syndrome former and from the syndrome sequence (b) identify error-free and erroneous blocks of the estimate, and decoder decodes only the erroneous blocks.

In the coding theory, the syndrome sequence is understood to be that sequence which results from multiplication of a received and possibly erroneous coded information sequence with a test matrix, the syndrome sequence being completely zero, if there are no errors, or by a respective "1" in the sequence indicates defective area.

Thus, according to the invention, the syndrome sequence makes it possible to identify error regions or entire error blocks within the estimate of the coded information sequence. According to the invention, in contrast to the known turbo method, the probabilities for all bits of the coded information sequence estimated by the channel equalizer are no longer calculated, but only the decoding and thus the calculation of the probabilities to the erroneous blocks in the decoder are performed.

The invention thus describes a method for iterative channel equalization and channel decoding in which the number of arithmetic operations of the channel decoder decreases as the number of iterations increases, ie as the number of errors decreases, which is due to the integration of syndrome based decoding of convolutional codes into the concept of turbo equalization is realized. According to the invention, computing power is only necessary for the faulty blocks of the coded information sequence estimated by the channel equalizer.

Crucial here is that with almost the same quality of the estimate (in terms of error rate) significantly fewer arithmetic operations are needed than in conventional implementations. With appropriate implementation, this directly affects the energy consumption of a corresponding receiver.

Energy consumption is particularly critical for mobile applications (eg mobile communications). However, in the current environment of rising energy prices and growing environmental awareness, energy efficiency also plays a role in wired devices, such as mobile phones. B. from the entertainment sector, an increasingly important role.

The method can be used in receivers for both broadcast systems and communication systems. In principle, the method according to the invention can be used in all communication methods which hitherto use the turbo method in order to optimize the energy consumption. In broadcasting systems in particular, a high level of savings is to be expected, since the majority of users find above-average reception conditions, whereas the receiver was designed for the "worst case". Since there is no return channel for the adaptation of the transmission power or modulation in broadcasting, the good reception conditions can be utilized directly with the described method in order to save decoding operations. As an example, a possible integration into a receiver for the American terrestrial television system ATSC is pointed out. The applicability of the method to trellis-coded modulation, as used in the ATSC system, has been demonstrated by means of simulations.

In an advantageous development, it can be provided that with the channel decoder new probabilities are calculated only for the bits of faulty blocks. Furthermore, provision may be made for the bits associated with error-free blocks to set a predetermined probability for the coded information sequence estimated by the channel equalizer. It may be provided in one possible embodiment that these set probabilities remain unchanged in subsequent iterations. It may also happen in another embodiment that the syndrome is changed by changing the sequence in the channel equalizer and other areas are determined to be free from errors and / or errors.

For the feedback of the probabilities of all bits to the channel equalizer, which is necessary in the context of the modified turbo method, the probabilities formed by the decoder to bits of erroneous blocks can then be combined with the set probabilities to form bits of error-free blocks.

It may be provided in the context of the method that, for contiguous blocks of zeroes in the syndrome sequence having a length greater than a predetermined minimum length, the corresponding blocks of the coded information sequence estimated by the channel equalizer minus an initial length and an end length are assumed to be error-free. According to the invention, the blocks thus determined undergo no further decoding in the decoder, and it can furthermore be assumed that the number of error-free blocks and / or the size of error-free blocks increases as the iteration progresses.

In the feedback of probabilities to all bits of the encoded information sequence estimated by the channel equalizer, it will be provided in an advantageous embodiment to undo the de-interleaving and de-mapping done between equalizer and decoder, by a mapper and a device for interleaving. Mapping and interleaving correspond to the procedures used for sending. In a further advantageous modification to the known turbo method, it can be provided in the invention that the decoder uses the trellis of the inserted Sydromformers for decoding faulty blocks.

As with the known turbo method, the iteration loop can be terminated when z. B. a predetermined number of iterations is achieved or in a preferred embodiment, when the syndrome is zero, in particular if this condition occurs before reaching a predetermined number of iterations. In addition to the reduction of channel decoder complexity by the previously described restriction of decoding only to the erroneous blocks in the encoded information sequence estimated by the channel equalizer, in an advantageous development by evaluating the syndrome weight defined by the number of '1' digits in the syndrome sequence after each iteration, adapting the method with respect to the channel equalizer used, d. H. realized the algorithm used.

This means that with a high syndrome weight, which suggests a high number of errors, a powerful and more complex channel equalizer (eg MAP) is used. If the syndrome weight then drops after a few iterations, eg. B. below a predetermined threshold, another, z. B. less complex Kanalentzerrer be used. Thus, depending on the criterion of the syndrome weight, a suitable channel equalizer can be adaptively selected for the respective situation. This leads to a further reduction of the number of required arithmetic operations for the channel equalizer at higher iteration runs.

Further details of the prior art, in particular the basis of the turbo process and the invention are explained in detail below. If concrete algorithms are mentioned in these explanations, these represent only an example. The method can also be carried out with other algorithms not explicitly mentioned here.

I. INTRODUCTION

Soft-input-soft-output (SISO) decoding is an important prerequisite for iterative receiver structures that follow the turbo principle, as used in turbo decoding [1] and turbo equalization [2]. In the case of convolutional codes, the SISO decoder is typically based on the BCJR algorithm [3], which uses the trellis structure of the encoder to compute the a posteriori information.

The BCJR algorithm can also be applied to the trellis of the syndrome shaper of the code, as described in [4]. The structure of this trellis depends on the syndrome sequence, which is a function of the error in the receiving sequence. That is, error-free sections in the receive sequence lead to null sequences in the syndrome sequence. Taking this into account, error-free regions in the receive sequence can be estimated by analyzing the syndrome sequence before starting the decoding process. This property of the syndrome decoding allows a considerable reduction of the decoding complexity by decoding only erroneous sections and, in any case, not processing error-free sections [5]. In [6] we used this approach to reduce the decoding complexity of the DVB-T channel decoder.

The reduction in decoding complexity depends on the number of errors in the sequence to be decoded. In conventional systems this is a function of the SNR: a higher SNR leads to lower decoding complexity. However, considering a system using turbo equalization, the number of remaining errors in the sequence to be decoded depends not only on the SNR, but also on the current iteration step: for higher iteration steps, a reduced number of errors is expected, leading to lower decoding complexity leads.

This article is structured as follows: Section II explains the basic principle of turbo equalization and the equalizer used. The subject of Section III is the Adaptive Complex Log MAP Decoder. After the description of the syndrome-based preprocessing (III-A), the principle of syndrome-based MAP decoding will be discussed (III-B). Simulation results are presented in Section IV. Conclusions are taken in Section V.

II. TURBOENT CREATION

This section summarizes the basic principles of turbo equalization and the equalizer used.

A. Basics

We take a transfer as in 1 A binary information sequence represented by a K × 1 vector u = {u _k } is encoded with a rate R convolutional code. The resulting code sequence v = {υ _k } of length L = K / R is interleaved, v '= Π (v), mapped to modulation symbols and transmitted over the frequency-selective channel. The received sequence can by y = H _c v '+ n, where H _{c is} the (L + M-1) × L channel convolution matrix associated with the channel of length M, and n additive white Gaussian noise (AWGN) with noise power σ 2 / n represents.

The task of the receiver is to compute a fitting estimate û of the original information sequence. Following the turbo principle, this task is solved by iterating between a SISO equalizer and a SISO channel decoder. Both components exchange their estimates of the probabilities of each bit υ _k , resulting in an iterative improvement of the estimate to some limit. The probabilities are expressed as Log Likelihood Ratios (LLRs) represented by L (·). The important underlying principle is that both components produce independent, extrinsic LLRs L _E (·).

2 shows the structure of the turbo-detector: The equalizer generates a posteriori estimates using the perturbed sequence y and, after the first iteration, additional a-priori information L d / E (υ '/ k) about the code bits. Modulation / demodulation is needed to transform between bits and modulation symbols. Extrinsic information is generated by the a-pirori LLRs from the a-posteriori values L ^e (υ '/ k) subtracted from, L e / E (υ '/ k) = L ^e (υ' / k) - L d / E (υ '/ k). (1)

The decoder receives the non-nested sequence L e / E (υ _k ) as input data and generates the a-posteriori estimate L ^d (υ _k ). Extrinsic information L d / E (υ _k ) the code bits υ _k is calculated by L d / E (υ _k ) = L ^d (υ _k ) - L e / E (υ _k ) (2) and the nested extrinsic LLRs L d / E (υ '/ k) will be routed to the equalizer in the next iteration. In the last iteration, the decoder also outputs an estimate û of the information sequence.

Maximum a-posteriori probability (MAP) Variants of equalizers and decoders can be realized on the basis of the trellis representation of channel and code. Alternatively, a linear realization (Minimum Mean Squared Error Linear Equalizer, MMSE LE) has been proposed for the equalizer [7]. For the simulations presented in this work, the MMSE LE is used. Therefore, this is summarized in the following section for the case of a BPSK.

B. Linear MMSE equalizer

• • c_k der (N × 1) Filtervektor mit N = N₁ + N₂ + 1 ist.
• • y_k ein Vektor bestehend aus den empfangenen Symbolen y_k-N₁ bis y_k+N₂ ist.
• • H_b ein N × (N + M – 1) Block aus H_c ist.
• • v ' / k ein (N + M – 1) × 1 Vektor bestehend aus den Erwartungswerten υ ' / k-M-N₂+1 bis υ ' / k+N₁ ist, der entsprechend υ ' / n = tanh(L d / E(υ ' / n/2) mit n = k – M – N₂ + 1, ..., k + N₁ aus den LLRs berechnet werden kann. Das Element υ ' / k wird zu Null gesetzt.
• • s die (N₂ + M)-te Spalte von H_b ist.

The equalizer calculates the extrinsic LLRs L e / E (υ '/ k) by applying the time-variant filter c _k to the normalized residual of the received symbols y _k and the prediction H _b v '/ k the received symbols, L e / E (υ '/ k) = 2c H / k (y _k - H _b v '/ k) / (1 - s ^H c _k ), (3) in which

• • c _{k is} the (N × 1) filter vector with N = N ₁ + N ₂ + 1.
• • y _{k is} a vector consisting of the received symbols y _k-N₁ to y _{k + N₂} .
• • H _{b is} an N × (N + M - 1) block of H _c .
• • v '/ k an (N + M - 1) × 1 vector consisting of the expectation values υ '/ kM-N₂ + 1 to υ '/ k + N₁ is that appropriate υ '/ n = tanh (L d / E (υ' / n / 2) with n = k - M - N ₂ + 1, ..., k + N ₁ can be calculated from the LLRs. The element υ '/ k is set to zero.
• • s is the (N ₂ + M) -th column of H _b .

The filter vector is calculated as a weighted MMSE estimator, c _k = (σ 2 / n 1 _N + H _b V _k HH / b) ^-1 s, (4) where V _{k is} a diagonal matrix, V _k = diag (1 - | υ '/ kM-N₂ + 1 | ² , ..., 1 - | υ '/ k + N₁ | ² ). (5)

Analogous to the setting of υ '/ k = 0, the (N ₂ + M) -th diagonal element of V _{k is set} to 1. This guarantees that the filter is an estimate L e / E (υ '/ k) generated independently of L d / E (υ '/ k) is. Considering that equalizers and decoders are separated by an interleaver, it follows that L e / E (υ '/ k) which is extrinsic LLR.

III. ADAPTIVE LOG MAP DECODER WITH LOW COMPLEXITY

The basic idea of the proposed adaptive decoding concept is to preprocess the hard decision of the decoder input sequence and split it into blocks that are considered error free and blocks that are corrupted. Only the faulty blocks are actually processed by the decoder, while the error-free blocks are provided only with a high security and passed on directly to the successive stage. The proposed concept is based on the syndrome decoding (SD) principle of convolutional codes [8], which means that the decoding algorithm works on the trellis of the syndrome shaper rather than on the trellis of the encoder. In the SD approach, by Schalkwijk et. al. [9], this trellis is searched for the maximum likelihood error sequence, which can then be used to correct the transmission errors in the receive sequence.

In this work a MAP decoder based on syndrome former trellis is proposed. Note that compared to turbo codes, the decoder generates LLRs for the code bits, not for the information bits. This makes a syndrome trellis-based implementation less complicated compared to [4]. Section III-A below describes the syndrome-based preprocessing, while Section III-B presents the syndrome-based Log MAP decoder.

A. Syndrome-based preprocessing

Given a convolutional code C represented by an encoder G (D), the syndrome shaper H ^T (D) is the transpose of an encoder H (D) of the dual code C ^⊥ . It is true that G (D) H ^T (D) = 0, (6) ie H ^T (D) is orthogonal to all code sequences of C.

Let r = {r _k } be the hard decision of L e / E (υ _k ), so that

Note that r changes in each iteration. Then the sequence r of length L in the time domain can be represented as r = uG ⊕ e = v ⊕ e, (8) where e represents the remaining channel error. The application of the time domain representation H ^T of the syndrome shaper to r yields the syndrome sequence b of length L (1-R): b = rH ^T = uGH ^T ⊕ eH ^T = eH ^T (9)

In (9) it can be stated that because of the orthogonality of H ^T to the code, b depends only on the channel error. In the case that r is completely error-free, it is completely orthogonal to H ^T and thus the syndrome sequence b is zero. However, in the general case, if r contains errors, this may only be partially orthogonal to H ^T. This means that error-free subsequences of a certain minimum length in r will propagate into a sequence of consecutive zeroes in b. Thus, it is possible to estimate error-free blocks in r by analyzing b.

• 1) Berechne die Harddecisionsequenz r nach (7).
• 2) Berechne die Syndromsequenz b = rH^T.
• 3) Zerlege r in fehlerhafte und fehlerfreie Blöcke durch Analyse von b: Für Blöcke mit ≥ l_min aufeinander folgenden Nullsymbolen in b werden die korrespondierenden Blöcke in r als fehlerfrei betrachtet. Zwei zusätzliche Parameter l_on und l_off werden benutzt um eine Erweiterung der fehlerhaften Blöcke am Anfang bzw. am Ende zu definieren. Die Bedeutung der Parameter ist in 3 dargestellt. Es gilt, dass l_on + l_off ≤ l_min.
• 4) Die einzelnen Blöcke werden wie folgt verarbeitet: a) Die fehlerhaften Blöcke werden dem Decoder zugeführt. Diese Blöcke sind unabhängig voneinander und werden als im Nullzustand terminiert und initialisiert betrachtet. Die Anzahl der fehlerhaften Blöcke pro Rahmen wird als J bezeichnet und die Anzahl der Trellisabschnitte pro Block j als T_j. Der syndrombasierte MAP Decoder berechnet die LLRs L^d(υ_k) für jeden der J Blöcke (siehe Abschnitt III-B). b) Die verbleibenden Blöcke werden als fehlerfrei betrachtet. Daher werden sie nicht vom Decoder verarbeitet und den entsprechenden Bits wird ein unendliches LLR zugewiesen: L^d(υ_k) = ∞·(2r_k – 1) (10) Man beachte, dass dies für den Entzerrer schlichtweg bedeutet, dass der Erwartungswert der entsprechenden verschachtelten Bits gesetzt wird zu υ ' / k = 2r ' / k – 1. (11)
• 5) Während der Iterationen werden die LLRs L^d(υ_k) unter Verwendung von (2) in extrinsische LLRs transformiert und zum Entzerrer zurück gekoppelt. Nach der letzten Iteration wird eine Harddecision v ^ von L^d(υ_k) genommen und unter Verwendung der rechten Inversen der Generatormatrix û = v ^G^–1 zur Schätzung der Informationssequenz û zurück transformiert.

Based on this observation, adaptive reduced complexity can be realized as follows:

• 1) Compute the hard decision sequence r after (7).
• 2) Calculate the syndrome sequence b = rH ^T.
• 3) Decomposition r into erroneous and error-free blocks by analyzing b: For blocks with ≥ l _min consecutive zero symbols in b, the corresponding blocks in r are considered to be error-free. Two additional parameters l _on and l _off are used to define an extension of the faulty blocks at the beginning or at the end. The meaning of the parameters is in 3 shown. It holds that 1 _on + 1 _off ≤ 1 _min .
• 4) The individual blocks are processed as follows: a) The faulty blocks are fed to the decoder. These blocks are independent of each other and are considered to be terminated and initialized at zero state. The number of bad blocks per Frame is referred to as J and the number of trellis sections per block j as T _j . The syndrome-based MAP decoder calculates the LLRs L ^d (υ _k ) for each of the J blocks (see Section III-B). b) The remaining blocks are considered error free. Therefore, they are not processed by the decoder and the corresponding bits are assigned an infinite LLR: L ^d (υ _k ) = ∞ · (2 r _k - 1) (10) Note that this simply means to the equalizer that the expected value of the corresponding interleaved bits is set υ '/ k = 2r' / k - 1. (11)
• 5) During the iterations, the LLRs L ^d (υ _k ) are transformed into extrinsic LLRs using (2) and coupled back to the equalizer. After the last iteration, a hard decision v ^ is taken from L ^d (υ _k ) and using the right-hand inverse of the generator matrix û = v ^ G ^-1 to estimate the information sequence û transformed back.

This concept reduces the decoding overhead because only the defective parts are processed by the MAP decoder. The reduction depends on the input bit error rate of the decoder: the lower the input bit error rate, the more and longer error free blocks can be identified, and thus the higher the reduction of the decoding effort. On the other hand, in the worst case, if no error-free blocks can be identified (J = 1), the entire sequence must be processed and the overhead is identical to that of the conventional decoder. In turbo equalization, in the case of convergence, the input bit error rate of the decoder improves from one iteration to the next. This results in increasing savings in decoding overhead during the iteration process.

• • die LLRs für die fehlerhaften Blöcke nur basierend auf einzelnen Blöcken, nicht der gesamten Sequenz, berechnet werden,
• • einzelne Blöcke fälschlicherweise als initialisiert und terminiert im Nullzustand betrachtet werden und
• • fehlerfreie Blöcke fälschlicherweise als fehlerfrei betrachtet werden und somit einzelnen fehlerhaften Bits hohe Sicherheiten zugewiesen werden.

Processing only portions of the input sequence and assigning high confidence to the remaining suspected error-free blocks may obviously degrade the bit error rate performance of the turbo-equalizer system. Origins of the performance reduction can be that

• • the LLRs for the faulty blocks are calculated based only on individual blocks, not the entire sequence,
• • Individual blocks are mistakenly considered as initialized and terminated in the null state and
• • error-free blocks are erroneously regarded as error-free and thus high levels of security are assigned to individual erroneous bits.

The choice of design parameters (1 _min , 1 _on , 1 _off ) is thus critical to keeping bit error rate performance equivalent to that of the optimal decoder. Generally, larger values for 1 _{min will} reduce the influence of the aforementioned decreasing factors. On the other hand, smaller values will increase the reduction of the effort. Therefore, the design parameters must be carefully selected for a given system and the underlying code. In fact, it is possible to select parameter values so that the bit error rate performance does not suffer and the reduction of the effort is still significant. This aspect will become clear from the simulation results presented in Section IV.

In comparison to the actual MAP decoding, we consider the complexity of the preprocessing steps irrelevant: syndrome computation and application of the right inverse are realized by XOR operations. The decomposition into blocks can be implemented by counting only successive zeroes in b [10].

B. Syndrome-based Log MAP decoder

The structure of the syndrome-based Log MAP decoding algorithm (Log MAP SD) is identical to the known Log MAP [3], [11]. However, the Log MAP SD is based on the trellis of the syndrome shaper, while the latter works on the encoder trellis. More specifically, it works on the trellis, which is defined by b = rH ^T , where in each time step only the transitions corresponding to the current syndrome symbol are considered. This ensures that all trellis paths are allowable error sequences, ie result in valid code sequences when applied to r.

der Codebits υ_k basierend auf der beobachteten Eingangssequenz r ~ = {L e / E(υ_k)}. Unter Verwendung der Trellisdarstellung des Codes kann (12) umformuliert werden als

wobei p und q Trelliszustände zu Zeitpunkten t beziehungsweise (t + 1) sind und S₀ beziehungsweise S₁ Übergänge darstellen, die zu υ_k = 0 beziehungsweise υ_k = 1 führen.The decoder appreciates the LLRs

the code bits υ _k based on the observed input sequence r ~ = {L e / E (υ _k )}. Using the trellis representation of the code, (12) can be rewritten as

where p and q trellis states at times t and (t + 1) and S ₀ and S _{1 represent} transitions, which lead to υ _k = 0 or υ _k = 1.

The forward and backward state metrics α _t (p) and β _t (q) are calculated recursively as

The calculations (14) and (15) are usually implemented in the log domain. Therefore, the calculation of the transition metric γ _t (p, q) is also formulated in the log domain as logγ _t (p, q) = 1/2 <r ~ ^(t) , (2 (e ^{(p, q)} ⊕ r ^(t) ) - 1)>, (16) in which r ~ ^(t) and r ^{(t) represent} n soft-decision values and n corresponding hard-decision bits at time t. The vector e ^{(p, q)} contains the n error bits associated with the transition from state p to state q, and <·, ·> describes the inner product.

The application of syndromformertrellis-based Log MAP SD to the complete sequence r provides identical LLRs as the conventional log MAP, which works on the encoder trellis: This is easy to see because the transitions v ^{(p, q) of} the encoder trellis are connected to the junctions e ^{(p, q) of} the syndrome former trellis r ^(t) = v ^{(p, q)} ⊕ e ^{(p, q)} . (17)

undFor the proposed reduced complexity decoding method, the Log MAP SD is applied separately to the J erroneous blocks identified in the preprocessing step (Section III-A). In the following, this approach is therefore referred to as Log MAP BSD (Blockwise SD). These blocks are terminated and initialized to zero state, therefore, the forward and backward metrics for each block j must be properly initialized

and

IV. SIMULATIONS

A. Parameter Settings

• • ISI-Kanal der Länge M = 5 und Kanalimpulsantwort h = [0.227, 0.46, 0.688, 0.46, 0.227],
• • Nicht-rekursiver, terminierter Rate R = 1/2 Faltungscode mit G(D) = [D² + 1, D² + D + 1] und entsprechendem Syndromformer H^T(D) = [D² + D + 1, D² + 1]^T,
• • 2¹⁵ Datenbits pro Rahmen, was für den Code mit Rate 1/2 einem Trellis mit T = 2¹⁵ Sektionen pro Rahmen entspricht,
• • 14 Iterationen und BPSK-Modulation.

The proposed reduced complexity decoder, Log MAP BSD, is evaluated in a turbo equalization system with the following parameters:

• • ISI channel of length M = 5 and channel impulse response h = [0.227, 0.46, 0.688, 0.46, 0.227],
• • Non-recursive, scheduled rate R = 1/2 convolutional code with G (D) = [D ² + 1, D ² + D + 1] and corresponding syndrome shaper H ^T (D) = [D ² + D + 1, D ² + 1] ^T ,
• • 2 ¹⁵ data bits per frame, which corresponds to the rate 1/2 code of a trellis with T = 2 ¹⁵ sections per frame,
• • 14 iterations and BPSK modulation.

In the following, we will use the Log MAP SD, which processes the entire sequence without preprocessing, as a reference. It is important to emphasize that the performance and complexity of the Log MAP SD are identical to the conventional Log MAP decoder.

The design parameter set (l _min , l _on , l _off ) is determined heuristically by means of simulation results for achievable bit error rates and effort reduction. The parameters can be precalculated and are independent of the equalizer or the current channel conditions. These depend only on the code used. Here we select the parameters (l _min , l _on , l _off ) = (9, 4, 4), (20) which allows optimal Bitfehleratenperformanz, but a significant reduction of the effort.

B. Results

4 shows the bit error rate (BER) of the Turbo Equalizer after 1, 2, 3, 5, 8 and 14 iterations. A low cost decoder (Log MAP BSD) is compared to a reference implementation based on Log MAP SD. It is easy to see that the Log MAP BSD behaves exactly like the reference system.

ausgedrückt werden. 5 zeigt R(i) in Prozent für verschiedene E_b/N₀.The interesting point is the analysis of the reduction of the decoding effort. This reduction can be measured as the ratio of the accumulated size of erroneous (decoded) blocks to the length T of the entire received sequence. If we denote the number of identified erroneous blocks in iteration i with J (i) and the length of the block j with T _j (i), then this ratio can be iterated by i

be expressed. 5 shows R (i) in percent for different E _b / N ₀ .

It can be seen that the low-iteration decoder handles almost the entire sequence (R (i) ≈ 1), which is the cost of the conventional decoder. For increasing iteration number, however, R (i) decreases towards a lower limit. This lower limit decreases with increasing SNR. For example, at 6 dB, the decoder processes only about 59% and 42% of the received sequence in the 6th and 7th iterations, respectively.

In order to make the complexity analysis independent of the complexity of the equalizer, the parameters are chosen so that an identical convergence behavior is achieved, ie the complexity reduced decoder reaches the lower bit error rate limit with the same number of iterations as the reference. In 6 the convergence of the bit error rate (BER) is plotted over the equivalent iterations. The number of equivalent iterations will be canceled Σ I / i = 1 R (i) calculated for iteration I and represents the computational effort measured in iterations of the reference decoder.

Out 6 can be read that the Log MAP BSD reaches the lower bit error rate limit with the same number of iterations as the reference decoder. For example, both decoders reach the lower limit at 5 dB after about 12 iterations. For the Log MAP BSD this can be understood by the graphene marking (×). However, the computational effort needed to reach the bit error rate limit is only 10.5. For the other noise levels we can see a saving of 1.8 to 2 iterations compared to the reference decoder, without affecting the bit error rate performance.

In summary, the Log MAP BSD provides the same bit error rate as the reference decoder in the system under consideration, but requires only 71% to 87% of the operations to reach the lower bit error rate limit.

V. CONCLUSIONS

In this article, a syndrome-based MAP decoding method with reduced adaptive complexity is presented, and its application for turbo-equalization is shown. The basic idea is to avoid decoding supposedly error-free regions in the decoder's input sequence.

If a suitable set of design parameters is chosen, this does not affect the performance of the system. However, it can reduce the decoding overhead by up to 30% compared to the reference system.

In addition to the reduction of the decoding effort, the proposed concept can also increase the speedup of a MAP decoder implemented in parallel on a multi-core platform: The identification of error-free blocks is equivalent to the state identification and can therefore be used to overlap between parallel-processed sub-blocks avoid [5], [10].

REFERENCES

• [1] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near-Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes," in IEEE International Conference on Communications (ICC 93), vol. 2, Geneva, Switzerland, May 1993, pp. 1064-1070 vol. 2 ,
• [2] C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative Correction of Intersymbol Interference: Turbo-Equalization," European Transactions on Telecommunications, vol. 6, no. 5, pp. 507-511, 1995 ,
• [3] L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rates," IEEE Transactions on Information Theory, vol. 20, no. 2, pp. 284-287, March 1974 ,
• [4] M. Tajima, K. Shibata, and Z. Kawasaki, "Relation between encoders and syndromes former variables and symbol reliability estimation using a trellis syndrome," IEEE Transactions on Communications, vol. 51, no. 9, pp. 1474-1484, Sept. 2003 ,
• [5] J. Geldmacher, K. Hueske, and J. Goetze, "Syndrome based block decoding of convolutional codes," in Proceedings of the IEEE International Symposium on Wireless Communication Systems (ISWCS '08), Reykjavik, Iceland, Oct. 2008, pp. 542-546 ,
• [6] In "Proceedings of the International Conference on Modern Ultra Modern Telecommunications" (ICUMT 2009), St. Petersburg, Russia, Oct. 2003, "An adaptive and complexity reduced decoding algorithm for convolutional codes and its application to digital broadcasting systems." 2009 ,
• [7] M. Tuchler, R. Koetter, and A. Singer, "Turbo equalization: principles and new results," IEEE Transactions on Communications, vol. 50, no. 5, pp. 754-767, May 2002 ,
• [8th] G. Forney Jr., "Convolutional codes I: Algebraic structure," IEEE Trans. On Information Theory, vol. 16, no. 6, pp. 720-738, Nov. 1970 ,
• [9] J. Schalkwijk and A. Vinck, "Syndrome decoding of binary rate-1/2 convolutional codes," IEEE Transactions on Communications, vol. 24, no. 9, pp. 977-985, Sept. 1976 ,
• [10] K. Hueske, J. Geldmacher, and J. Götze, "Multi-core performance of a block syndrome decoder for convolutional codes," at 6th Karlsruhe Workshop on Software Radios (WSR10), Karlsruhe, Germany, 2010 ,
• [11] P. Robertson, E. Villebrun, and P. Hoeher, "A comparison of optimally and sub-optimal map decoding algorithms operating in the log domain," in Proceedings of the IEEE International Conference on Communications (ICC '95), vol. 2, Seattle, June 1995, pp. 1009-1013 ,

The 7 further shows a concrete embodiment of the channel decoder according to the invention. It can be seen here that the estimated likelihood values L ^e _E (v _k ) of the channel equalizer, in particular after de-mapping and deinterleaving, are fed to the decoder shown as dashed edge as input values for each bit v _{k of} the received coded information sequence. The coded information sequence estimated by the channel equalizer is thus available as a so-called "soft decision".

In the decoder, a decision maker who performs so-called "hard decisions" estimates a specific value for each bit, namely either "0" or "1", depending on the probability values of the information sequence estimated by the channel equalizer, so that after the decision maker an estimated value encoded information sequence consisting of "hard decisions" exists, which is further referred to here as the estimated coded information vector r.

On the information vector r, a check matrix H ^{T is} applied, which is orthogonal to the generator matrix of the code, whereby the syndrome sequence b is formed, based on which of the information vector r formed by the decision maker and / or the information sequence formed by the channel equalizer into blocks with and blocks without errors is split.

This is possible insofar as erroneous sites in the information vector r lead to '1' sites in the syndrome sequence b. Thus, erroneous areas in the information vector r can be estimated by analyzing the '1' locations in b. Since defective regions in the coded information sequence estimated by the channel equalizer correspond to the defective regions in the information vector r, they result simultaneously in the same way.

As shown, for each bit of an error-free block of the information vector r or the information sequence, the probabilities to be fed back to the channel equalizer are set high, e.g. B. here to "infinite". It is generally the stated probabilities, those probabilities, that the coded bits estimated in particular in the "soft decisions" match the actual originally transmitted coded bits.

Only with the error-prone blocks of the information vector r or the information sequence of the channel equalizer are new probabilities calculated for their respective coded bits, in particular with the aid of the trellis of the syndrome shaper. Here, however, other than the mentioned method Log MAP SD can be used.

After the calculation of the new probabilities, these are combined with the set probabilities and thus the probabilities L ^d (v _k ) are fed back to the channel equalizer to all bits of the coded information sequence, in particular indirectly via a mapper and interleaver. This is followed by a next iteration and estimation of the probability values L ^e _E (v _k ) by the channel equalizer, which are then returned to the decoder.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• EP 0808538 B1 [0002]

Cited non-patent literature

• Schalkwijk et. al. [0047]

Claims (9)

A method for estimating an original information sequence from a particular erroneous receive sequence by means of a channel equalizer and a subsequent decoder, wherein the decoder forms probabilities to the bits of a coded information sequence and in an iteration loop with each iteration the probabilities are fed back to the coder bits from the decoder to the channel equalizer until an abort condition occurs and the decoder outputs the estimate of all bits of the information sequence, characterized in that with each iteration an estimate (r) is made of all bits of the encoded information sequence estimated by the channel equalizer, and with a syndrome shaper the syndrome sequence associated with the estimate (b) is calculated and from the syndrome sequence (b) error-free and erroneous blocks of the estimate (r) are identified and the decoder decodes only the erroneous blocks. Method according to Claim 1, characterized in that new probabilities are calculated only for the coded bits of erroneous blocks. Method according to Claim 1 or 2, characterized in that a predetermined probability is set for the bits of the estimated coded information sequence which belong to error-free blocks. Method according to one of the preceding claims, characterized in that, in order to feed back the probabilities of all encoded bits to the channel equalizer, the probabilities formed by the decoder are combined into coded bits of erroneous blocks with the set probabilities into coded bits of error-free blocks. Method according to one of the preceding claims, characterized in that the iteration is terminated when a. a predetermined number of iterations is achieved, or b. the syndrome is zero. Method according to one of the preceding claims, characterized in that depending on the syndrome weight, in particular which is calculated at each iteration, a Kanalentzerrungsverfahren to be used is selected from a plurality of available Kanalentzerrungsverfahren. Method according to one of the preceding claims, characterized in that the decoder for decoding faulty blocks uses the trellis of the Sydromformers. Method according to one of the preceding claims, characterized in that, for contiguous blocks of zeros in the syndrome sequence (b) having a length greater than a predetermined minimum length (l _min ), the corresponding blocks of the information sequence (r) minus an initial length (l _on ) and an end length (l _off ) are assumed to be error-free. A receiving system for receiving a particular erroneous receive sequence comprising a channel equalizer and a subsequent decoder, the decoder is arranged to form probabilities to the bits of a coded information sequence and return the probabilities in an iteration loop with each iteration to all coded bits to Kanalentzerrer until an abort condition occurs and by the decoder, the estimation of all bits of the information sequence can be output, characterized in that it is arranged to carry out a method according to one of the preceding claims.

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