COMMITTEE T1 TELECOMMUNICATIONS Working Group T1E1.4 (DSL Access) Lisle, IL, May 3, 2000

Transcription

1 COMMTTEE T TELECOMMUCTOS Woring Group TE. (DSL ccess) Lisle, L, May 3, 000 TE./ COTRBUTO TTLE: ew proposal of Turbo codes for DSL modems SOURCE: VOCL Technologies Ltd PROJECT: TE., DSL Enhancements BSTRCT This paper describes a new technique for coding and decoding signals that use turbo codes with QM modulation for error correction. Contact: Juan lberto Torres, jatorres@vocal.com, Frederic Hirzel, fhirzel@vocal.com Victor Demjaneno, victord@vocal.com VOCL Technologies Ltd. 00 John James udubon Parway Buffalo, Y 8 Phone: (76) Fax: (76) OTCE This contribution has been prepared to assist ccredited Standards Committee T Telecommunications. This document is offered to the Committee as a basis for discussion and is not a binding proposal on VOCL Technologies Ltd. or any other company. The requirements are subject to change in form and numerical value after more study. VOCL Technologies specifically reserves the right to add to, amend, or withdraw the statements contained herein.

2 Lisle, L TE./ TRODUCTO. Turbo codes present a new and very powerful error control technique, which allows communication very close to the channel capacity. Since its discovery in 993, a lot of research has been done in the application of turbo codes in deep space communications, mobile satellite/cellular communications, microwave lins, paging, in OFDM and CDM architectures. Turbo codes have outperformed all previously nown coding schemes regardless of the targeted channel. The extra coding gain offered by turbo codes can be used either to minimize bandwidth or to reduce power requirements in the lin budget. Standards based in turbo codes have already been defined or are currently under investigation. Here are some examples: nmarsat s new multimedia service is based on turbo codes and 6QM that allows the user to communicate with existing nmarsat 3 spot beam satellites from a noteboo-sized terminal at 6 bit/s. The Third Generation Partnership Project (3GPP) proposal for MT-000 includes turbo codes in the multiplexing and channel coding specification. The MT-000 represents the third generation mobile radio systems worldwide standard. The 3GPP objective is to harmonize similar standards proposals from Europe, Japan, Korea and the United States. S s next-generation deep-space transponder will support turbo codes and implementation of turbo decoders in the Deep Space etwor is planned by 003. The new standard of the Consultative Committe for Space Data Systems (CCSDS) is based on turbo codes. The new standard outperforms by.5 to.8 db the old CCSDS standard based on concatenated convolutional code and Reed-Solomon code. The new European Digital Video Broadcasting (DVB) standard has also adopted turbo codes for the return channel over satellite applications. n this paper we present a new perspective of the use of turbo codes for systems with different order of QM modulations woring at the same time. This perspective that avoids the most difficult part of turbo coding: the computing requirements. The way to avoid these computing requirements is to treat the QM signal lie two M modulations (one in the direction and one in the Q direction) and use the probabilities of the and Q M values as an input to the turbo code process. Papers presented so far for DSL modems using turbo codes give details of only 6QM, and the computational effort is important. nother innovation of the technique proposed here is the mapping used for the modulated signal, providing the most protected bits for the information bits and the least protected bits for the parity bits. n this paper we present the different possible puncturing for each order of a QM modulated signal and we choose the one that provides better performance. This is the first investigation in the performance of turbo codes for all constellation sizes, up to 0 QM. The recommended solutions achieve a target BER very close to the channel capacity for the respective spectral efficiency response. The turbo code schemes proposed here are more power efficient than the trellis coded modulation schemes used traditionally with V.3.bis or V.3 standards. The larger the constellation is the more improvements that this technique provides (i.e. for 6QM the probabilities to compute in a classical turbo code are 6 points with 6 elements each point, with this technique the probabilities to compute are 8 ( in each dimension) with elements each, so if we use 0 iterations the computational savings is more VOCL Technologies Ltd.

3 Lisle, L TE./ than 0*(6*6/8*) = 80 (almost two orders of magnitude); for 56QM the computational savings is more than 0 * (56*56) / (3*6) = 80) (over three orders of magnitude). n the case of the G.99. this technique allow the system to wor at the information rate bit of 00 bps with E b / 0 below db (assuming QM and spectral efficiency of bit/s/hz symbols/s and 00 tones). We propose the use of square QM constellations with different puncturing values as function of the signal-to-noise ratio. The square constellations allow for use of very efficient blind equalization techniques an effective maintaining and Q independent. Taing into account the values of bi and gi we decide which constellation to use and with which parity.. CPCTY BOUDS The minimum E b / 0 values to achieve the Shannon bound, QM, 8QM, 6QM, 3QM, 6QM, 8QM, 56QM, 5QM and 0QM bounds for spectral efficiencies from /3 up to 7 bits/s/hz respectively are as in Table for a BER=0-5. Spectral efficiency η [bit/s/hz] Shannon bound Table. Shannon and QM bounds. QM bound [db] 6 QM bound [db] 6 QM bound [db] 56 QM bound [db] 0 QM bound [db] [db] / The conversion from E s / 0 to E b / 0 is performed using the following relation E b / 0 [db] = E s / 0 [db] - 0 log 0 (η) [db] () where η is the number of information bits per symbol. The required C/ 0 given a certain E b / 0 can be found using the following relation: C/ 0 [db-hz] = E b / 0 [db] + 0 log 0 (R b ) [db-hz] () where R b is the information bit rate. For a D-dimension modulation the following formulae are used: E [ ] E [ ] av SR = a = a = E E [ w ] D D (3) s η b () SR= E = E 0 0 D D VOCL Technologies Ltd.

4 Lisle, L TE./ where is the noise variance in each of the D dimension and η is the number of information bits per symbol. From the above relations: - η = E (5) av 0 3. CODG The proposed coding scheme is shown in Figure.The two systematic recursive codes (SRC) used are identical and are defined in Figure. The code is described by the generating polynomials 35o and 3o. d i + d i nterleaver / SRC p i nput + D D D D / SRC q i Output Figure Figure. MODULTO FOR BT/S/HZ SPECTRL EFFCECY. The scheme proposed in this case combines a rate / coding scheme with QM.. Puncturing n order to obtain a code rate of /, every other bit of the parity bits p and q from Figure are punctured. The puncturing pattern is given in Table. Table. Puncturing and Mapping for Rate / QM. nformation bit (d) d d Parity bit (p) p - Parity bit (q) - q M symbol () (u ) = (d ) (u ) = (d ) M symbol (Q) (u ) = (p ) (u ) = (q ) QM symbol (, Q) (,Q) = (u, u ) = (d, p ) (,Q) = (u, u ) = (d, q )..Modulation QM scheme is shown in Figure 3. n equivalent M modulation is shown in Figure. 0 Q - [d ] = [ 0 ] Figure 3 Figure t time, the symbol u = (u, u ) is sent through the channel and the point r in two dimensional space is received. For a QM constellation with points at - and, The E av is: ( + ) Eav= = (6) [ ] VOCL Technologies Ltd.

5 Lisle, L TE./ For a rate / code and QM, the noise variance is: η x x = Eav = = (7).3 Bit probabilities. For an WG channel the following ressions need to be evaluated: ( ) [- - a, i ] [- ( - ) ] )= i= LLR(u log = log [- ( - a ) ] [- ( - ) ] (8) 0, i 0 i= [- ( Q - a ), i ] [- ( )] Q - B i= LLR(u )= log = log [- ( Q - )] [- ( Q - B )] (9) a 0, i 0 i= The above LLRs are used as inputs to the turbo encoder. There is no need to compute the LLRs for all symbols because and Q signals are treated independently. lso the simulations for the bit-llr values are reduced to one term each. Due to the puncturing, with one in two parity bits being transmitted, the ected performance will be lower when compared with the nonpunctured scheme.. Simulations Results. Figure 5 shows the performance of a turbo code using a 0 bit S-type interleaver. The target BER of 0-7 for a,0 information bit interleaver can be achieve at E b / 0 =. db BER for Rate / QM =,0 bits WG Channel E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it QM bound Shannon bound.00e-06.00e-07.00e /o [db] Figure 5 VOCL Technologies Ltd.

6 Lisle, L TE./ CODG D MODULTO FOR BT/S/HZ SPECTRL EFFCECY. The investigated combines / coding scheme with 6QM. 5. Puncturing. n order to obtain a rate / code, every other bit of the parity bits p and q from Figure are punctured. The puncturing patter is given in Table 3. Table 3. Puncturing and Mapping for Rate / 6QM. nformation bit (d) d d parity bit (p) p - parity bit (q) - q M symbol () (u, u ) = (d, p ) M symbol (Q) (u 3, u ) = (d, p ) 6 QM symbol (, Q) (, Q) = (u, u, u 3, u ) = (d, p, d, p ) 5. Modulation t time, the symbol u = (u, u, u 3, u ) is sent through the channel and the point r in two dimensional space is received. For a 6QM constellation with points at -3, -, and 3, The E av is: ( + )+8( +9 )+(9 +9 ) E = = 0 (0) av 6 For a rate / code and 6QM, the noise variance in each dimension is: η x x =.5 = E = 0 () av t is assumed that the time, u and u modulate the component and u 3 and u modulate the Q component for a 6QM scheme. The symbol u symbol has the following mapping: u = (u, u, u 3, u ) = (d i, p i, d i+,q i+ ). The parity bits are mapped to the least protected bits of the QM symbol. ote that denotes the symbol time index and i the information bit time index. This means a puncturing of one in two parity bits. Considering two independent Gaussian noise sources with identical variance, the LLR can be determined independently for each and Q. t the receiver, the and Q signals are treated independently in order to tae advantage of the simpler formulae for the bit-llr values. The mapping of the information bit is made to the most protected bit in each dimension (u for the signal and u 3 for the Q signal). n order to estimate the performance of this scheme, rate / turbo code and M modulation is used, instead of 6QM modulation. 5.3 Bit probabilities. For an WG channel the following ressions need to be evaluated: ( ) [- - a, i ] [- ( - ) ]+ [- ( - ) ] 3 i= )= = LLR(u log log [- ( - a ) ] [- ( - ) ]+ [- ( - ) ] () 0, i 0 i= - - VOCL Technologies Ltd.

7 Lisle, L TE./ ( ) [- -a, i ] [- ( - ) ]+ [- ( - ) ] 3 i= LLR(u )= log = log [- ( -a ) ] [- ( - ) ]+ [- ( - ) ] (3) 0, i 0 i= [- ( Q -a ), i ] [- ( Q - B) ]+ [- ( )] Q - B3 i= LLR(u 3 )= log = log [- ( Q -a )] [- ( Q - B )]+ [- ( Q - B )] () 0, i 0 i= [- ( Q - a ), i ] [- ( Q - B) ]+ [- ( )] Q - B3 i= LLR(u )= log = log [- ( Q - )] [- ( Q - B )]+ [- ( Q - B )] (5) a 0, i 0 i= The above LLRs are used as inputs to the turbo encoder. There is no need to compute the 6LLRs for all symbols because and Q signals are treated independently. lso the simulations for the bit-llr values are reduced to terms each. Due to the puncturing, with one in two parity bits being transmitted, the ected performance will be lower when compared with the non punctured scheme. 5. Simulations Results. The rate / 6QM scheme described in this chapter achieves the target BER at less than.5 db from capacity. The implementation in hardware is feasible and it can be used at very high data rates. The target BER of 0-7 can be achieved at E b / 0 =.5 db for =0 information bits, as shown in Figure 6. BER for Rate / 6QM, =0 bits S-type, WG Channel.E+00.E-0 (BER).E-0.E-03.E-0.E-05.E-06 it it it QM bound Shannon bound.e-07.e /o [db] Figure 6 VOCL Technologies Ltd.

8 Lisle, L TE./ CODG D MODULTO FOR 3 BT/S/HZ SPECTRL EFFCECY. Three options are investigated in this section. The first scheme combines a rate 3/ coding scheme with 6QM. The second scheme combines a rate 3/ coding scheme with 6QM. 6. Option Rate 3/ Turbo code and 6QM 6.. Puncturing. n order to obtain a rate 3/ code, the puncturing pattern given in Table is used. Table. Puncturing and Mapping for Rate 3/ 6QM nformation bit (d) d d d 3 d d 5 d 6 parity bit (p) - p parity bit (q) q 5 - M symbol () (d, d ) (d, d 5 ) M symbol (Q) (d 3, p ) (d 6, p 5 ) 6 QM symbol (,Q) (,Q) = (d, d, d 3, p ) (, Q) = (d, d 5, d 6, q 5 ) 6.. Modulation t is assumed that at time, u and u modulate the component and u 3 and u modulate the Q component of a 6QM scheme. n order to estimate the performance of this scheme, rate 3/ turbo codes and M modulation are used. For a rate 3/ code and 6QM, noise variance is: η x3x 0 = = Eav = 0 (6) The puncturing and mapping scheme is shown in Table for 6 consecutive information bits that are encoded into 8 coded bits, therefore two 6QM symbols Bit Probabilities For each received symbol, the bit probabilities are computed as described in equations ()-(5). 6.. Simulation Results Figure 7 shows the simulation results for 6, information bits with S-type interleaver. BER of 0-7 can be achieved after 8 iterations at E b / 0 = 5.75 db for = 6 information bits. 6. Option Rate 3/6 Turbo code and 6QM 6.. Puncturing. n order to obtain a rate 3/6 code, the puncturing patter used is given in Table 5. Table 5. Puncturing and Mapping for Rate 3/6 6QM nformation bit (d) d d d 3 d d 5 d 6 parity bit (p) p - p 3 - p 5 - parity bit (q) - Q - q - q 6 8M symbol () (d, d, p ) (d, d 5, q ) 8M symbol (Q) (d 3, p 3, q ) (d 6, p 5, q 6 ) 6 QM symbol (, Q) (,Q)=(d,d, p,d 3, p 3,q ) (,Q)= (d,d 5, q,d 6, p 5,q 6 ) VOCL Technologies Ltd.

9 Lisle, L TE./ BER for Rate 3/ 6QM, =6, bits S-type, WG Channel.E+00.E-0 (BER).E-0.E-03.E-0.E-05.E-06 it it it QM bound Shannon bound.e-07.e /o [db] 6.. Modulation Figure 7 t time, the symbol u = (u, u, u 3, u, u 5, u 6 ), is sent through the channel and the point r in two dimensional space is received. t is assumed that at time u, u and u 3 modulate the component and u, u 5 and u 6 modulate the Q component of a 6QM scheme. For 6QM constellations with points at -7, -5, -3, -,, 3, 5, 7 The E av is: E av = (8(9+5+9+)+8( )+8(5+9+5+)+8(9+)) / 6= (7) For a rate 3/6 code and 6QM, the noise variance in each dimension is: η x3x = = Eav = (8) 0 n order to estimate the performance of this scheme, when rate 3/6 turbo codes and 8M modulation is used. The puncturing and mapping scheme is shown in Table 5 for 6 consecutive information bits that are encoded into coded bits, therefore two 6QM symbols Bit Probabilities For an WG channel, the following ressions need to be evaluated for the dimension: = LLR(u ) = log i= i= [- [- - a ] = - a ] (,i) ( 0,i) [- ( - ) ]+ [- ( - 5) ]+ [- ( - 6) ]+ [- ( - 7) ] n log [- ( - 0) ]+ [- ( - ) ]+ [- ( - ) + [ ( - 3) ] (9) VOCL Technologies Ltd.

10 Lisle, L TE./ = = log log LLR(u ) = i= i= [- [- - a ] = - a ] (,i) ( 0,i) [- ( - ) ]+ [- ( - 3) ]+ [- ( - 6) ]+ [- ( - 7) ] n [- ( - 0) ]+ [- ( - ) ]+ [- ( - ) + [ ( - 5) ] LLR(u ) = log 3 i= i= [- [- - a ] = - a ] (,i) ( 0,i) [- ( - ) ]+ [- ( - 5) ]+ [- ( - 3) ]+ [- ( - 7) ] n [- ( - 0) ]+ [- ( - ) ]+ [- ( - ) + [ ( - 6) ] log (0) () n identical computation effort is required for the Q dimension, the being replaced with the Q demodulated value in order to evaluate LLR(u ), LLR(u 5 ) and LLR(u 6 ). 6.. Simulation Results Figure 8 shows the simulation results for 6, information bits with S-type interleaver. BER of 0-7 can be achieved after 8 iterations at E b / 0 = 6. db for = 6, information bits. This result is 0.5 db worse than the performance of the rate 3/ 6QM scheme. BER for Rate 3/6 6QM, =6, bits S-type, WG Channel.E+00.E-0 (BER).E-0.E-03.E-0.E-05 it it it QM bound Shanon bound.e-06.e-07.e /o [db] Figure 8 VOCL Technologies Ltd.

11 Lisle, L TE./ CODG D MODULTO FOR BT/S/HZ SPECTRL EFFCECY. This section investigated four schemes for transmission of information bits in a 6 QM symbol. The mapping used for 6QM constellation has a very significant impact on the performance of these schemes. The first scheme uses independent and Q mapping and also uses Gray mapping in each dimension. The second scheme uses independent and Q mapping, but natural mapping in each dimension. The third scheme used a conventional trellis coded modulation approach based on Ungerboec set partitioning of the 6QM set. This partitioning technique splits the constellation in sub-constellations with increased Euclidian distance. n these schemes all the information bits are coded. The fourth scheme used the same conventional trellis coded modulation approach based on Ungerboec set partitioning of the 6QM set. However, only two information bits are encoded by a rate / code. The four coded bits select a subpartition of four points. The other two information bits, which are sent uncoded, identify the transmitted point. 7. Option Rate /6 6QM with independent and Q and with Gray Mapping. 7.. Puncturing n order to obtain a rate /6 code, the puncturing patter used is shown in Table 6. Table 6. Puncturing and Mapping for Rate /6 6QM Option nformation bit (d) d d d 3 d parity bit (p) p parity bit (q) - - q 3-8M symbol () (d, d, p ) 8M symbol (Q) (d 3, d, q 3 ) 6 QM symbol (, Q) (,Q)=(d,d, p,d 3, d,q 3 ) 7.. Modulation Gray mapping was used in each dimension. Four information bits are required to be sent using a 6QM constellation. For a rate /6 code and 6QM, the noise variance in each dimension is - η x x = Eav = = 5.5 () The puncturing and mapping scheme is shown in Table 6 for consecutive information bits that are encoded into 6 coded bits, therefore one 6QM symbol.the turbo encoder with the puncturing presented in Table 6 is a rate /6 turbo code which in conjunction with 6QM gives a spectral efficiency of bits/s/hz. Considering two independent Gaussian noises with identical variance, the LLR can be determined independently for each and Q. t is assumed that at time u, u and u 3 modulate the component and u, u 5 and u 6 modulate the Q component of the 6QM scheme. t the receiver, the and Q signals are treated independently in order to tae advantage of the simpler formulae for the LLR values Bit Probabilities From each received symbol, the bit probabilities are computed as follows: - - VOCL Technologies Ltd.

12 Lisle, L TE./ [- = log [- [- = log [- [- = log [- ( - ) ( - ) ] = ] ( - ) ] + [- ( - ) ] + [- ( - ) ] + [- ( - ) ( - ) ] + [- ( - ) ] + [- ( - ) + [ ( - ) ] 0 LLR( u )= log i= i= [- [- 5 a a, i 0, i ( - ) ( - ) 6 ] = ] n ( - ) ] + [- ( - ) ] + [- ( - ) ] + [- ( - ) ( - ) ] + [- ( - ) ] + [- ( - ) + [ ( - ) ] 0 LLR( u )= log i= i= [- [- 3 a a, i 0, i ( - ) ( - ) 6 ] = ] ( - ) ] + [- ( - ) ] + [- ( - ) ] + [- ( - ) ( - ) ] + [- ( - ) ] + [- ( - ) + [ ( - ) ] 0 LLR( u3 )= log i= i= [- [- 5 a a, i 0, i 3 n n ] ] ] (3) () (5) For dimension. n identical computation effort is required for the Q dimension, the being replaced with the Q demodulated value in order to evaluate LLR(u ), LLR(u 5 ) and LLR(u 6 ). 7.. Simulation Results Figure 9 shows the simulation results for,096 information bits with S-type interleaver. BER of 0 7 can be achieved after 8 iterations at E b / 0 = 8.3 db. 7. Option Rate /6 6QM with independent and Q and atural Mapping. 7.. Puncturing n order to obtain a rate /6 code, the puncturing patter used is shown in Table 7. Table 7. Puncturing and Mapping for Rate /6 6QM Option nformation bit (d) d d d 3 d parity bit (p) p parity bit (q) - - q 3-8M symbol () (d, d, p ) 8M symbol (Q) (d 3, d, q 3 ) 6 QM symbol (, Q) (,Q)=(d,d, p,d 3, d,q 3 ) VOCL Technologies Ltd.

13 Lisle, L TE./ BER for Rate /6 6QM =,096 bits WG Channel, Gray Mapping.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it QM bound Shannon bound.00e-06.00e-07.00e /o [db] 7.. Modulation Figure 9. atural mapping is used in each dimension. Four information bits are required to be sent using a 6QM constellation. This is equivalent to a rate /3 coding scheme. For a rate /6 code and 6QM, the noise variance in each dimension is = E av η 0 - b = xx E 0 - b = 5.5 E 0 - (6) The puncturing and mapping scheme is shown in Table 7 for consecutive information bits that are encoded into 6 coded bits, therefore one 6QM symbol. The turbo encoder with the puncturing presented in Table 7 is a rate /6 turbo code which in conjunction with 6QM gives a spectral efficiency of bits/s/hz. Considering two independent Gaussian noises with identical variance, the LLR can be determined independently for each and Q. t is assumed that at time u, u and u 3 modulate the component and u, u 5 and u 6 modulate the Q component of the 6QM scheme. t the receiver, the and Q signals are treated independently in order to tae advantage of the simpler formulae for the LLR values Bit Probabilities From each received symbol, the bit probabilities are computed as described in equations (3) () and (5) for dimension. n identical computation effort is required for the Q dimension, the being replaced with the Q demodulated value in order to evaluate LLR(u ), LLR(u 5 ) and LLR(u 6 ). VOCL Technologies Ltd.

14 Lisle, L TE./ Simulation Results Figure 0 shows the simulation results for,096 information bits with S-type interleaver. BER of 0 7 can be achieved after 8 iterations at E b / 0 = 0.5 db..00e+00 BER for Rate /6 6QM =,096 bits WG Channel, atural Mapping.00E-0.00E-0.00E-03.00E-0.00E-05 it it it QM bound Shannon bound.00e-06.00e-07.00e /o [db] Figure 0 8. CODG D MODULTO FOR 5 BT/S/HZ SPECTRL EFFCECY. This section investigated a rate 5/8 coding scheme with 56QM. 8. Puncturing n order to obtain a rate 5/8 code, the puncturing patter used is shown in Table 8. Table 8. Puncturing and Mapping for Rate 5/8 56QM nformation bit (d) d d d 3 d d 5 d 6 d 7 d 8 d 9 d 0 parity bit (p) p p p parity bit (q) - - q 3 - q q 0 6M symbol () (d, d, d 3, p ) (d 6, d 7, d 8, q 6 ) 6M symbol (Q) (d, d 5, q 3,p 5 ) (d 9, d 0, p 8,q 0 ) 56 QM symbol (, Q) (d,d,d 3,p,d,d 5,q 3, p 5 ) (d 6,d 7,d 8,q 6,d 9,d 0,p 8, q 0 ) 8. Modulation For a 56QM constellation with points at 5, -3, -, -9, -7, -5, -3, -,, 3, 5, 7, 9,, 3, 5. E av is: VOCL Technologies Ltd.

15 Lisle, L TE./ E av = 70 (7) t is assumed that at time the symbol u = (u, u, u 3, u, u 5, u 6, u 7, u 8 ) is sent though the channel. t is assumed that at time the symbol u, u, u 3 and u modulate the component and u 5, u 6, u 7 and u 8 modulate the Q component of a 56QM scheme. For a rate 5/8 code and 56QM, the noise variance is: - η x 5 x = = Eav = (8) 0 n order to study the performance of this scheme, a rate 5/8 turbo code and a 6M is used. The 56QM scheme will achieve a similar performance in terms of bit error rate (BER) at twice the spectral efficiency, assuming an ideal demodulator. The puncturing and mapping scheme shown in Table 8 is for 0 consecutive information bits that are coded into 6 encoded bits, therefore, one 56QM symbol. The turbo encoder is a rate 5/8 turbo code, which in conjunction with 56QM, gives a spectral efficiency of 5 bits/s/hz. 8.3 Bit Probabilities The 6M symbol is defined as u = (u, u, u 3, u ), where u is the most significant bit and u is the least significant bit. The following set can be defined.. bit--is-0 = { 0,,, 3,, 5, 6, 7 }. bit--is- = { 8, 9, 0,,, 3,, 5 } 3. bit--is-0 = { 0,,, 3, 8, 9, 0, }. bit--is- = {, 5, 6, 7,, 3,, 5 } 5. bit-3-is-0 = { 0,,, 5, 8, 9,, 3 } 6. bit-3-is- = {, 3, 6, 7, 0,,, 5 } 7. bit--is-0 = { 0,,, 6, 8, 0,, } 8. bit--is- = {, 3, 5, 7, 9,, 3, 5 } From each received symbol, R, the bit probabilities are computed as follows: - - R i LLR( )= i b i t--i s- u log (9) - R - j b i t--i s-0 j - - R i LLR( )= i b i t--i s- u log (30) - R - j b i t--i s-0 j - - R i b i t-3-i s- i LLR( u3 )= log (3) - R - j b i t-3-i s-0 j - - R i i LLR( u )= b i t--i s- log (3) - R - j b i t--i s-0 j - - VOCL Technologies Ltd.

16 Lisle, L TE./ Simulation Results Figure shows the simulation results for 5,0 information bits (,0QM symbols) with S- type interleaver. BER of 0 7 can be achieved after 8 iterations at E b / 0 =.8 db. BER for Rate 5/8 56QM =5,0 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05.00E-06 it it it QM bound Shannon bound.00e-07.00e /o [db] Figure 9. CODG D MODULTO FOR 6 BT/HZ SPECTRL EFFCECY This section investigates a rate 6/8 coding scheme with 56QM. 9. Puncturing n order to obtain a rate 6/8 code, the puncturing patter used is shown in Table 9. Table 9. Puncturing and Mapping for Rate 6/8 56QM Option nformation bit (d) d d d 3 d d 5 d 6 parity bit (p) p parity bit (q) q - - 6M symbol () (d, d, d 3, p ) 6M symbol (Q) (d, d 5, d 6, q ) 56QM symbol (, Q) (,Q ) = (d,d, d 3, p, d,d 5, d 6, q ) 9. Modulation t is assumed that at time the symbol u = (u, u, u 3, u, u 5, u 6, u 7, u 8 ) is sent though the channel. t is assumed that at time the symbol u, u, u 3 and u modulate the component and u 5, u 6, u 7 and u 8 modulate the Q component of a 56QM scheme. VOCL Technologies Ltd.

17 Lisle, L TE./ For a rate 6/8 code and 56QM, the noise variance is: - η x 6 x = = Eav = (33) The puncturing and mapping scheme shown in Table is for 6 consecutive information bits that are coded into 8 coded bits, therefore, one 56QM symbol. The turbo encoder is a rate 6/8 turbo code, which in conjunction with 56QM, gives a spectral efficiency of 6 bits/s/hz. 9.3 Bit Probabilities The 6M symbol is defined as u = (u, u, u 3, u ), where u is the most significant bit and u is the least significant bit. The following set can be defined.. bit--is-0 = { 0,,, 3,, 5, 6, 7 }. bit--is- = { 8, 9, 0,,, 3,, 5 } 3. bit--is-0 = { 0,,, 3, 8, 9, 0, }. bit--is- = {, 5, 6, 7,, 3,, 5 } 5. bit-3-is-0 = { 0,,, 5, 8, 9,, 3 } 6. bit-3-is- = {, 3, 6, 7, 0,,, 5 } 7. bit--is-0 = { 0,,, 6, 8, 0,, } 8. bit--is- = {, 3, 5, 7, 9,, 3, 5 } From each received symbol, R, the bit probabilities are computed as equations (9) to (3). 9. Simulation Results Figure shows the simulation results for 6, information bits (,0QM symbols) with S- type interleaver. BER of 0 7 can be achieved after 8 iterations at E b / 0 =. db. BER for Rate 6/8 56QM =6, bits WG Channel E+00.00E-0.00E-0.00E-03.00E-0.00E-05.00E-06 it it it QM bound Shannon bound.00e-07.00e /o [db] Figure VOCL Technologies Ltd.

18 Lisle, L TE./ CODG D MODULTO FOR 7 BT/HZ SPECTRL EFFCECY This section investigated one scheme that use independent and Q modulation. The scheme combines a rate 7/0 coding scheme with 0QM. 0. Puncturing n order to obtain a rate 7/0 code, the puncturing patter used is shown in Table. Table. Puncturing and Mapping for Rate 7/0 0QM nformation bit (d) d d d 3 d d 5 d 6 d 7 d 8 d 9 d 0 d parity bit (p) p p p d d 3 d parity bit (q) - - q q q 3-3M symbol () (d, d, d 3, p, q 3 ) (d 8, d 9, d 0, d, q 8 ) 3M symbol (Q) (d, d 5, d 6, d 7, p 6 ) (d, d 3, d, p, q 3 ) 0QM symbol (d,d, d 3, p, q 3,d,d 5, d 6,d 7,p 6 ) (d 8,d 9,d 0,d,q 8,d,d 3,d,p,q 3 ) 0. Modulation t is assumed that at time the symbol u = (u, u, u 3, u, u 5, u 6, u 7, u 8 u 9, u 0 ) is sent though the channel. t is assumed that at time the symbol u, u, u 3, u and u 5 modulate the component and u 6, u 7, u 8, u 9 and u 0 modulate the Q component of a 0QM scheme. For a 0QM constellation with points at -3, -9, -7, -5, -3, -, -9, -7, - 5, -3, -, -9, -7, -5, -3, -,, 3, 5, 7, 9,, 3, 5, 7, 9,, 3, 5, 7, 9, 3. E av is: E av = 68 (3) For a rate 7/0 code and 5QM, the noise variance is: - η x 7 x = = Eav = (35) The puncturing and mapping scheme shown in Table is for consecutive information bits that are coded into 0 coded bits, therefore, two 0QM symbols. The turbo encoder is a rate 7/0 turbo code, which in conjunction with 0QM, gives a spectral efficiency of 7 bits/s/hz. 0.3 Bit Probabilities The 3M symbol is defined as u = (u, u, u 3, u, u 5 ), where u is the most significant bit and u 5 is the least significant bit. The following set can be defined.. bit--is-0 = { 0,,, 3,, 5, 6, 7, 8, 9, 0,,, 3,, 5 }. bit--is- = { 6, 7, 8, 9, 0,,, 3,, 5, 6, 7, 8, 9, 30, 3 } 3. bit--is-0 = { 0,,, 3,, 5, 6, 7, 6, 7, 8, 9, 0,,, 3 }. bit--is- = { 8, 9, 0,,, 3,, 5,, 5, 6, 7, 8, 9, 30, 3 } 5. bit-3-is-0 = { 0,,, 3, 8, 9, 0,, 6, 7, 8, 9,, 5, 6, 7 } 6. bit-3-is- = {, 5, 6, 7,, 3,, 5, 0,,, 3, 8, 9, 30, 3 } 7. bit--is-0 = { 0,,, 5, 8, 9,, 3, 6, 7, 0,,, 5, 8, 9 } 8. bit--is- = {, 3, 6, 7, 0,,, 5, 8, 9,, 3, 6, 7, 30, 3 } 9. bit-5-is-0 = { 0,,, 6, 8, 0,,, 6, 8, 0,,, 6, 8, 30 } 0. bit-5-is- = {, 3, 5, 7, 9,, 3, 5, 7, 9,, 3, 5, 7, 9, 3 } - - VOCL Technologies Ltd.

19 Lisle, L TE./ From each received symbol, R, the bit probabilities are computed as follows: - - R i LLR( )= i b i t--i s- u log (36) - R - j b i t--i s-0 j - - R i LLR( )= i b i t--i s- u log (37) - R - j b i t--i s-0 j - - R i b i t-3-i s- i LLR( u3 )= log (38) - R - j b i t-3-i s-0 j - - R i i LLR( u )= b i t--i s- log (39) - R - j b i t--i s-0 j - - R i i b i t-5-i s- LLR( u )= log (0) 5 - R - j b i t- -i s-0 j 5 0. Simulation Results Figure 3 shows the simulation results for,08 information bits (,0QM symbols) with S- type interleaver. BER of 0 7 can be achieved after 8 iterations at E b / 0 = 7 db. BER for Rate 7/0 0QM =,0 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05.00E-06 it it it QM bound Shannon bound.00e-07.00e /o [db] VOCL Technologies Ltd. Figure 3

20 Lisle, L TE./ POWER VS. BDWDTH WG CHEL This section gives an estimate of the trade off which can be achieved between minimum required E b / 0 and bandwidth efficiency. n information data rate of,08 Mbit/s and a maximum transmitter delay of ms is considered. The corresponding interleaver size is,08 bits.. Channel model ll the simulations assumed the additive white Gaussian noise (WG) channel model, with independent and Q signals.. Simulation Results Simulations were run for bandwidth efficiencies from to 7 bit/symbol using the recommended coding and modulation schemes. The results are shown in Figures to 0. BER for Rate / QM =,00 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure VOCL Technologies Ltd.

21 Lisle, L TE./ BER for Rate / 6QM =,00 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure 5 BER for Rate 3/ 6QM =,00 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure 6 VOCL Technologies Ltd.

22 Lisle, L TE./ E+00 BER for Rate /6 6QM =,00 bits WG Channel.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure 7 BER for Rate 5/8 56QM =,00 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure 8 VOCL Technologies Ltd.

23 Lisle, L TE./ BER for Rate 6/8 56QM =,00 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure 9 BER for Rate 7/0 0QM =,00 bits WG Channel.00E+00.00E-0.00E-0.00E-03.00E-0.00E-05 it it it.00e-06.00e-07.00e /o [db] Figure 0 VOCL Technologies Ltd.

24 Lisle, L TE./ Conclusions Table summarizes the minimum E b / 0 required to achieve a BER of 0 7. Table Minimum E b / 0 required to achieve a BER of 0 7 Spectral efficiency η [bits/s/hz] Coding Rate nd Modulation Symbol Rate [sym/s] E b / 0 For BER = 0-7 [db] / and QM 08. / and 6QM / and 6QM /6 and 6QM /8 and 56QM /8 and 56QM /0 and 0QM The results show the potential reduction in bandwidth for a given signal-to-noise ration for a particular channel. f an E b / 0 of 7 db or more is available, the symbol rate can be reduced from 0 sym/s to 9 sym/s, a reduction of more than 70%.. COCLUSOS Table summarizes all simulation results from this study. Table. Summary of Some Simulation Results. Spectral nterleaver size Required QM efficiency Coding Modulation E b / 0 bound η[bits/s/hz] Rate [nformation [db] [db] bits] / QM,0..0 / 6QM / 6QM / 6QM,0.5. / 6QM,08.. / 6QM 3, / 6QM, / 6QM, /6 6QM, /6 6QM, /6 6QM-, /6 6QM-, /6 6QM 5, /8 56QM, /8 56QM 5, /8 56QM, /8 56QM 6, /0 0QM, PROPOSL We propose that the TE. committee supports to include in the G.99..bis and G.99..bis this proposal for Forward Error Correction DSL without Reed Solomon codes. These results are so close to the QM bounds that the Reed-Solomon is not needed. nstead of using Reed-Solomon as outer encoder we propose to use a longer interleaver in the turbo coder, up to 3768 information bits, that allow better results with the same global delay. VOCL Technologies Ltd.