Adaptive Channel Coding for Mobile Channels — Or Why Wasting Bandwidth for Error Detection

Adaptive Channel Coding for Mobile Channels—Or Why Wasting Bandwidth

for Error Detection?

C.Wei?,T.Stockhammer,J.Hagenauer

Institute for Communications Eng.(LNT)

Munich University of Technology

chris,tom,hag@lnt.ei.tum.de

A.Donner

German Aerospace Center(DLR) Institute of Communications and Navigation

anton.donner@dlr.de

Abstract

We present a new channel coding system which combines error detection and error correction using a single high-memory convo-lutional code,i.e.,no dedicated error detection code is required. Since the state complexity of high-memory convolutional codes makes maximum-likelihood decoding impractical,a modi?ed se-quential decoder–the Far End Error Decoder(FEED)–is pro-posed.FEED adds to the conventional sequential decoding pro-cedure a post processing operation which allows to compute the path reliability of the decoded path.With this path reliability the ?rst error in the decoded frame can be localized,thus,enabling combined error correction and detection with a single code.The advantage of the proposed scheme over applying a dedicated error detection code is demonstrated at the example of the GSM Full-rate Speech Codec.Although the Fullrate Speech Codec is by far not the most suited source coding scheme for our new approach, a gain of up to dB in SegSNR or dB in channel SNR can be achieved with a peak complexity equal to the standard GSM sys-tem.However,in average FEED uses a signi?cantly lower number of operations.Moreover,FEED has a scalable complexity and is self-adaptive to varying channel conditions.

1Introduction

In many communication systems channel coding is inevitable to reliably communicate over the error-prone transmission channel. Usually,the design of these channel coding systems is based on the achievable(average)bit or word error probability which inher-ently assumes that the reconstructed source quality is insensitive to the position of the(channel)decoding error in the source data block.However,recent investigations on still image coding[1] and speech coding[2]have shown that the reconstruction quality of ef?cient source coding schemes is severely affected by residual errors in the most signi?cant source data.In these most signi?-cant parts it is of advantage,if one does not reconstruct corrupted data but rather relies only on the correctly decoded information of lower layers in image coding or uses appropriate concealment techniques[2].Thus,it is vital for these source decoders to be supplied only with the error-free part in the most sensitive parts. Hence,the error protection scheme has to detect errors,or even better to localize errors in order to decide if at least parts of the received data can be used in the reconstruction process.

To meet this requirement,recently a channel coding system for SPIHT(set partitioning in hierarchical trees,[3])coded im-ages has been proposed where in a change of paradigm the system was designed such that the length of the error-free decoded sub-block(where a subblock begins with the?rst symbol of the data block)was maximized rather than to exclusively minimize the(av-erage)bit or word error probability[4,5].This was achieved by a novel channel decoder that in contrast to conventional decod-ing algorithms allows to combine error correction and localization based on a single convolutional code,i.e.,no additional redun-dancy(bandwidth)is spent for a dedicated error detection code.

In this work we use the Fullrate Speech Codec of the GSM (Global System for Mobile communications)system[6]as an ex-ample to demonstrate that the bene?ts of the new approach to chan-nel coding are not restricted to image transmission but generally apply to any source coding scheme where different parts of the source data frame have different signi?cance for the reconstruc-tion quality.It also serves to prove that the system which was ini-tially presented in combination with progressively coded sources can also be used with source coders which are not designed explic-itly in a progressive manner,but have an inherent progressive or at least hierarchical property.

In Section2we give a brief system overview and outline which parts of the channel coding system of the GSM Fullrate Codec are changed by our new approach to channel coding which is based on the FEED algorithm.Since the FEED algorithm is an extension of sequential decoding to the computation of path reliabilities,Sec-tion3gives an introduction into these topics.Finally,in Section4 we present simulation results that indicate the improvement poten-tial offered by the FEED principle.

2System Overview

As already outlined in the introduction our main goal is not to provide a new channel coding system for the GSM system but to show the potentials of the FEED algorithm for speech transmission over wireless channels.For this reason we specify a well-de?ned system environment which models mobile speech transmission ap-propriately and,furthermore,allows for a simple setup which can easily be rebuilt for comparison purposes.The relevant compo-nents,source and channel coder,and the corresponding decoders are used according to the GSM system.

Let us brie?y de?ne and justify our transmission system.GSM as well as most other2G systems use a TDMA approach to sep-arate different users within one cell.For GSM Fullrate transmis-sion a total of radio slots are accessible for each speech frame,each consisting of channel symbols to be used

for the channel coded speech frame.As two speech frames share one radio burst we obtain a total of channel symbols per speech frame.For slow to moderate user mobility it can be as-sumed that the channel encounters slowly time-varying frequency-?at Rayleigh fading.In addition,as most2G systems have intro-duced the capacity increasing feature of frequency hopping,the assumption of statistical independent Rayleigh fading within two radio bursts is appropriate.Rayleigh fading is used as it serves as a worst-case assumption without any direct signal path component between base station and mobile.Although GSM uses a partial response GMSK modulation scheme with appropriate equaliza-

tion techniques at the receiver to combat intersymbol interference and multi-path fading,in general,BPSK with Nyquist signaling excluding intersymbol interference and equalization results in an accurate model[7].Therefore,assuming a soft-decision detector and additive white Gaussian noise,we adopt the following time-discrete signal model.

Let us de?ne the speech frame as vector

where the components are binary random vari-ables that represent the output samples of the speech encoder.This speech frame is the input to a rate convolutional encoder that maps a bit to a binary-tuple of code bits,i.e.,the encoder outputs at time in response to the in-put symbol.Clearly,since is a binary random variable also the components are binary random variables. In channel decoding it has proven to be useful to de?ne the log-likelihood ratio of a binary random variable as

(2)

assuming that we have given the conditional probability describing the transmission channel.

We now continue to describe the transmission system and will afterwards de?ne the mapping of channel code symbols to trans-mitted symbols.In our model the user has access to trans-mission radio slots to transmit the speech frame.Slots are de-noted by their index.Let,

and be the received signal,the transmitted signal and the noise encountered in slot, respectively.The average transmission energy is given as

and noise is assumed Gaussian and i.i.d.with variance .The propagation channel is assumed slowly time-varying and frequency-?at for each time slot.In particular,the channel gain over slot is assumed to be constant over the entire slot.The received signal of slot is then given by.

We assume that the receiver has perfect knowledge of the chan-nel gain and of the signal-to-noise ratio(SNR)

for all where denotes the channel power gain.Without loss of generality we assume for the remainder of this work that

and,therefore,the average SNR is

.Estimation of the channel gain and of the SNR is achieved in practice by evaluating the inserted training symbols in each ra-dio slot.

Finally,we de?ne the mapping of the channel symbols to the transmission frames as a bijective mapping of the index pair ,with and,to the index pair, with and.With this mapping,we de?ne the log-likelihood value

3The Far End Error Decoder

A distinctive feature of FEED is that it allows to combine error cor-

rection and localization based on a single convolutional code,i.e.,

no additional redundancy(bandwidth)has to be spent for a ded-

icated error detection code.The FEED algorithm employs high-memory(e.g.,)convolutional codes which due to their large number of states cannot be decoded using a Viterbi decoder;

instead a modi?ed sequential decoder has to be used.In the follow-

ing,we?rst discuss some basic properties of sequential decoding.

Then we extend the sequential decoding procedure such that it can provide path reliabilities for the partially decoded frame which can be used to localize the?rst decoding error.

3.1Principles of Sequential Decoding

The basic idea behind any sequential decoding algorithm is to ex-

tend at any time instant only the most promising path where each

path of the code tree corresponds to a(partial)code word.Hence,

during the decoding process only a subtree of the entire code tree is explored.As a consequence a metric is required that enables us to compare paths of different lengths.The well known Fano metric [10](written in-values[11])

(4) where denotes the metric increment for the transition from state to state of a convolutional encoder,ful?lls this requirement.The most commonly used sequential decoding algo-rithms–the Fano algorithm as well as the Stack algorithm–both base on this metric.For a detailed description of these algorithms we refer to[12].

A characteristic feature of sequential decoders is that the num-ber of operations to decode a given frame is not?xed but depends on the channel state.If the frame can be decoded in the given time constraint then due to the favorable distance properties of high-memory convolutional codes,the decoded frame is guaranteed to be error-free.Sequential decoders work well as long as the code rate stays below the cut-off rate[12].However,the cut-off rate decreases with decreasing channel quality.Therefore,in a mobile system we might encounter a situation where the code rate exceeds the instantaneous channel cut-off rate and the required

number of operations1is likely to result in a violation of a given delay constraint,i.e.,a given maximum number of operations–the computational limit–is exceeded.In this case the sequential de-coder cannot decode the entire frame.Decoding rather ends with a partially explored tree(see Fig.3)with an incompletely decoded most promising path of length.This partially explored code tree de?nes a set of variable length code words

and the set of cor-responding information words that generate these codewords[13].

3.2Path Reliability for Incomplete Decoding Since sequential decoders are used with convolutional codes of large memory,incorrect decoding is very unlikely if the sequen-tial decoder completes decoding without exceeding the computa-tional limit.In fact,the performance of sequential decoders is usually not measured in terms of error probability but rather in terms of erasure probability.However,in the following we discuss where and denotes the set of all informa-tion sequences of with common subpath.The reliability vector of subpaths with increasing length is then de?ned as

The reliability is monotonically increasing with decreasing sub-block length,i.e.,,.There-fore,if the decoder is required to deliver a subblock to the source decoder that is error-free with reliability,the decoder simply de-livers the longest subpath of with.

Fig.4illustrates the principle of the FEED algorithm.If de-coding of the frame exceeds the computational limit,then our de-coder uses the path reliability to determine the error free part of the incompletely decoded path and passes only this part to the source decoder.

The computation of the path reliability can easily be added to any sequential decoding algorithm(e.g.,the Fano or stack algo-rithms)with almost no increase in complexity.This is due to the fact that the metrics required to compute the path reliability are already calculated in the decoding process of any sequential de-coder.Moreover,the sum over exponential functions required in

the computation of the reliability can be ef?ciently implemented in

the logarithmic domain using Jacobian logarithms.Additionally,

the reliability calculation is a post processing operation performed after the estimate has already been determined.For that reason the new decoder is called Far End Error Decoder(FEED).Due

to the properties of sequential decoding,for the FEED algorithm

the number of operations performed per decoded bit can be cho-sen arbitrarily,leading to a scalable computational complexity in contrast to the prede?ned complexity of most other decoding al-gorithms[4],e.g.,the Viterbi algorithm.With this property it is possible to trade performance versus battery life.Moreover,the FEED algorithm is self-adaptive to varying channel conditions:If the transmission is error-free,the decoder spends only a single op-eration per decoded bit,however,if the received block contains many channel errors pertaining to a bad channel quality,the num-ber of operations per decoded bit increases and,hence,the decoder automatically adapts to the channel

state.

Fig.4.Principle of FEED:Decoding as far as possible,reliability determination,shortening.

4Experimental Results

4.1Simulation Environment

As already mentioned in Section2the proposed method only re-places the channel coding/decoding part(including the reordering of the speech frame)of the standard GSM system.Instead of pro-tecting the182class1bits with a rate memory code,the new error correction scheme employs a powerful rate mem-ory convolutional code that is decoded using the FEED algorithm of Section3.The FEED algorithm allows to determine the contiguously error-free part of this data block which has two important consequences:First of all,the bit CRC error detec-tion code of the standard GSM system can be removed,since the FEED decoder inherently provides error localization which obvi-ously goes beyond simple error detection.Second,the convolu-tional encoder does not have to be terminated.This is illustrated in Fig.5where the redundancy pro?le of the convolutional code used in the GSM system and our modi?ed approach is depicted.2 Whereas in GSM the convolutional code is terminated and is of rate over the entire frame(except for the50class1a bits that have a slightly higher rate due to the3bit CRC),in the FEED based system at the end of the data frame we progressively increase the number of punctured bits until we end with rate according to an uncoded system.The puncturing was based on a puncturing period of which allows to change the code rate every th information bit (see,e.g.,[4,5]).Hence,the FEED based approach saves the re-dundancy required by the standard GSM system for error detection and termination of the encoder.Therefore,in Fig.5with our mod-i?ed approach some of the uncoded bits of the standard GSM system have a redundancy greater than.However,since in the FEED based system the encoder is not terminated,the reordering has to be modi?ed such that the most important bits are placed at the beginning of the frame.This modi?ed system as well as the standard GSM system are in the following used to communicate

5

10

15

20

-1012345678

S N R i n d B

Es/N0 in dB

SegSNR FEED SegSNR GSM SNR FEED SNR GSM

Fig.6.SNR and Segmental SNR over average channel SNR

for GSM and FEED based system.

for higher channel SNR.For example,for dB the av-erage work load is smaller than computations per decoded bit which is only of the standard GSM system despite the im-proved quality of the new method.Moreover,this property of our decoder reduces battery drain.

0.0001

0.001

0.01

0.1

-1

1

2

3

4

5

6

7

8

u n d e t e c t e d b a d f r a m e s

Es/N0 in dB

GSM FEED

Fig.7.Probability of undetected bad frames over average channel SNR for GSM and FEED based system.

5Conclusions

We have presented a new approach to channel coding for speech transmission over mobile channels.The fundamental idea behind this system is that for many applications it is more important to localize the ?rst channel decoding error than to (exclusively)min-imize the (average)bit error probability.With the knowledge of the ?rst error position the source decoder can then take the appro-priate action;e.g.,for many sources a signi?cant quality improve-ment results,if the reconstruction is based solely on the error-free part of the decoded data block.The key ingredient in our novel channel coding system is the Far End Error Decoder which allows to localize the ?rst error with an adjustable probability.Most im-portant,the FEED algorithm combines error correction and local-ization using a single extremely powerful code and,thus,avoids the bandwidth expansion typically required in unequal error pro-tection schemes to implement an error detection mechanism,e.g.,by a dedicated error detection code.Therefore,a channel coding system based on FEED can apply an arbitrary number of hierar-chy classes which principally allows to supply each receiver with the quality that is supported by its transmission channel.Since

the computational complexity of sequential decoding depends on the channel state,the Far End Error Decoder adapts automatically to the given channel and provides the receiver with the currently supported quality.Furthermore,FEED has a scalable complexity which enables us to simultaneously devise low-end and high-end receivers.Although the GSM Fullrate Speech Codec is by far not the most suited application for our system it has been chosen as a testbed,since it is widely available as a reference system.The pre-sented simulation results show that the FEED based system outper-forms the standard GSM system in all quality measures of interest.E.g.,a gain of up to dB in channel SNR can be achieved with a computational complexity that is lower than in the GSM system.

References

[1] D.Mukherjee and S.K.Mitra,“A vector set partitioning

noisy channel image coder with unequal error protection,”IEEE JSAC ,vol.18,pp.829–840,June 2000.[2]N.G¨o rtz,“Zero-redundancy error protection for CELP

speech codecs,”in Proc.Europ.Conf.Speech Comm.and Tech.,Rhodes,Greece,Sept.1997,vol.3,pp.1283–1286.[3] A.Said and W.A.Pearlman,“A new,fast and ef?cient image

codec based on set partitioning in hierarchical trees,”IEEE Trans.on Circuits and Systems for Video Technology ,vol.6,pp.243–250,June 1996.[4]J.Hagenauer,T.Stockhammer,C.Wei?,and A.Donner,

“Progressive source coding combined with regressive chan-nel coding on varying channels,”in Proc.3rd ITG Conf.Source and Channel Coding ,Munich,Germany,Jan.2000,pp.123–130.[5]T.Stockhammer and C.Wei?,“Channel and complexity

scalable image transmission,”Accepted for Presentation at ICIP 2001,Aug.2001.

[6]GSM 06.10ETS 300580-2,Full rate speech transcoding ,

ETSI,Sep.1994.

[7] E.Biglieri,J.Proakis,and S.Shamai (Shitz),“Fading chan-nels:Information-theoretic and communication aspects,”

IEEE https://www.360docs.net/doc/ab17371026.html,.Theory ,vol.44,no.6,pp.2619–2692,Oct.1998.[8]P.Vary,K.Hellwig,R.Hofmann,R.J.Sluyter,C.Galand,

and M.Rosso,“Speech codec for the european mobile radio system,”in Proc.ICASSP 1988,New York,NY ,May 1988,pp.227–230.[9]GSM 06.11ETS 300580-3,Substitution and muting of lost

frames for full rate speech channels ,ETSI,Sep.1994.[10]R.M.Fano,“A heuristic discussion of probabilistic decod-ing,”IEEE https://www.360docs.net/doc/ab17371026.html,.Theory ,vol.IT–9,pp.64–74,1963.[11] C.Wei?,S.Riedel,and J.Hagenauer,“Sequential decoding

using a–priori information,”Electronics Letters ,pp.1190–1191,June 1996.[12]S.Lin and D.J.Costello,Jr.,Error Control Coding –Fun-damentals and Applications ,Prentice-Hall,1983.[13]James L.Massey,“Variable-length codes and the Fano met-ric,”IEEE https://www.360docs.net/doc/ab17371026.html,.Theory ,vol.IT–18,no.1,pp.196–198,Jan.1972.[14] C.Wei?,T.Stockhammer,and J.Hagenauer,“The Far End

Error Decoder with application to image transmission,”sub-mitted to Globecom 2001.[15]Anton Donner,“FEED -Angepasster Fehlerschutz f¨u r

hochkomprimierte Quellen,”M.S.thesis,Inst.for Com-mun.Eng.,Munich University of Technology,May 1999.