Seminar

Ausgewählte Kapitel der Nachrichtentechnik, WS 2009/2010

LTE:Der Mobilfunk der Zukunft

Channel Coding and Link Adaptation

Shahram Zarei

16. December 2009

Abstract — In this work channel coding and link adaptation in LTE are considered,which are important issues in modern digital communication systems. With chan-nel coding, errors caused by distortion during transmission are detected and/orcorrected. In LTE both convolutional and Turbo codes are used. The structure ofconvolutional codes in LTE is presented here. Turbo codes and internal contention-free interleaver, which is an important part of the Turbo encoder are also topics ofthis work. The concept of the circular buffer, which is used in the rate matchingmodule and HARQ is discussed, too. Another key feature used in LTE is the linkadaptation. Link adaptation makes the efficient use of the channel capacity possi-ble, matching the transmission parameters, modulation scheme and coding rate tothe channel conditions.

1 Introduction

Channel coding is one of the most important aspects in digital communication systems, whichcan be considered as the main difference between analog and digital systems making error de-tection and correction possible. Error correction exists in two main forms: ARQ (AutomaticRepeat Request) and FEC (Forward Error Correction). With ARQ the receiver requests re-transmission of data packets, if errors are detected, using some error detection mechanism. InFEC some redundancy bits are added to the data bits, which is done either blockwise (so-calledblock coding) or convolutional, where the coded bit depends not only on the current data bitbut also on the previous bits. In LTE both block codes and convolutional codes are used. Thereis also an enhanced coding technique used in LTE, called Turbo code, which has performanceswithin a few tenth of a dB from the Shannons limit.

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Another feature of LTE, which is considered here, is link adaptation. Link adaptation isreferred to a mechanism matching automatically transmission parameters to the channel. Asan example for older systems of link adaptation the early versions of UMTS (Universal MobileTelecommunication System) can be mentioned, where fast closed-loop power control used tosupport an almost constant data rate. In UMTS the UE (User Equipment) transmitter adjustsits output power in accordance with one or more Transmit Power Control (TPC) commandsreceived in the downlink, in order to keep the received uplink Signal-to-Interference Ratio (SIR)at a given SIR target.

In HSPA (High Speed Packet Service Access) and LTE the transmitted information data rateis adjusted dynamically to use the channel capacity efficiently.

2 Link adaptation and feedback computation

2.1 Link adaptation in LTE

In LTE, link adaptation is based on the Adaptive Modulation and Coding (AMC). AMC canadapt modulation scheme and code rate in the following way:

• Modulation scheme: if the SINR (Signal-to-Interference plus Noise Ratio) is sufficientlyhigh, higher-order modulation schemes with higher spectral efficiency (hence with higherbit rates) like 64QAM are used. In the case of poor SINR a lower-order modulationscheme like QPSK, which is more robust against transmission errors but has a lowerspectral efficiency, is used.

• Code rate: for a given modulation scheme, an appropriate code rate can be chosen de-pending on the channel quality. The better the channel quality, the higher the code rateis used and of course the higher the data rate.

In LTE for data channels a Turbo encoder with a mother code rate of 1/3 is used. There isa Rate Matching (RM) module following the Turbo encoder, which makes it possible to getother code rates, if desired. Increasing and decreasing the code rate is done via puncturing andrepetition, respectively. Both, puncturing and repetition are integrated in the Rate Matchingmodule.

In Fig. 1 the whole signal generation chain of the LTEs physical layer with Turbo coding andmodulation modules can be seen, which are parts of the link adaptation system.

2.2 CQI feedback in LTE

In LTE downlink, the quality of channel is measured in the UE and sent to the eNodeB inthe form of so-called CQIs (Channel Quality Indicator). The quality of the measured signaldepends not only on the channel, the noise and the interference level but also on the qualityof the receiver, e.g. on the noise figure of the analog front end and performance of the digital

Channel Coding and Link adaptation 3

Figure 1: Signal generation chain in LTE

signal processing modules. That means a receiver with better front end or more powerfull signalprocessing algorithms delivers a higher CQI. The signal quality measurments are done usingreference symbols.

Depending on the SNR (Signal-to-Noise Ratio) a combination of modulation scheme and coderate is selected to ensure that the BLER (Block Error Rate) is less than 0.1. This can be seenin Fig. 2

Figure 2: BLER versus SNR for various combinations of modulation scheme and code rate

In Fig. 3 a list of 4-bit CQIs corresponding to the 16 possible combinations of modulationscheme and code rate is shown. As can be seen in this table, CQI = 1 refers to the most robusttransmission parameters i.e. QPSK as modulation scheme and the lowest code rate of 0.076,which is selected for the worst channel quality.

With increasing channel quality, higher order modulation schemes and higher code rates canbe selected. The highest order of modulation and highest code rate, which can be selected are64QAM and 0.93 respectively and correspond to a CQI value of 15.

In the above discussions it is assumed, that the considered channel is a slow fading channel.In other words, between two CQI measurments, channels behaviour does not change or thecoherent time of the channel is at least as long as the CQI measurment period.

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Figure 3: 4-bit CQI table

Here, only the link adaptation for downlink is discussed. The link adaptation in uplink is verysimilar. The difference is, that eNodeB estimates channel quality by evaluating the channelusing SRSs (Sounding Reference Signals).

In the LTE physical layer, resources are managed with the so-called RM Modules (ResourceManagement), which assign incoming data blocks to resource blocks. One resource block con-sists of 12 sub-carriers and one time slot. The resource management in LTE can be seen in Fig.4. CQI values are used also to select the optimum resource block i.e. the optimum sub-carrierand the optimum time slot.

Figure 4: Two dimensional resource management in LTE

There are two kinds of CQI reporting: periodic and aperiodic, where the PUCCH (PhysicalUplink Control CHannel) is used for periodic CQI reporting only and PUSCH (Physical UplinkShared CHannel) for aperiodic CQI reporting. Periodic CQIs are reported by the UE in periodictime intervals. If the eNodeB wishes channel quality information at a specific time, aperiodicCQIs are triggered.

In order to define the frequency granularity of the CQI, the whole system bandwidth is dividedinto N sub-bands, each consisting of k contiguous Physical Resource Blocks (PRBs). The

Channel Coding and Link adaptation 5

number of sub-bands is given by N = d NDLRB/k e and determines the frequency granularity

of the CQI reporting, where NDLRB is the number of resource blocks (RB) in the whole system

bandwidth (DL stands for Downlink).

2.3 Periodic CQI reporting

The periodic reporting of the CQIs is done over the PUCCH. Periodic CQI can be eitherwideband or UE-selected sub-band feedback for all downlink transmission modes. The type ofCQI is decided by the eNodeB.

In the wideband mode, one CQI value is measured in the whole system bandwidth and sentto the eNodeB. In the UE-selected sub-band feedback the total number of sub-bands N in thewhole system bandwidth is divided into j fractions called bandwidth parts. In each bandwidthpart a particular sub-band is selected and the measured channel quality in this sub-band withits position in the bandwidth part is sent to eNodeB.

In Fig. 5 sub-band size (k) and bandwidth parts (J) versus downlink system bandwidth NDLRB

can be seen.

Figure 5: Number of resource blocks in the whole system bandwidth (NDLRB), number of resource

blocks in a sub-band (k) and bandwidth parts (J) in periodic CQI using UE-selected sub-bands

2.4 Aperiodic CQI reporting

Normally periodic CQIs are used but if eNodeB needs channel quality information at timesrather than time raster of the periodic CQI, it can also wish aperiodic transmission of the CQIsby the UE. Loss of synchronization or handover situations are also cases, where aperiodic CQIsare used. Aperiodic CQI reporting is done over the PUSCH and requested by the eNodeB bysetting a CQI request bit on the Physical Downlink Control CHannel (PDCCH). The type ofCQI is set by the eNodeB and can be one of the following modes:

• Wideband feedback: in this mode as in the periodic reporting, the UE reports one CQIvalue for the whole system bandwidth.

• eNodeB-configured sub-band feedback: there are two kinds of CQI reported in this mode,one for the whole system bandwidth and one for the sub-bands. In the calculation of sub-band CQIs, it is assumed that transmission takes place only in the relevant sub-band.

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• UE-selected sub-band feedback: as in the eNodeB-configured mode, two types of CQIs areused, one wideband CQI value for the whole system bandwidth and one for reporting theaverage measured CQI inM selected sub-bands each of the size k. The UE decides, whichsub-bands are selected. The UE sends also the position of the M selected sub-bands.

Number of resource blocks in the whole system bandwidth, number of resource blocks in asub-band (k) and number of selected sub-bands (M) by the UE for the UE selected sub-bandfeedback CQI reports can be seen in Fig. 6.

Figure 6: Parameters of the aperiodic CQI report for UE-selected sub-bands feedback

3 Channel coding in LTE

One of the most important issues in digital communication systems is error correction. Errorcorrection can be considered in two main categories: ARQ (Automatic Repeat Request) andFEC (Forward Error Correction). With ARQ the receiver requests retransmission of the datapackets, if errors are detected and this will be done, until the received packets are error-free ora maximum number of retransmissions is reached.

For FEC redundancy bits are added to data bits, making error correction possible. FEC hastwo main types: block codes and convolutional codes. In block codes, the input data blocks,which can be considered as vectors are multiplied by a generator matrix, generating a codeword vector. In contrast to block codes, convolutional codes have a similar structure like FIR(Finite Impulse Response) filters and operate bitwise. Convolutional codes have memory, whichmeans the coded output bit depends not only on the current bit but also on the m previousbits, where m is the number of registers in the convolutional encoder. In LTE both blockcodes and convolutional codes are used. CRC (Cyclic Redundancy Check) which is a cycliclinear block code is used for HARQ as an error correction technique. Control channels anddata channels in LTE use convolutional and Turbo codes, respectively, where the later is anenhanced development of convolutional codes achieving near-Shannon performance.

3.1 Convolutional encoder in LTE

A convolutional encoder C(k, n,m) consists of a shift register with m stages, whose outputs areadded (XOR) together to build the output bit. Per k bit input information bits, n output bits

Channel Coding and Link adaptation 7

are produced from the encoder. The rate of the code is defined as: R = k/n. The structureof LTEs convolutional encoder with k = 1, n = 3, m = 6 and resulting code rate of 1/3 canbe seen in Fig. 7. The n outputs in the convolutional encoder are calculated via n generatorsequences: G = [g0, . . . , gn−1]. The generator sequences used in LTE are:

g0 = [1 3 3](oct) , g1 = [1 7 1](oct), g2 = [1 6 5](oct)

Figure 7: LTEs convolutional encoder

3.1.1 Decoding of convolutional codes

In order to minimize the bit-error probability, in receiver a sequence should be selected, whichmaximizes the so-called MAP (Maximum A-Posteriori) probability:

x̂ = argmaxx

P (x|y) (1)

Where x denotes the transmitted sequence and y the received sequence. If the codewords areequiprobable, the MAP criterion is equivalent to Maximum Likelihood (ML) criterion:

x̂ = argmaxx

P (y|x) (2)

Instead of maximizing P (y|x), log P (y|x) can be maximized, because log(.) is a monotonicallyincreasing function, which leads to the loglikelihood function for a memoryless channel:

logP (y|x) =L+m−1∑

i=0

n−1∑j=0

logP (yi,j|xi,j) (3)

For an AWGN channel we have:

P (yi,j|xi,j) ∼ N(√Ebxi,j, N0), (4)

where Eb is the transmitted bit energy and N0 the variance of the white gaussian noise.

Hence we get:

logP (y|x) ∝ ‖yi −√Ebxi‖2 (5)

In order to maximize equation (5) , in receiver a codeword should be selected, whose euclideandistance to the received sequence is minimum. But examining all of the possible candidates forthe input sequence is very costly and has exponential complexity.

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A very efficient method to decode convolutionally coded sequences is the viterbi algorithm,which has much less computational complexity using the trellis diagram.

The trellis diagram is a state diagram, where the time progress is also presented among thex-axis as can be seen in Fig. 8.

In the example considered here, there are two registers in the convolutional encoder and there-fore four states in the trellis diagram. Starting at an initial state and depending on the inputbit, the next state is determined. Therfore, each input sequence can be represented with a pathin the trellis, if the initial state is known.

In order to decode a convolutionally encoded sequence the initial and final states should beknown to the receiver. There are several methods to do this, two of them are:

• Insertion of termination bits (or tail bits) at the end of the information block to reset allshift registers to zero at the end of the encoding process.

• Tail-biting, where the initial and final states of the encoder are identical. Tail-biting isdone by initializing the shift register contents with the last m information bits in theinput block. The advantages of this method is the uniform protection of the informationbits and that there is no rate loss.

3.1.2 Viterbi algorithm

The Viterbi algorithm searches the best path in the trellis diagram with known initial and finalstates, which matches to the input sequence. Each path consists of branches, which connectstwo states and have certain cost (metric). The overal cost of a path is the accumulated metricof its branches. The aim in the viterbi algorithm is to find the path with the minimum cost.

Branch metric at the ith trellis step (the cost of choosing a branch at the trellis step i) is definedas:

M(yi|xi) =n−1∑j=0

logP (yi,j|xi,j) (6)

At the lth transition in the trellis, a partial path metric can be derived, which is the accumulatedmetric of branches between the initial state and the considering lth transition, following aspecific path inside the trellis. The partial path metric can be defined as:

M ls(y|x) =

l∑i=0

M(yi|xi) =M l−1s′ (y|x) +M(yl|xl) (7)

Viterbi algorithm finds the best path through the trellis, by comparing all of the arriving edgesin the state s and selecting a survivor edge with the best metric. It can be shown, the best edgeis the one with the smallest hamming distance between the received sequence and the statesequence.

At each step the survivor partial paths with the smallest accumulated metrics are selected andfinally the best path between the initial and final state with smallest metric is selected, whichcorresponds to a specific input bit-sequence.

Channel Coding and Link adaptation 9

Figure 8: Trellis diagram of a convolutional encoder

3.2 Turbo coding in LTE

Turbo codes were first introduced by Berrou, Glavieux and Thitimajshima in 1993 and havePerformances within a few tenth of a dB from the Shannon limit. The Turbo encoder in LTEis a systematic parallel concatenated convolutional code (PCCC) with two 8-state constituentencoders (the same as in UMTS) and one Turbo code contetntion free internal interleaver(different from UMTS). Where the encoders are based on RSC (Recursive Systematic Con-volutional) codes and their generator polynomial is given by G=[1, g0/g1], where g0=[1011](feedback) and g1=[1101] (feedforward).

The structure of the Turbo encoder used in LTE can be seen in Fig. 9.

Figure 9: Structure of the LTE Turbo encoder (dotted lines are for trellis termination)

As can be seen in Fig. 9, the output of the LTE Turbo encoder consists of three parts, asystematic bit and two parity bits. The systematic bit (Xk) is the untouched input bit. Thefirst parity bit (Zk) is the output of the first convolutional encoder with the original input (Ck)as input and the second parity bit (Z ′k) is the output of the second convolutional encoder after

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interleaving (by the Turbo code internal interleaver) of the input bit (C ′k) as its input.

For trellis termination the tail-bits X ′k are inserted.

Turbo coding is used in LTE for following channels: UL-SCH (Uplink Shared CHannel), DL-SCH (Downlink Shared CHannel), PCH (Paging CHannel) and MCH (Multicast CHannel)

3.2.1 Turbo encoders internal contention-free interleaver

The internal contention-free interleaver is one of the key parts of the LTE Turbo encoder.The main difference between the Turbo encoders in LTE and UMTS is that the interleaverin LTE is in contrast to the one in UMTS contention-free. Contentions occur, when parallelworking processeses try to write or read to/from the same memory address simultaneously.Because the two SISO (Soft-Input Soft-Output) MAP decoder engines of the Turbo decoder usesuch processes, the contention-free concept becomes survival for designing the Turbo encodersinternal interleaver efficiently.

A contention-free interleaver π(i), 0 ≤ i ≤ K should satisfy the following inequality, where Wis the window size and 0 ≤ νW, u1 ≥ 0, u2 < M for all U1 6= U2:

bψ(u1W + ν)

Wc 6= bψ(u2W + ν)

Wc (8)

The above inequality satisfies for both interleaver ψ = π and deinterleaver ψ = π−1 andindicates, that the memory addresses (both sides of the inequality), accessed by M processeson the νth step must be different.

There were two candidates for the LTE internal interleaver: Almost Regular Permutation(ARP) and Quadrature Permutation Polynomial (QPP), which are very similar. However QPPis chosen for LTE because it offers more parallelism. The QPP interleaver for a block size of Kis defined as following:

π(i) = (f1i+ f2i2) mod K (9)

Where i is the input index and π(i) the output index and f1 and f2 are permutation parameters,which can be get from the standard.

3.2.2 Turbo decoder in LTE

The Turbo decoder in LTE is based on two SISO (Soft-Input Soft-Output) decoders, whichwork together in an iterative manner. Each SISO decoder has two inputs, namely a normalinput and an a-priori Log Likelihood Ratio (LLR) input, and two outputs, an a-posteriori LLRand an extrinsic LLR. In each iteration the (de)interleaved version of the extrinsic output ofa decoder is used as the a-priori information for the other decoder. Typically after 4 to 8iterations, the a-posteriori LLR output can be used to obtain the final hard decision estimatesof the information bits. The structure of the LTE Turbo decoder can be seen in Fig. 10.

Channel Coding and Link adaptation 11

Figure 10: Turbo decoder

3.3 Rate matching in LTE

As can be seen in Fig. 9, the mother code rate of LTE Turbo encoder is 1/3. In order to getother code rates, if desired, repetition or puncturing has to be performed, which both are doneby a rate matching module. The rate matching module consists of three so-called sub-blockinterleavers for the three output streams of the Turbo encoder core and a bit selection andpruning part, which is realized by a circular buffer.

The sub-block interleaver is based on the classic row-column interleaver with 32 columns anda length-32 intra-column permutation.

The bits of each of the three streams are written row-by-row into a matrix with 32 columns(number of rows depends on the stream size). Dummy bits are padded to the front of eachstream to completely fill the matrix. After a column permutation, bits are read out from thematrix column-by-column. The column permutation of the sub-block interleaver is given asfollowing:

[0, 16, 8, 24, 4, 20, 12, 28, 2, 18, 10, 26, 6, 22, 14, 30, 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27,7, 23, 15, 31]

For example if column 1 has to be read orginally, after permutation column 16 will be read.

Figure 11: Turbo encoder with rate matching module

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3.3.1 Circular buffer in LTE

The circular buffer is the most important part of the rate matching module, making puncturingand repetition of the mother code possible. The structure of the Turbo encoder with ratematching module is shown in Fig. 11 The interleaved systematic bits are written into thecircular buffer in sequence, with the first bit of the interleaved systematic bit stream at thebeginning of the buffer. The interleaved and interlaced parity bit streams are written intothe buffer in sequence, with the first bit of the stream next to the last bit of the interleavedsystematic bit stream. Fig. 12 shows the internal structure of the circular buffer. The white cellscontain systematic bits and red and blue cells contain parity 0 and parity 1 bits, respectively.Green cells are the RV (Redundancy Version) points, which are considered with more detailsin HARQ section.

The number of coded bits (depending on the code rate), are read out serially from a certainstarting point specified by RV points in the buffer. If the end of the buffer is reached and morecoded bits are needed for the transmission (in the case of a code rate smaller than 1/3), thetransmitter wraps around and continues at the beginning of the buffer.

Figure 12: Structure of a circular buffer for the LTE rate macthing module

3.4 HARQ and redundancy versions

HARQ, which stands for Hybrid ARQ, is an error correction mechanism in LTE based onretransmission of packets, which are detected with error. The functionality of the HARQ canbe seen in Fig. 13. The transmitted packet arrives after a certain propagation delay in receiver.Receiver produces either an ACK for the case of error-free transmission or a NACK, if someerrors are detected. The ACK/NACK is produced after some processing time and sent backto transmitter and arrives there after a propagation delay. In the case of a NACK, after acertain processing delay in transmitter, the desired packet will be sent again. The bits, whichare read out from the circular buffer and sent in each retransmission are different and dependon the position of the RV (Redundancy Version). There are four RVs (0, 1, 2, 3), which definethe position of the starting point, where the bits are read out from the circular buffer. TheRVs can be seen in the Fig. 12 and are presented as green cells. As can be seen in Fig. 12,in the first retransmission, more systematic bits are sent and with the progressing number ofretransmissions, RV becomes higher and therefore less systematic and more parity bits are readout from the circular buffer for the retransmission.

Channel Coding and Link adaptation 13

Figure 13: HARQ mechanism in LTE

3.5 Convolutional coding for control channels in LTE

In control channels like Physical Downlink Control CHannel (PDCCH) and Physical BroadcastCHannel (PBCH) a convolutional code is used. The reason is that the code blocks are muchmore smaller than in data channels and for small blocks the Turbo codes internal interleaverdoes not work efficiently. Because of the small number of bits carried in PDCCH and PBCHand in order to avoid overhead, the tail-biting approach instead of inserting tail bits is usedas terminating method. The initial value of the shift register of the encoder shall be set tothe values corresponding to the last 6 information bits in the input stream so that the initialand final states of the shift register are the same. The decoder can be either a circular Viterbialgorithm or a MAP algorithm. The rate-matching for the convolutional code in LTE uses asimilar circular buffer method as for the Turbo code.

4 Summary

LTE uses Adaptive Modulation and Coding (AMC) as the link adaptation technique to adapttransmission parameters, modulation scheme and code rate dynamically to the channel. Thehigher the channel quality, the higher is the used modulation order and code rate. Channelquality in downlink is measured in UE using the reference symbols. Upon this measurement,so-called CQIs, which are channel quality indicators are generated and sent to eNodeB. EachCQI value corresponds to a specific modulation scheme and a specific code rate, which areselected by eNodeB for the downlink transmission.

LTE uses both convolutional and Turbo encoding for control and data channels respectively.With Turbo codes performance up to a few tenth of a dB from the Shannons limit can beachieved. One of the highlights of the Turbo encoder in LTE is the internal contention-freeinterleaver, which makes it possible, that the Turbo decoder works with very high bit rates.Another feature of the LTE Turbo encoder is the concept of the circular buffer in the ratematching module. It allows a simple realization of rate matching in respect of HARQ.

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References

[1] S. Sesia, I. Toufik, M. Baker: LTE - The UMTS Long Term Evolution: From Theoryto Practice, John Wiley and Sons, 2009.

[2] W. Koch: Lecture script "Fundamentals of Mobile Communications", University ofErlangen-Nuremberg, 2008.

[3] J. Cheng, A. Nimbalker, Y. Blankenship, B. Classon, K. Blankenship: Analysis ofCircular Buffer Rate Matching for LTE Turbo code

[4] M. Stambaugh: HARQ Process Boosts LTE communications, Agilent technologies,2008.

[5] C. Berrou, A. Glavieux, P. Thitimajshima: Near Shannon limit error-correcting codingand decoding: Turbo codes (1), 1993.

[6] Third Generation Partnership Project; Technical Specification Group Radio AccessNetwork; Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing andchannel coding (Release 8)