CA2353426A1 - A method and system for turbo encoding in adsl - Google Patents

Abstract

In a coding system for ADSL communications, a method of encoding a sequence of information bits is provided comprising the steps of dividing the information bits into encoding bits and parallel bits; encoding the encoding bits to produce encoded bits;
mapping the encoded bits and the parallel bits into first and second PAM
signals; and generating a QAM signal from these first and second PAM signals.

Description

;'i A METHOD AND SYSTEM FOR TURBO El'JCODING IN ADSL
The invention relates to the field of asynchronous digital subscriber line ("ADSL"}
communication systems. More specifically, the invention :relates to a system and method for encoding signals applied to ADSL.
BACKGROUND OF THE INVENTION
Channel coding methods are used in order to design reliable digital communication systems. Although channel coding improves error performance through the mapping of input sequences into code sequences, this adds redundancy and memory to the transmission. Shannon's Theorem holds that small error rates are achievable provided that the rate of transmission is less than the capacity of the channel.
In the early 1990s, a very powerful channel coding scheme was developed which used concepts related to block and trellis codes. The encoding scheme used simple convolutional codes separated by interleaving stages to produce generally low rate block codes. Decoding was performed by decoding the convoluti.onal encoders separately using a "soft" output Viterbi algorithm and sharing bit reliability information in an iterative manner. This new coding scheme was called "Turbo Coding" and it was found to be capable of near Shannon capacity performance as described in C. Berrou, and A.
Glavieux, "Near Optimum Error Correcting Coding And L>ecoding: Turbo-Codes", IEEE
Trans. Commun., vol. COM-44, No. 10, October 1996, pp.1261-1271.
In general, a turbo encoder is a combination of two simple; encoders where the input is a block of lVL information bits. The two encoders generate; parity symbols using simple recursive convolutional encoders each with a small numlber of states. The information bits are also transmitted uncoded. A key innovation of turbo encoders was the use of an interleaver which permutes the original M information bits before input to the second encoder. The permutation is generally such that input ;>equences for which the first encoder produces low-weight code-words will typically cause the second encoder to produce high-weigh code-words. Thus, even though the constituent codes may be individually weak, the combination code is powerful. 'This resulting code has features that are similar to a random block code with M information lbits. Random block codes are known to achieve Shannon-limit performance as M increases but with a corresponding increase in decoder complexity.
Turbo codes may achieve the performance of random codes (for large M) using an interative decoding algorithm based on simple decoders that are individually matched to the constituent codes. In a typical turbo decoder, each constituent decoder generally sends a posteriori likelihood estimates of the decoded bits to th.e second decoder and uses the corresponding estimates from the second decoder as a priori likelihood estimates. The decoders generally use the maximum a posteriori ("MAF"') bitwise decoding algorithm which requires the same number of states as the well-knovm Viterbi algorithm.
The turbo decoder iterates between the outputs of the two constituent decoders until reaching satisfactory convergence. The final output is a "hard" quantized version of the likelihood estimates of either of the decoders.
As turbo codes have a near Shannon limit, error correcting performance, they are of potential use in a wide range of telecommunications applications. As mentioned, turbo codes were originally proposed for binary modulation using two binary convolutional component codes separated by an interleaver. For moderate QAM (quadrature amplitude modulation) constellation modulation, bit-level turbo coded QAM and symbol-level turbo TCM (trellis coded modulation) have been proposed as described in P.
Robertson, and T.
Worz, "Bandwidth-Efficient Turbo Trellis-Coded Nl'odulation Using Punctured Component Codes", IEEE J-SAC, vo1.16, No.2, Feb., 1998, pp.206-218; S. L.
Goff, A.
Glavieux, and C. Berrou, "Turbo-Codes and High Spectral Efficiency Modulation", IEEE
ICC94; pp. 645-649, 1994; and, "New Proposal of Turbo Codes for ADSL Modems", ITU
Standard Contribution, Study Group 15/4, BA-02081, Antwerp, Belgium, June. 19-23, 2000.
Typically, bit-level turbo coded QAM combines the binary turbo codes with large constellation modulation using Gray mapping whereas symbol-level turbo TCM
uses TCM codes as component codes that are separated by a symbol-level interleaver.

--_.#~.. --~- -_ A problem arises in the deployment of turbo codes in ADSL (asynchronous digital subscriber line) communication systems where these codes are combined with very large modulation constellations. These constellations may be as large as 215=32768 QAM
symbols. For conventional bit-level turbo coded QAM using Gray mapping, the de-mapper, which calculates the soft information bits from the received constellation signal, requires an excessive number of computations. In addition, the turbo decoder's complexity (i.e. length) is proportional to the number of bits transmitted in one constellation symbol. Therefore, the overall receiver becomes very complicated. For symbol-level turbo TCM using two-dimensional or four-dimensional set partitioning mapping, the turbo decoder's length is independent of the; number of bits transmitted in one constellation symbol, but its de-mapper still requires and excessive number of computations. Furthermore, the decoder uses a much more complicated symbol MAP
decoder. Consequently, the very large constellation size used in ADSL systems makes both conventional bit-level turbo coded QAM and symbol-level turbo TCM very 1 S complicated to decode at the receiver end. In other words, conventional bit-level turbo coded QAM and symbol-level turbo TCM both have very high decoding complexity for large ADSL related constellations. These techniques are described in S.
Benedetto, D.
Divsalar, G. Montorsi, and F. Pollara, "Paralell Concatenated Trellis Coded Modulation", IEEE ICC96, 1996, pp.974-978; L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimum Decoding of Linea~° Codes for Minimizing Symbol Error Rate", IEEE Trans.
Inform. Theory, vol. IT-20, pp. 284-287, Mar. 1974; J. Hagenauer and P.
Hoeher, "A
Vite~bi Algorithm with Soft-Decision Outputs an:d Its Application", IEEE
GLOBECOM89, pp.47.1.1-47.1.7, Nov. 1989; D. Divsalar, "Turbo Codes for PCS
Applications", IEEE ICC95, pp. 54-59, 1996; P. Robertson, "Illuminating the Structure of Parallel Concatenated Recursive Systematic (TURBO) Codes", IEEE GLOBECOM94, pp. 1298-1303, Nov. 1994; S. Benedetto, D. Divsalar, G. Montorsi, and F.
Pollara, "Parallel Concatenated Trellis Coded Modulation", IEEE ICC96, 1996, pp.974-978; and, G. Ungerboeck, "Channel Coding with MultilevellPhase Signals", IEEE traps., Inform.
Theory, vol. IT-28, No. l, January 1982, pp.55-67.
A need therefore exists for a method and system that will. allow for the effective use of turbo coding in ADSL communication systems.

SUMMARY OF THE INVENTION
In accordance with this invention there is provided a method for the encoding sequence of information bits in a digital signal. The method comprises the steps of dividing the information bits into encoding bits and parallel bits; encoding the encoding bits to 5 produce encoded bits; mapping the encoded bits and the p<~rallel bits into first and second PAM signals; and generating a QAM signal from these first and second PAM
signals.
According to another aspect of the invention there is provided a coding system monitoring data representing sequences of instructions which when executed cause the above-described method to be performed. The coding system generally includes parallel-to-serial transfer means, interleaver means, encoder means, puncturing means, mapper means, and mode control means.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention may best be understood by referring to the following description and accompanying drawings which illustrate the invention. In the drawings:
FIG. 1 is a block diagram of a turbo coding system in accordance with a preferred embodiment of the invention;
FIGS. 2 (a), (b) and (c) are line diagrams illustrating a concatenated gray mapping for an 4-ASK, 8-ASK, and 16-ASK respectively in accordance with a preferred embodiment of the invention;
FIG. 3 is a block diagram of a turbo coding system with coding rate 2m/(2m+2), where m>0, in accordance with one embodiment of the invention;
FIG. 4 is a block diagram of a turbo coding system with coding rate (2m+1)/(2m+2), where m>0, in accordance with another embodiment of the. invention;

.--..-..,..,..-,~.F.. , a:a....m.~.,a:3 ~......a. r,~:,gRrpqy2,,p,.~y~p~p. ..
. .... -__.--a v FIG. 5 is a block diagram of a universal turbo coding system using mode control with coding rates 2m/(2m+2) and (2m+1 )/(2m+2), where m>0, in accordance with the invention;
FIG. 6 is a block diagram of a general turbo coding system using an arbitrary turbo coding method with coding rate 2m/(2m+2), where rn>0, in accordance with one embodiment of the invention;
FIG. 7 is a block diagram of a general turbo coding system using any turbo coding method with coding rate (2m+1)/(2m+2), where m>0,, in accordance with another embodiment of the invention;
FIG. 8 is a block diagram of a universal turbo coding system similar to the embodiment of figure 5 using mode control and any turbo coding method with coding rates 2m/(2m+2) and (2m+1 )/(2m+2), where m>0;
FIG. 9 is a block diagram of a turbo product or low-density parity check coding system with coding rate 2m/(2m+2), where m>0, in accordance with a preferred embodiment;
FIG. 10 is a block diagram of a turbo product or low-density parity check coding system with coding rate (2m+1)/(2m+2), where m>0, in accordance with a preferred embodiment;
FIG. 11 is a block diagram of a universal turbo product or low-density parity check coding system using mode control with coding rates 2n~/(2m+2) and (2m+1)/(2m+2), where m>0, in accordance with a preferred embodiment;
FIG. 12 is a block diagram of a turbo coding system with coding rate 2m/(2m+2), where m>0, where the six least significant bits are encoded by turbo codes, and where the puncturing rate is 3/, in accordance with a preferred embodiment;
FIG. 13 is a block diagram of a turbo coding system with coding rate (2m+1)/(2m+2), where m>0, where the six least significant bits are encodedl by turbo codes, and where the puncturing rate is 9/10 in accordance with a preferred embodiment;

Y
FIG. 14 is a block diagram of a bit level turbo TCM system in accordance with the prior art;
FIG. 15 is a block diagram of a turbo TCM encoder system with coding rate R=1/2 for 4QAM or a group of two 2QAM in accordance with a preferred embodiment;
FIG. 16 is a block diagram of a turbo TCM encoder system with coding rate R=(2+2m)/(4+2m) for MQAM, where M> 16 and M=2m, in accordance with a preferred embodiment;
FIG. 17 is a block diagram of a turbo TCM encoder system with coding rate R=(3+2m)/(4+2m) for MQAM, where M>16 and M=2m;
FIG. 18 is a block diagram of a universal turbo TCM encoder system MQAM in accordance with a preferred embodiment;
FIG. 19 is a block diagram of a symbol level turbo TCM system in accordance with the prior art; and, FIG. 20 is a block diagram of a turbo TCM encoder system for small constellation sizes in accordance with a preferred embodiment.
DETAILED DESCRIPTION OF THE PREFERRED EME~ODIMENTS
In the following description, numerous specific details are set forth to provide a thorough understanding of the invention. However, it is understood that the invention may be practiced without these specific details. In other instances, well-known software, circuits, structures and techniques have not been described or shown in detail in order not to obscure the invention. In the drawings, like numerals refer to like structures or processes.
The term asymmetric digital subscriber line ("ADSL") is used herein to refer to a technology for transmitting digital information which simultaneously transports high-bit-rate digital information downstream to a subscriber or customer, lower-bit-rate data upstream from the subscriber, and analog voice typically via a twisted-wire-pair.
The term amplitude shift keying ("ASK") is used herein to refer to a modulation technique that uses one signal of constant frequency, but varies the strength of the signal according to the state of the digital information to be conveyed.
The term binary phase shift keying ("BPSK") is used herein to refer to a modulation technique wherein the phase of the RF carrier is shifted 1 f~0 degrees in accordance with a digital bit stream.
The term discrete mufti-tone ("DMT") is used herein to refer to a multicarrier transmission technique that uses a Fast Fourier Transforrn ("FFT") and Inverse FFT to allocate the transmitted bits amoung many narrowband QAM modulated tones depending on the transport capacity of each tone.
The term "G.lite" is used herein to refer to a consumer-driendly splitter-less version of ADSL that typically offers downstream data rates of up to 1.5 Mbps and upstream date rates of up to 384 kbps.
The term "G.dmt" is used herein to refer to a second standard for ADSL that typically offers downstream data rates of up to 8 Mbps and upstream data rates of up to 1.5 Mbps.
G.dmt requires the installation of a splitter at the consumer's premises.
The term "Gray code" is used herein to refer to a binary code in which consecutive decimal numbers are represented by binary expressions that differ in the state of one, and only one, bit.
The term low-density parity check ("LDPC") code is used herein to refer to a binary code for which the parity check matrix is very sparse, having a. small, fixed number of parity equations checking each bit, and each parity equation checking the same number of bits.
The term maximum a posterio~i ("MAP") decoder is used herein to refer to a maximum likelihood decoder.

s The term pulse amplitude modulation ("PAM") is used Therein to refer to a modulation technique in which the amplitude of each pulse is controlled by the instantaneous amplitude of the modulating signal at the time of each pulse.
The term quadrature amplitude modulation ("QAM") is used herein to refer to a passband modulation technique which represents information changes in carrier phase and amplitude (i.e. real and imaginary parts). QAM is a method of combining two amplitude-modulated ("AM") signals into a single channel, thereby doubling the effective bandwidth. QAM is used with PAM in digital systems. hn a QAM signal, there are two carriers, each having the same frequency but differing in phase by 90 degrees.
The two modulated carriers are combined at the source of transmission. At the destination, the carriers are separated, the data is extracted from each, and then the data is combined into the original modulating information.
The term recursive systematic convolutional ("RSC" or "SRC") code is used herein to refer to a code that takes the desired sequence to be transnnitted as an input and produces an output sequence that contains the original signal plus a shifted, weighted version of it, which introduces redundancy. Its implementation is typically carried out in hardware using shift registers, which basically consist of registers (i.e. memory allocations) and a clock which controls the shifting of the data contained in t:he registers that is added to the original sequence to produce the output. The word "recursive" in the term RSC
code refers to the presence of a feedback connection. The word "convolutional" in the term RSC code indicates that the code depends on the current bit sequence and the encoder state.
The term trellis coded modulation ("TCM") is used herf;in to refer to a convolutional code that provides coding gain without increasing bandwidth.
Finally, the term "coding system" is used herein to refer to any machine for ADSL
related encoding and decoding, including the circuitn,~, systems and arrangements described herein.

In general, the invention described herein provides a method and system for turbo coding in ADSL communication systems. It is an advantage of the invention that its de-mapper requires fewer computations than are required for a conventional de-mapper for bit-level coded QAM and symbol-level turbo TCM. It is a further advantage of the invention that its decoder is independent of the number of bits transmitted in the constellation signal. It is further advantage of the invention that the overall number of computations is less than that required for both bit-level and symbol-level turbo decoders. It is a further advantage of the invention that its mapping efficiently maximizes the minimum Euclidean distance of uncoded bits while providing good performance for turbo coded bits. It is a further advantage of the invention that not only does it have as good an error performance as conventional bit-interleaved turbo coded QAM and s~,~mbol-interleaved turbo TCM
methods, but it also has low decoding complexity when compared with conventional bit-interleaved turbo coded QAM.
In general, the method for turbo coding comprises the following steps:
(a) Information bits are divided into two categories: encoding bits and parallel bits.
The encoding bits are passed into a turbo encoder. The parallel bits bypass the turbo encoder. The encoder outputs are coded bits which consist of systematic bits and parity bits (i.e. either all parity bits or partial parity bits).
(b) The coded bits and parallel bits are mapped into two PAM signals. For small PAM, there are no parallel bits. The coded bits are used as least significant bits, and the parallel bits are used as the most significant bits. The number of coded bits to be mapped to PAM is preferably two for b-ansrnitting an even number of bits and preferably three for transmitting an odd number of bits. The mapping of coded bits and parallel bits to PAM signals is performed using concatenated Gray mapping where concatenated Gray mapping is a serial concatenation of an inner Gray mapping and an outer Gray mapping. The inner Gray mapping is used for the coded bits. The outer Gray mapping is used for the parallel bits.
(c) A QAM signal is generated by two PAM signals,, one for the real part and the other for the imaginary part.

(d) To transmit an even number of bits, say 2m bits, preferably 2m-2 bits of the total 2m bits are parallel bits that will bypass the turbo encoder. The remaining preferably 2 bits will pass through the turbo encoder. Two parity bits are generated after puncturing. The overall bandwidtl:~ efficiency is 2m bits/Hz using QAM.
(e) To transmit an odd number of bits, say 2m+1 bits, :preferably 2m-2 bits of the total 2m+1 bits are parallel bits that will bypass the turbo encoder. The remaining preferably 3 bits will pass through the turbo encoder. One parity bit is generated after puncturing. The overall bandwidth efficiency is 2m+1 bits/Hz using QAM.
(~ Mode control may be employed in which a first mode may be used for transmitting an even number of bits and a second mode may be used for transmitting an odd number of bits.
(g) Alternate turbo codes such as serial concatenated turbo codes or multiple turbo codes may be used. Rather than using a turbo encoder, turbo product codes or LDPC codes may be used.
(h) Although the number of coded bits to be mapped to PAM is preferably two, this number may be greater than two.
The corresponding coding system has stored therein data representing sequences of instructions which when executed cause the above-described method to be performed.
The coding system generally includes parallel-to-serial transfer means, interleaver means, encoder means, puncturing means, mapper means, and mode control means.
Bit Level Turbo Encoder Protecting A Few LSB Bits. For ADSL communication systems, there is a choice between using symbol-level turbo TCM or bit-level turbo TCM. However, in terms of decoding complexity, bit-level turbo TCM is superior for the following reasons. Firstly, symbol-level turbo TCM uses two-dimensional, four dimensional, or eight-dimensional set partitioning mapping at the encoder end.
For very large constellations, this kind of set partitioning mapping typically requires a very complicated receiver de-mapper. Secondly, a symbol MAP decoder is typically more complicated than a bit MAP decoder. Thirdly, the complexity of a bit-level turbo coded QAM scheme may be reduced by protecting only a few least significant information bits.

In fact, the decoder's length and complexity are proportional to the number of information bits. For example, consider 214 QAM. If only four least significant bits are protected and a coding rate 1 /2 convolutional encoder is used as a component encoder, then the computational complexity of the decoder will be approximately six times lower than the computational complexity of a scheme where all bits are protected.
Referring to FIG. 1, there is shown a block diagram of a turbo coding system 100 in accordance with one embodiment of the invention. The i:urbo coding system is suitable for application in ADSL communication systems. The turbo coding system 100 includes information bits 110 consisting of parallel bits 120 and encoding bits 130, turbo encoder means 140, puncturing means 150, coded bits 160, and Gray mapping and QAM
modulation means 170. The encoding system 100 may have stored therein data representing sequences of instructions which when execui;ed cause the method described herein to be performed. Of course, the encoding system 100 may contain additional software and hardware a description of which is not nf;cessary for understanding the invention.
A portion of the information bits 110, referred to as parallel bits 120, are mapped 170 to the signal constellation point directly without any coding. The remaining portion of the information bits 110, referred to as encoding bits 130, axe coded by a turbo encoder 140.
The parallel bits 120 and coded bits 160 are mapped into one QAM signal 170.
In order to achieve both low computation complexity for the de-mapper and good performance, a method in which two independent one-dimensional mappings with concatenated Gray mapping is used. This method will be described below.
Two Independent One Dimensional Mappings In typical'. prior art bit-level turbo coded QAM schemes, all the transmitted bits are protected by a turbo encoder. These transmitted bits may be either systematic bits or parity bits. The de-mapper in typical prior art schemes has to calculate soft information for all the transmitted bits. In the method and system of the present invention, the transmitted bits to be mapped to a QAM
symbol are of three categories: parallel bits (i.e. which <~.re not protected by the turbo code), systematic bits, and parity bits. In the method and system of the present invention, the receiver de-mapper only needs to calculate the soft information for the systematic and parity bits. For example, in the case of turbo TCM, for 21x4=16384 QAM, with the present invention only 4 soft bits need be calculated rather than 14E soft bits.
The de-mapper calculates the soft information bits from the received constellation signal for the turbo decoder by calculating ~'J('Sm ~ f"k ) SmES+
'~k,.i = log (1) ~p(Sn ~~"k) SnEs where ~.k,~ is the jth soft bit in the kth QAM symbol, S-"~ is the constellation signal set corresponding to the jth bit set to "1", S- is the constellation signal set corresponding to the jth bit set to "0", and rk is the received complex sample for the kth QAM
symbol.
Now, let M represent the number of information bit. For a 2'1~ QAM
constellation, the size of S+ or S- is 2M-1 (i.e. assuming a two dimensional set-partitioning mapping) and thus can be very large for a large M. As a result, the soft bit calculation in equation (1) becomes computationally intense. However, if one-dirnensional mapping is used, the size of S+ or S- becomes 2''~ ~ 2-1. 'This results in a complexity saving factor of 2 'l~ ~ 2 , as shown in Table 1 below. For large constellations, this complexity saving can be very significant. Note that the number of addition and multiplication operations for the soft bit calculation is proportional to the size of S+ or S-, which is approximately as large as a multiple of 16384 for a 16384 QAM signal.
M 2D mapping 1D mapping Saving factor Table 1: Complexity Comparison of 1 D and 2D Mapping Cohcatehated Gray Mapping. In order to achieve good performance, the present invention employs a mapping scheme which will be refi~rred to as "concatenated Gray mapping". In concatenated Gray mapping, two Gray mappings (i.e. inner and outer Gray mappings) are concatenated serially. The inner mapping is for the turbo coded bits that include both systematic bits and parity bits, and the outer mapping is for the uncoded parallel bits. Referring to FIG. 2, there are shown line dia,~ams 200 of three examples of this mapping technique, namely, for 4-ASK 210 (Gra.y mapping), 8-ASK 220 (set partition mapping plus Gray mapping), and 16-ASK 230 (concatenated Gray mapping).
In these examples, the two least significant bits are coded 1'~its and are used for inner Gray mapping, and the remaining bits are used for outer Gray Mapping. Since the two least significant bits are either systematic bits or parity bits, t:he Gray mapping can provide equal protection for them. Furthermore, the minimum Euclidean distance for the uncoded parallel bits is also maximized by the outer Gray mapping. Therefore, this technique ensures good error protection for the encoded bits and the uncoded parallel bits. A
detailed example of this mapping technique is provided below.
Turbo Coded QAM System with Coding Rate R=2ml(2m+2). Refernng to FIG. 3, there is shown a block diagram of a turbo coding system 300 with coding rate 2ml(2m+2), where m>0, in accordance with another embodiment of the invention. Here, the turbo coded QAM system with coding rate R=2ml(2m+2) is used to transmit an even number of information bits in one QAM symbol. In this embodinnent, 2m information bits 310, 311, 3I2, 313, 314 are transmitted in each 2 2m+2 QA;M signal 320. Two identical recursive systematic convolutional ("RSC") encoders 330, 340 with coding rate %2 are employed. Parallel-to-serial 305 and interleaver 370 means are employed. T'he outputs of the two encoders 330, 340 are four parity bits 331, 341 for two information bits 313, 314 and are punctured alternatively (i.e, with different puncturing phase) 350, 360. For every two information bits (ul , u2 ) 313, 314, two parity bits are left after puncturing. One parity bit pul 351 is the parity bit for ul 314, and the other parity bit put' 361 is the parity bit for the interleaved 370 version u2 313. Now, in order t:o have equal protection for all information bits, it would be desirable that each information bit have one parity bit. This requires that the interleaver 370 permutates the bits at even number positions to even number positions and that it permutates the bits at odd mamber positions to odd number positions. The two vectors (vo , vl ,..., vm ) 380 and (wo , wl ,..., wm ) 390 will be mapped 320 into two 2m+1-ASK signals independently. For low d;~ta rates, if the uncoded bits are absent, (vo , vl ) 380 or (wo , wl ) 390 may be mapped iinto one 4QAM signal or two BPSK signals.
In addition, this embodiment employs "concatenated Gray mapping". The vector (vo , vl ,..., vm ) 380 consists of coded bits (vo, vl ) _ (pu2', u1 ) and uncoded bits (v2 , v3 ,..., vm ) . As discussed above in reference to FIG. 2, the coded bits (vo , v~ ) may form an inner Gray mapping and the uncoded bits (vz , v3 ,..., v"~ ) may form an outer Gray mapping. These two mappings are then concatenated.
Tables 2 through 7 below illustrate the relationship.between QAM size, parallel bits and encoded bits, and puncturing pattern and puncturing rate. fn these tables, the subscript of the symbol "d" represents the index of QAM symbols in the time domain. The turbo coded QAM system of this embodiment may be used for are least the following:
1. Coding rate 2/4 16QAM with bandwidth efficiency of 2bits/Hz;
2. Coding rate 4/6 64QAM with bandwidth efficiency of 4bits/Hz;
3. Coding rate 6/8 256QAM with bandwidth efficiency of 6bits/Hz;
4. Coding rate 8/10 1024QAM with bandwidth efficiency of 8bits/Hz;
5. Coding rate 10/12 4096QAM with bandwidth efficiency of lObits/Hz;
6. Coding rate 12/14 16384QAM with bandwidth efficiency of l2bits/Hz; and, 7. Coding rate 1/2 4QAM with bandwidth efficiency of lbits/Hz.

Information data dk d~ d2 Encoder input data d~ d2 Parity bit from encoderpl' -Parity bit from encoder- p2' 4ASK symbol (I) (dr'.,, pl ) 4ASK symbol (Q) (d2 , p2 ) 16QAM (dl '~ PI
', dz , pa') Table 2: Puncturing and Mapping for 16QAM with Rate 2/4 (transmitting 2 bits) Information data dk d~ d3 , d4 Encoder input data dl dz Parity bit from encoderp~' -Parity bit from encoder- p2' BASK symbol (I) (d3', d,~
, pl') 8ASK symbol (Q) (d4', d,-~
, p2') 64QAM (d3', dl', pl', d4 , d2', p2') * d31, d41 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 3: Puncturing and Mapping for 64QAM with Rate 4/6 (transmitting 4 bits) Information data dk dl , d2 ,~d3 ,-d4 , ds , d6 Encoder input data dT d2 Parity bit from encoderpl' -Parity bit from encoder- p2' 16ASK symbol (I) (ds , d3 , dr , pl ) ,~ _ _.~..~

16ASK symbol (Q) (d6~, d4 , d2 , pa ) 256QAM (ds-~ ~ yl p ~ d6 , d4 , d2 , pa ) * d31, d4', ds~, d61 do not go through the cortvolutional encoder in order to reduce the decoder complexity.
Table 4: Puncturing and Mapping for 256QAM witch Rate 6/8 (transmitting 6 bits) Information data ~d2 ,~d3 ,-d4 dk , ds , d6 , d~ , d8 Encoder input data dT d2 Parity bit from encoderpl' -Parity bit from encoder_ pa' 32ASK symbol (I) (d~', ds', d3 , dl', pr') 32ASK symbol (Q) (d8', d6', d4 , d2', pz') 1024QAM (d~', ds', d3', d~', pl ~ ds'~
d6', da', da',pz') * d31, d41, ..., dal, d81 do hot go through the convolutional encoder in order to reduce the decoder complexity.
Table 5: Puncturing and Mapping for 1024QAM with Rate 8/10 (transmitting 8 bits) Information data dk d~ , dl , d3 , d4 , ds , d6 , d~ , d8 , d9 , dlo Encoder input data d? d2 Parity bit from encoderp1' -Parity bit from encoder- p2 f i 64ASK symbol (I) (d9 , d~ , ds , d3 , dl , pr ) 64ASK symbol (Q) (d,ro , ds , d6 , da , d2 , p2 ) 4096QAM (d9', d~', ds', d:~ ~ dl'~ pl'~ dlo'~
ds'~ d6'~ da'. dz'~ pa') * d31, dal, ..., d91, dlol do not go through the' convolutional encoder in order to reduce the decoder complexity.
Table 6: Puncturing and Mapping for 4096QAM with Rate 10/12 (transmitting 10 bits) Information data dl , d~ d4 , ds , dk d6 , d~ , ds , d9 , dlo dll , dlz Encoder input data dl d2 Parity bit from pl' -encoder 1 Parity bit from - p2' encoder 2 128ASK symbol (I) (drlh d91, d~ , ds , d3 , dl , pi ) 128ASK symbol (Q) (dl2 , dlo , ds , d6 , da , dz , p2 ) 16384QAM (dl~', d9', d~', ds', d3 , dl'npl'~ drag dro'. ds'~ d6'. da'.
da',pa') * d31, dal, ..., dll', d121 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 7: Puncturing and Mapping for 16384QAM with Rate 12/14 (transmitting 12 bits) Turbo Encoder with Coding Rate R=(2m+1)l(2m+2) for MQAM (M?16). Referring to FIG. 4, there is shown a block diagram of a turbo coding system 400 with coding rate (2m+1)l(2m+2), where m>0, in accordance with another embodiment of the invention.
Here, the turbo coded QAM system with coding rate R=(2m+1)l(2m+2) is used to transmit an odd number of information bits in one QAM symbol. In this embodiment, 2m+1 information bits 410, 411, 412, 413, 414 are transmitted in each 22m+z QAM signal 420. For every three information bits 412, 413, 414 pas;>ed into the two RSC
encoders 430, 440, six parity bits 431, 441 are generated. Parallel-to-serial 405 and interleaver 470 means are again employed. The parity bits generated by each RSC encoder are punctured 450, 460 with the puncturing rate 5/6 (i.e. 5 of 6 parit~,~ bits are punctured). The two puncturing phases (or patterns) 450, 460 are offset three bits from each other. The unpunctured bits from the two encoders are multiplexed 495 to obtain the remaining parity bits. For each group of three information bits (ul , u,, , u3 ) 412, 413, 414, one parity bit vo 496 is generated. The parallel bits and coded bits are mapped 420 into a one-dimensional ASK signal using concatenated Gray mapping as described above and as illustrated in FIG. 2.
Tables 8 through 13 below illustrate the relationship between QAM size, parallel bits and encoded bits, and puncturing pattern and puncturing rate. In these tables, the subscript of the symbol "d" represents the index of QAM symbols in the time domain. The turbo coded QAM system of this embodiment may be used for at least the following:
1. Coding rate 3/4 16QAM with bandwidth efficiency of 3bits/Hz;
2. Coding rate 5/6 64QAM with bandwidth efficiency of Sbits/Hz;
3. Coding rate 7/8 256QAM with bandwidth efficiency of 7bits/Hz;
4. Coding rate 9/10 1024QAM with bandwidth efficiency of 9bits/Hz;
5. Coding rate 11/12 4096QAM with bandwidth efficiency of 1 lbits/Hz; and, 6. Coding rate 13/14 16384QAM with bandwidth efficiency of l3bits/Hz.
Information data dk ~, d2 , d3 , dl , d2 , d3 Encoder input data dl d2 d3 dl d2 d3 Parity bit from encoder- p2 - - -Parity bit from encoder- _ _ _ pZl -4ASK symbol (I) (d3', (d31, dl') dll) 4ASK symbol (Q) (d2', (dZl' pa') pll) 16QAM ~ (ds', dl', da'~ P2') ~ ~d3z~ dr ~ dz ~ P2 ) Table 8: Puncturing and Mapping for 16QAM with Rate 3/4 (transmitting 3 bits) Information data ~~ dl dk , dT
d4 , ds , dl , dl , d3 , d4 , ds Encoder input data dl d2 d3 dl d2 d3 Parity bit from encoder- p2' - - _ _ Parity bit from encoder- _ _ _ p2z -8ASK symbol (I) (ds', (ds'.
d3', dsh dr'.) drl) 8ASK symbol (Q) (d4', (da'~
da', dzl, PZ',) Pal) 64QAM (ds', (ds'~
d3', d3', dl', drh d4', dal, di dah ~ Pa') Pal) I

S * d41, dsl, d42, ds2 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 9: Puncturing and Mapping for 64QAM with. Rate 5/6 (transmitting 5 bits) Information data dl ,adz dk ,- d3 , d4 , ds , d6 , d~ , dl , d2 , d3', d4 , ds , d6 , d~
*

Encoder input data d~ d2 d3 dl d2 d3 Parity bit from - p2' - _ _ encoder 1 Parity bit from - - _ _ p2 _ encoder 2 16ASK symbol (I) (d~ , ds (d~
, d3 , , dl ) ds , d3 , dl ) 16ASK symbol (Q) (d6', d4', (d6 d2', pa') , d4 , d2 , pz ) 256QAM (d~', ds', (d~
d31 dl ~
~ d6 ~ ds da , de , ,p d3 ~
dl ~
d6 .
da , d p ) * d3', ..., d~', d32, ..., d~2 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 10: Puncturing and Mapping for 256QAM wiith Rate 7/8 (transmitting 7 bits) Information data dl ,~dzr, dk dTd4 ,~dsT,-d6 d;- , d8 , d9 , dl , d2 , d3', d4 , ds d6 , d~
, d8 , d2*

Encoder input data dl' d2' d3 a'IZ d2 d3 Parity bit from - pl _ _ _ _ encoder 1 Parity bit from - - - _ -p2 _ encoder 2 32ASK symbol (I) (d9', d~', (d9Z, ds', d3', d~~
dl') ds , d3 , dl ) 32ASK symbol (Q) (d8', d6', (a8 da'. d2', ' pa') d6 , d4 , d2 ~
pa ) 1024QAM (d9', d~', (d9Z, ds', d3', d~
d~', , d81 ~ d6'~ ds d4u dzl , ~ pa') d3 , dl , d82~
d6 , d42.
da2, pat) * d3', ..., d9', d32, ..., d92 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 11: Puncturing and Mapping for 1024QAM with Rate 9/10 (transmitting 9 bits) Information data dl~, d2 dk , d3 , d4 , ds , d6 , d~ , d8 , d9 , dlo , dll , dl , d2 , d3 d4 , ds , d6Z~ d~2 ds2, d92, dloZ. dlrz Encoder input data dl' d2' d3 dl~ d2 d3 Parity bit from encoder- p2 _ _ _ _ Parity bit from encoder- - - _ p2 _ 64ASK symbol (I) (dll', d9', (dm d~', ds', .
dj', dl dv ) .
d~
~
ds , d3 , dl ) 64ASK symbol (Q) (dlo , d8 (dro , d6 , , d4 , da da ~ pa~ ~
d6 ~
d4 .
da ~
pz ) 4096QAM (dm'~ dv', (dllz.
d~', ds', d92~
d3', d'r d~z.
~ ds dloh d8', ~
d6', d4', d3 da', pa') ~
dl dloz, ds2:
d62, d42, d22, p2z) * d31... dlll, d3z... d112 do hot go through th:e convolutional encoder in order to reduce the decoder complexity.
Table 12: Puncturing and Mapping for 4096QAM with Rate 11/12 (transmitting 11 bits) Information data dl , d2 dk , d3 , d4 , d 6 h , d8 , d9 , dlo , dll , d12 ~ dl3 , dl d2 .
d32~ d42.
ds2 d62~
d;2, dgZ, d92, d142.
4112 d122, d132 ~

Encoder input data dl d2 d3 dl d2 d3 Parity bit from encoder- p2 - - _ _ Parity bit from encoder- - - - p2 -128ASK symbol (I) (dl3 . (dl3 dll . ~ dll d9 , d~ ~ d9 , ds ~ ~ d7 d3' ~ ~ ds dl ) ~ d3 ~ dl ) 128ASK symbol (Q) (dla', (dl2l~
dlo'. dloz~
dg'~ d6'~ d8z~
da'~ dl' d6Z~
~ j~2') d4z.
d2~~
p2 ) 16384QAM (dl3 , (d13 dm , d9 ~ dll , d~ , ~ d9 ds . d3' ~ d7 ~ d~ ~ ds I 1 1 1 ~ d3 I I 1 ~ dl dlz ~ dlo , ~ ds , 2 2 ds ~ d4 2 2 , da .~ 2 2 pz ) 2 dra ~ dlo ~ d$
, d6 ~ d4 ~ dz ~ p2 ) * d31... d131, d32... d132 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 13: Puncturing and Mapping for 16384QAM with Rate 13/14 (transmitting 13 bits) Universal Implementation of Turbo Coded QAM for MQAM. Referring to FIG. 5, there is shown a block diagram of a universal turbo coding system 500 using mode control with coding rates 2ml(2m+2) and (2m+1 )l(2m+2), where m>0, in accordance with another embodiment of the invention. Here, a universal implementation system applicable to the embodiments illustrated in FIG. 3 and FIG. 4 for coding rates R=2ml(2m+2) and R=(2m+1 )l(2m+2) is described. The puncture rate for each RSC encoder 530, 540 is either P=1/2 for coding rate R=2ml(2m+2) or P=5/6 for coding rate R=(2m+1)l(2m+2).
This puncture rate is controlled by a mode control signal 565 having states corresponding to even and odd numbers of information bits 510, 511, 512, 513, 514. The parity bits from the two conventional encoders are evenly and alternatively punctured 550.
The parallel-to-serial transfer means ("P/S") 505 is also controlled by the mode 565, which will control whether u3 512 is used or not by the P/S transfer 505 and the encoders 530, 540. Interleaver 570 means are again employed. The constellation mapper 520 is also controlled by the mode 565, which will indicate the posiltion of the least significant bit.
Finally, the bits passed into the RSC encoders 530, 540 and their parity bits are grouped into two 2-bit vectors (vo , vl ) and (wo , wl ) 580, 5'90. Then, (vo , vl ,..., vm ) and (wo, wl,..., wm ) 580, 590 are mapped 520 into an ASK signal format, if a large constellation MQAM (i.e. M516) is used, or they are mapped 520 into one 4QAM
signal or two BPSK signals, if 4QAM or BPSK is employed.
Geheral Coded QAM Using Ahy Turbo Codes The embodiments discussed above in reference to the turbo coded QAM systems of FIG. 3, FIfG. 4, and FIG. 5 used double parallel concatenated convolutional encoders, with each encoder employing a coding rate 1 /2 convolutional encoder. However, the invention may make use of different kinds of turbo codes (e.g. a parallel concatenated convolutional encoder with each encoder using a coding rate other than 1/2, a multiple parallel concatenated convolutional encoder (refer to D. Divsalar, and F. Pollara, "Multiple Turbo Codes for Deep-Space Communications", JPL TDA Progress Report 42-121, May 15, 1995), serial concatenated turbo codes (refer to S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollaxa, "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding", JPL
TDA
Progress Report 42-126, August 15, 1996), etc.). Referring to FIG. 6, there is shown a block diagram of a general turbo coding system 600 using any turbo coding method with coding rate 2ml(2m+2), where m>0, in accordance with another embodiment of the invention. In this embodiment, any kind of turbo code ma',~ be used for an overall coding rate of 2ml(2m+2). For every QAM symbol 620, two parity bits are used, the number of input bits 613, 614 to the turbo encoder 630 is two, and the number of parity bits after puncturing 650 is two. This embodiment has an output/input ratio 666 of 2/2.
Referring to FIG. 7, there is shown a block diagram of a general tort>o coding system 700 using any turbo coding method with coding rate (2m+1)l(2m+2), where m>0, in accordance with another embodiment of the invention. In this embodiment, any kind of turbo code may be used for an overall coding rate of (2m+1)l(2m+2). For every QAM symbol 720, one parity bit is used, the number of input bits 712, 713, 714 to the turbo encoder 730 is three, and the number of parity bits after puncturing 750 is one. This embodiment has an output/input ratio 766 of 1/3. Referring to FIG. 8, there :is shown a block diagram of a universal turbo coding system 800 using mode control anel any turbo coding method with coding rates 2ml(2m+2) and (2m+1)l(2m+2), where m»D, in accordance with another embodiment. In this embodiment, any turbo code m;ay be used for coding rates 2ml(2m+2) and (2m+1)l(2m+2). This embodiment employs mode control 865.
Coded QAM Using Turbo Product Codes and Low ~~ensity Parity Check (LDPC) Codes Other powerful coding schemes such as turbo product codes (refer to D.
Chase, "A Class of Algorithms for Decoding Block Codes", IEEE Trans. Inform. Theory, Vol.
IT-18, pp. 170-182, Jan. 1972; and, R. Pyndiah, "Near Optimum Decoding of Product Codes: Block Turbo Codes", IEEE Trans. Common., Vol. COM-46, No. 8, pp. 1003-1010, August 1998) and low-density parity check (LDPC) codes (refer to R. G.
Gallager, "Low-Density Parity Check Codes", IRE Trans. Inform. Theory, vol. IT-8, pp. 21-28, Jan. 1962; D. J. C. Mackay and R. M. Neal, "Near Shanfaon Limit Performance of Low Density Parity Check Codes", Electon. Lett., vol. 32, No. 18, pp.1645-1646, Aug. 1996;
and, D.J.C. Mackay, "Good Error-Correcting Codes Based on fiery Sparse Matrices", IEEE Tran. Inform. Theory, vol. 45, No. 2, pp. 399-431, nrlar. 1999) may also be used in the coded QAM system of the present invention. Referring to FIG. 9, there is shown a block diagram of a turbo product or low-density parity check ("LDPC") coding system 900 with coding rate 2ml(2m+2), where m>0, in accordan<;e with another embodiment of the invention. In this embodiment, a turbo product code or LDPC code 930 for the coding rate (2m+1 )l(2m+2) is employed. Referring to FIG. 10, there is shown a block diagram of a turbo product or low-density parity check ("LDPC") coding system 1000 with coding -.., .y.: ~.___ ....~~,.~. -__ __- ~~_.

rate (2m+1)l(2m+2), where m>0, in accordance with another embodiment of the invention. In this embodiment, a turbo product code or LDPC code 1030 for the coding rate (2m+1)l(2m+2) is employed. Referring to FIG. 11, there is shown a block diagram of a universal turbo product or low-density parity check ("LDPC") coding system S using mode control with coding rates 2ml(2m+2) and (:Zm+1)l(2m+2), where m>0, in accordance with another embodiment of the invention. In this embodiment, a turbo product code or LDPC code 1130, with mode control 1165, for the coding rates 2ml(2m+2) and (2m+1 )l(2m+2) are employed.
Extension Case: More Coded Bits for Turbo Codes wit~~ Coding Rate R=2ml(2m+2).
Although the number of coded bits to be mapped to Q is preferably two as described in the preceding embodiments, this number is not limitef, to two and may be greater.
However, in practice, coding more than six bits may be counter productive as the puncturing required may lead to diminished performance of the turbo code.
Referring to FIG. 12, there is shown a block diagram of a turbo coding; system 1200 with coding rate 2ml(2m+2), where m>0, where the four least significant bits are encoded by turbo codes, and where the puncturing rate is 3/, in accordance with another embodiment of the invention. In this embodiment, three coded bits are used in PAM mapping. Four information bits 1212, 1213, 1214, 1215 are inputted to two turbo encoders 1230, 1240 generating eight parity bits. At the output 1231, 1241 of the two encoders 1230, 1240, the parity bits are punctured 1250, 1260 with puncturing rate 3/ (i.e. three parity bits are punctured out of four bits). The puncturing phases for thc; two encoders 1230, 1240 are offset by two bits. For every four information bits (ur , u2, u3, u4 ) 1212, 1213, 1214, 1215, two parity bits (wo ; vo ) 1251, 1261 remain after puncturing 1250, 1260. The two vectors (vo , vi ,..., vm ) and (wo , wl ,..., wm ) 1280, 1290 arcs mapped 1220 into two 2 m+i -ASK signals independently using "concatenated Gray mapping". The coded bits (vo , vl , v2 ) (or (wo , wl , w2 ) ) consisting of systematic bits (vl , v2 ) (or (wi , w2 ) ) and one parity bit vo (or wo ) use Gray mapping and the uncoded bits (v3 , v4 ,..., vm ) (or (w3, w4,..., wm ) ) use Gray mapping. Tables 14 through 18 below illustrate the relationship between QAM size, parallel bits and encoded bits, and puncturing pattern and puncturing rate. In these tables, the subscript of the symbol "d"
represents the index of QAM symbols in the time domain. In addition, other codes such as LDPC codes and product turbo codes may be used in the manner of the embodiment described above in association with FIG. 9 but where the input bits are (~~l , u2 , u3 , u4 ) .
The turbo coded QAM system of this embodiment may be used for at least the following:
l . Coding rate 4/6 64QAM with bandwidth efficiency of 4bits/Hz;
2. Coding rate 6/8 256QAM with bandwidth efficien<;y of 6bits/Hz;
3. Coding rate 8/10 1024QAM with bandwidth efficiE,ncy of 8bits/Hz;
4. Coding rate 10/12 4096QAM with bandwidth efficiency of lObits/Hz; and, 5. Coding rate 12/14 16384QAM with bandwidth efficiency of l2bits/Hz.
As mentioned above, this system may be extended to encode six information bits by using a puncturing rate of 5/6 with an offset of three bits.
Information data dk d 2 , d3 , d4 Encoder input data dl d~ d3 d4 ~

Parity bit from encoderpl' - - -Parity bit from encoder_ _ p3' -8ASK symbol (I) (d3', dl , pl') 8ASK symbol (Q) (d4 , d2 , p3 ) 64QAM (d3'~
dl',~II
, G~4', d2', p3') Table 14: Puncturing and Mapping for 64QAM with Rate 4/6 (transmitting 4 bits) Information data dk dTTd3', d4 , ds , d6 Encoder input data dl d2 d3 d4 Parity bit from encoderpl' - - _ Parity bit from encoder- - p3 -16ASK symbol (I) (dsr, dd3 , dl , pl ) 16ASK symbol (Q) (d6', d4 , d2', p3') 256QAM (ds', d3', d j', pr , a'6', da', a'z' ~ ps') *dsl, d61 do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 15: Puncturing and Mapping for 256QAM with Rate 6/8 (transmitting 6 bits) Information data dk d~ , d~
da , ds , d6 , d~
, d8 *

Encoder input data dl d2 d3 d4 Parity bit from encoderpl' - - -Parity bit from encoder- - p3 -32ASK symbol (I) (d~
, ds , d3 , d~
, pl ) 32ASK symbol (Q) (d8 , cd6 , da , d2 , p3 ) 1024QAM (d~
~ ds ~ ds ~ dl ~pl ~ da ~ d6 ~ da ~ da ~p3 ) *dsl, d61, dal, d81 do not go through the convolutional encoder in order to seduce the decoder complexity.
Table 16: Puncturing and Mapping for 1024QAM with Rate 8/10 (transmitting 8 bits) Information data dk dl', d2', d3', d4 , ds', ..., d9', dlo' Encoder input data dl d2 d3 d4 Parity bit from encoderpl - - -Parity bit from encoder- - p3' -64ASK symbol (I) (d9', d~', ds , d3', dl', pl') 64ASK symbol (Q) (dlo', d8 , d6', d4', d2', p3') 4096QAM (d9', d~', ds', d3', dr', pl', d101.
d81,~
d61~
d41~
d21,j731) *dsl, d61, ..., d91, dlol do not go through the convolutional encoder in order to reduce the decoder complexity.
Table 17: Puncturing and Mapping for 4096QAM with Rate 10/12 (transmitting bits) Information data dk dl , d2 , d3 , d4 , ds , ..., dll , dlz *

Encoder input data dl d2' d3 d4 Parity bit from encoderpl' - - -Parity bit from encoder- - p3 -64ASK symbol (I) (dll', d9', d~
, ds', d3', dl', pl') 64ASK symbol (Q) (d12'.
dlo', ds , d6', da', d2', p3') 4096QAM (dll', d9', d~
, ds', d3', dl', pl', d121~
d101~
<~81~
d61~
d41~
d21~j~3') *dsl, d61, ..., dlll, d121 do not go through the' convolutional encoder in order to reduce the decoder complexity.

Table 18: Puncturing and Mapping for 16384QA1~!t with Rate 12/14 (transmitting 12 bits) Extension Case: Mope Coded Bits of Turbo Codes with Coding Rate R=(2m+1)l(2m+2). Referring to FIG. 13, there is shown a block diagram of a turbo coding system 1300 with coding rate (2m+1)l(2m+2), where m>0, where the six least significant bits are encoded by turbo codes, and where the puncturing rate is 9/10 in accordance with another embodiment of the invention. In this embodiment, three coded bits are again used in PAM mapping. Five information bits 1312, 1313, 1314, 1315, 1316 are inputted to two turbo encoders 1330, 1340 generatin;; ten parity bits. At the output 1331, 1341 of the two encoders 1330, 1340, the parity bits are punctured 1350, 1360 with puncturing rate 1/10 (i.e. nine parity bits are punctured out of ten bits).
The puncturing phases for the two encoders 1330, 1340 are offset by five bits. For every five information bits (u i , u2 , u3 , u4 , a 5 ) 1313, 1313, 1314, 1315, 1316, one parity bit vo 1396 is left after puncturing 1350, 1360. The two vectors (vo , vl ,..., vm ) and (wa , wl ,..., wm ) 1380, 1390 will be mapped 1320 into two 2m+i _ASK signals independently using "concatenated Gray mapping". The coded bits (vo , vl , v2 ) consisting of systematic bits (vl , v2 ) and one parity bit vo use Gray mapping, the coded bits (systematic bits only) (wo, wl, w2 ) use Gray mapping, and the uncoded bits (v3 , v4 ,..., vm ) (or (w3, w4 ,...; wm ) ) use Gray mapping. Tables 19 through 23 below illustrate the relationship between QAM
size, parallel bits and encoded bits, and puncturing pattern and puncturing rate. In these tables, the subscript of the symbol "d" represents the index of QA:M symbols in the time domain.
In addition, other codes such as LDPC codes and product turbo codes may be used in the manner of the embodiment described above in association with FIG. 10 but where the input bits are (ul , u2 , u3 , u4 , us ) . The turbo coded QAM system of this embodiment may be used for at least the following:
1. Coding rate 5/6 64QAM with bandwidth efficiency of Sbits/Hz;
2. Coding rate 7/8 256QAM with bandwidth efficiency of 7bits/Hz;

~.. __ .~._____ ,.~T__ _..

3. Coding rate 9/10 1024QAM with bandwidth efficiency of 9bits/Hz;
4. Coding rate 11/12 4096QAM with bandwidth efficiency of l lbits/Hz; and, 5. Coding rate 13/14 16384QAM with bandwidth efficiency of l3bits/Hz.
Again, this system may be extended to coding seven information bits by using a puncturing rate of 13/14 with an offset of 7 bits.
Furthermore, and in the manner of the embodiment described above in association with FIG. 8, a universal implementation may be obtained for the embodiments described in association with FIG. 12 and FIG. 13 for turbo codes. Moreover, and in the manner of the embodiment described above in association with FIG. 11, a universal implementation may be obtained for the embodiments described in association with FIG. 12 and FIG. 13 for LDPC and product codes.
Information data dl dl dk , , d2 d2 , , d3 d3 , , d4 d4 , , d~ ds ~

Encoder input data dl dZ d3 d4 d~ dl dl d3 d4 ds Parity bit from p3 encoder 1 Parity bit from p3' encoder 2 8ASK symbol (I) (ds', (ds', d3', d3', dl') dl') 8ASK symbol (Q) (d4', (d4', d2', d2', p3') p3') 64QAM (ds', (ds', d3', d3', dl', dl', da~d2~p3) d4~da~p3) Table 19: Puncturing and Mapping for 64QAM with Rate 5/6 (transmitting 5 bits) Information data dl dl dk , , d~, d2 d4 , ,ids d3 ,-...,d~ , d4 , ds , ..., d~

Encoder input data dl d2 ~ d4 dT dl dl d3 d4 ds d3 Parity bit from p3' encoder 1 - .. ~ ..~.~....~_-_____7..

Parity bit from ~ ~ p3 encoder 2 8ASK symbol (I) (d~ (d~
, , ds ds , , d3 d3 , , d~ dl ) ) 8ASK symbol (Q) (ds', (d6z.
d4', d4~, d2', d2 P3') , p3 ) 64QAM (d~', (d~
ds', , d3', ds dl', ~
d6,' d3 d41 ~
~ dl d2l d62~
p31 d42~
) d22~
p32) *d61, d~', d62, d~2 do hot go through the convolutional encoder in order to reduce the decoder complexity.
Table 20: Puncturing and Mapping for 256QAM with Rate 7/8 (transmitting 7 bits) Information data dl dl dk ,Tdzr, , dT d2 ,~, , ...,~~ d3 ~ , d4 , ds , ..., d9 Encoder input data ~ d2 d3 d4 ds dl d2 d3 d4 ds Parity bit from p3 encoder 1 Parity bit from p3 encoder 2 32ASK symbol (I) (d9', (d9 d~ ' , d7 ds', , d3', ds dl') , d3 , dl ) 32ASK symbol (Q) (ds'~ (dsz, d6'~ d6z, d4'~ daZ, da'~ da p3') ~
ps ) 1024QAM (d9', (d9z, d~', d~Z, ds', ds d3', , dl', d3 d81. , d61. dl da', , d2l d82.
p31) d62, da2, d22, p32) *d61, d~', d8', d9', d6 , d~2, d82, d92 do not go through the cohvolutional encoder in order to reduce the decoder complexity.
Table 21: Puncturing and Mapping for 1024QAM with Rate 9/10 (transmitting 9 bits) .~...~_ . ,_.. ~..

Information data dl dl dk , , d2 d2 , , d3 d3 , , d~..., d4 I~ , ds , ..., dll Encoder input data dl d2 d3 d4 ds dl d2 d3 d4 ds Parity bit from p3 encoder 1 Parity bit from p3 encoder 2 32ASK symbol (I) (dlll, ~a112' d91, d9 dal, d7 dsh , d31' d,5 dll~ , d3 , dl ) 32ASK symbol (Q) (dlo'; (d10'.
d8', d8'.
d6', d6'~
d4', d4', d2', d2', p3') p3') 1024QAM (dll (dll . ~
d9 dv ~ ~
do, d~
ds ~
, ds d3 , , ds dl , , dl d101~ , d81~ d102.
dbh d82~
d41, d62~
d21, d42, p31) d22, p32) *d61, dal, ..., dlll, d6 , d~2, ..., dll2 do not go through the convolutionczl encoder in order to reduce the decoder complexity.
Table 22: Puncturing and Mapping for 4096QAM with Rate 11/12 (transmitting 11 bits) Information data dl dl dk , , d2 d2 , , d3 d3 ,~d4 , ,-dsl, d4 ..., , dr3 ds , ...

Encoder input data dl d2 d3 d4 ds dl d2 ~ d~ ds d3 Parity bit from p3 encoder 1 Parity bit from p3 encoder 2 64ASK symbol (I) (dl3'~ (dl3'~
dll'~ dll~~
d9'~ dv'~
d7'~ d~'.
ds', dsh d3', d3h dl dl') ) 64ASK symbol (Q) (d12 (d12 , ~
dlo d10 ~ .
ds d8 ~ ~
d6 d6 ~ ~
d4 d~
, , dz p3 , ) p3 ) 16384QAM (d13', (d13~~
dll'. dll'.
d9', dv'~
di d~', , ds', ds', dsh d3', dh, dl 2 , 2 1 dl2 1 ~
dl2 d10 ~ .
d10 d8 ~ ~
d8 d6 ~ ~
d6 d4 . , d4 d2 , , d2 p3 , ) p3~
) *d61, dal, ..., 4131, d62, d~2, ..., d132 do not go t,~Crough the convolutional encoder in order to reduce the decoder com,~lexity.

Table 23: Puncturing and Mapping for 16384QAM: with Rate 13/14 (transmitting 13 bits) Referring to FIG. 8, the method of one embodiment ~of the invention will now be described. With this method turbo codes may be effectively used in ADSL
communication systems. At a step 1, M information bits 810, 811, 812, 813, 814 to be transmitted over an ADSL communication system are divided into two categories:
encoding bits 812, 813, 814 and parallel bits 810, 811.
At a step 2, after parallel-to-serial transfer 805, the encoding bits 812, 813, 814 are passed into a turbo encoder 830. The parallel bits 810, 811. bypass the turbo encoder 830.
The encoder outputs, after puncturing 850, are coded bits which consist of systematic bits and parity bits (i.e. either all parity bits or partial parity bi.ts).
Alternate turbo codes such as serial concatenated turbo codes or multiple turbo codes :may be used.
Rather than using a turbo encoder, turbo product codes or LDPC codes may be used.
At a step 3, the coded bits and parallel bits are mapped E~20 into two PAM
signals. For small PAM, there are no parallel bits. The coded bits are used as least significant bits, and the parallel bits are used as the most significant bits. The number of coded bits to be mapped to PAM is preferably two for transmitting an even number of bits and preferably three for transmitting an odd number of bits. The mapping of coded bits and parallel bits to PAM signals is performed using concatenated Gray mapping where concatenated Gray mapping is a serial concatenation of an inner Gray mapping and an outer Gray mapping.
The inner Gray mapping is used for the coded bits. The outer Gray mapping is used for the parallel bits. To transmit an even number of bits, say M 2m bits, preferably 2m-2 bits of the total 2m bits are parallel bits that will bypass the turbo encoder. The remaining preferably 2 bits will pass through the turbo encoder. Two parity bits are generated after puncturing. In this case, the overall bandwidth efficiency is 2m bits/Hz using QAM. To transmit an odd number of bits, say M--2m+1 bits, preferably 2m-2 bits of the total 2m+1 bits are parallel bits that will bypass the turbo encoder. The remaining preferably 3 bits will pass through the turbo encoder. One parity bit is generated after puncturing. In this r case, the overall bandwidth efficiency is 2m+1 bits/Hz using QAM. Mode control may be employed in which a first mode may be used for transmitting an even number of bits and a second mode may be used for transmitting an odd number of bits.
Although the number of coded bits to be mapped to PAM is preferably two, this number may be greater than two.
At step 4, a QAM signal is generated 820 from the two PAM signals, one for the real part and the other for the imaginary part. The QAM signal is tlhen transmitted over the ADLS
communication system.
G.lite and G.dmtADSL. Now, there have been a number of proposals to apply powerful turbo coding and decoding techniques to G.lite and G.dmt ADSL to improve transmission.
rate and loop reach (refer to C. Berrou and A. Glavieux, "Neat Optimum Error Correcting Coding and Decoding: Turbo-Codes", IEEE T'rans. Commun., vol. COM-44, No. 10, October 1996, pp. 1261-1271). Among them, thE;re are two typical turbo TCM
schemes. The first is a symbol-level turbo TCM scheme which was proposed by Robertson and Worz (refer to P. Robertson and T. Worz, "Bandwidth-E~cient Turbo Trellis-Coded Modulation Using Punctured Component Codes", IEEE J-SAC, vol.
16, No. 2, Feb. 1998, pp. 206-218; and, "Performance Simulation Results on Turbo Coding", ITU Standard Contribution, NT-112, Nashville, USA, November 1999).
The other is a bit-level turbo TCM scheme (refer to "Proposed Evaluation of Proposed TTCM
(PCCC) with R-S Code and without R-S Code", ITU Standard Contribution, D.748 (WPl/15), Geneva, Switzerland, April 2000; "Proposal and Performance Evaluation of TTCM (PCCC) with R-S Code", ITU Standard Contribution, FI-122, Fiji Island, Feb.
2000; and, "New Proposal of Turbo Codes for AZ)SL Modem", ITU Standard Contribution, BA-020, Antwerp, Belguim, June 2000). With respect to the bit-level scheme, several designs have been proposed (refer to S. Benedetto, D.
Divsalar, G.
Montorsi, and F. Pollara, "Parallel Concatenated Treli'is Coded Modulation", IEEE
ICC96, 1996, pp. 974-978).
Referring to FIG. 14, there is shown a block diagram of a bit level turbo TCM
system 1400 in accordance with the prior art. Information bits 14:10 are encoded by two parallel concatenated recursive systematic convolutional encoders (RSCs) 1420, 1430 with an interleaves 1440 between their inputs. The two encoders ,are identical and have a coding rate of R=1/2. The respective sets of parity bits output from the encoders are punctured 1450 in a predetermined pattern in order to reduce the parity overhead. Then, the systematical information bits and parity bits are grouped :1460 and subsequently mapped into a QAM constellation 1470. Although this prior art scheme has good error performance, it also has some drawbacks including the following: all information bits are passed into the convolutional encoders for protection, therefore the number of trellis transitions is very large and the decoder is very complicated; the puncturing and mapping patterns are different for different constellation sizes of QAM, which leads to high implementation complexity; and, high coding rates cannot be obtained for large constellation sizes because over puncturing will damage the code, and therefore high data rates cannot be achieved.
According to another embodiment of the invention, a universal turbo TCM system is provided which has both good error performance and low decoder complexity. In general, this TCM system comprises: a pair of recursive systematic; convolutional (RSC) encoders for generating parity bits from input bits; an interleaves for interleaving input bits to the encoders; a puncture unit for determining a puncture rate of the parity bits in response to an even and odd number of information bits; and, a bit grouping module for receiving the punctured bits and the input bits and grouping the bits for snapping into a symbol.
Referring to FIG. 15, there is shown a block diagram of a turbo TCM encoder system 1500 with a coding rate of R=1/2 for 4QAM or a group of two 2QAM in accordance with another embodiment of the invention. This turbo TCM encoder may be used to transmit 1 bit in one 4 QAM symbol or in two 2 QAM symbols. For each information bit 1510, two parity bits are generated by two recursive systematic convolutional (RSC) encoders 1520, 1530. The parity bits generated by each RSC encoder are; punctured 1540 alternatively, that is, one half of the total parity bits are punctured. The overall coding rate is R=1/2.
For each information bit v2 1550, one parity bit vl 1560 is generated. (vl, v2) are mapped 1570 into one 4QAM symbol using Gray mapping. The system includes an interleaves 1580 between the two encoders 1520, 1530.
Referring to FIG. 16, there is shown a block diagram of a turbo TCM encoder system 1600 with a coding rate of R=(2+2m)/(4+2m) for MQAM, where 111516 and M--2m, in accordance with another embodiment of the invention. Tlhis turbo TCM encoder system may be used to transmit an even number of information bits in one QAM symbol.
For every two information bits (v3, v4) 1610, 1620 passed into the RSC encoders 1630, 1640, four parity bits are generated by these encoders. The par.'~ty bits generated by each RSC
encoder are punctured alternatively, that is, one half of the total parity bits are punctured 1650, 1660. For every two information bits (v3, v4) 1610, 1620, two parity bits (vl, v2) 1670, 1680 are generated. (vl, v2, ... v2m) are mapped 1690 into one QAM
symbol using set-partition mapping (refer to G. Ungerboe;ck, "Channel Coding with MultilevellPhase Signals", IEEE trans., Inform. Theory, vol. IT-28, No. 1, January 1982, pp. 55-67) and Gray mapping. It is preferable that this mapping be operated in one dimension, that is two halves of (vl, v2, ... v2m) are mapped into two 2m-ASK
signals.
This system may be used for at least the following: coding rate 2/4 16QAM;
coding rate 4/6 64QAM; coding rate 6/8 256QAM; coding rate 8/10 1024QAM; coding rate 10/12 4096QAM; and, coding rate 12/14 16384QAM.
Referring to FIG. 17, there is shown a block diagram of a turbo TCM encoder system 1700 with a coding rate of R=(3+2m)/(4+2m) for MQAM, where lt?516 and M--2m, in accordance with another embodiment of the invention. This turbo TCM encoder system may is used to transmit an odd number of information bits in one QAM symbol.
For every 3 information bits passed into the two RSC encoders 1730, 1740, 6 parity bits are generated by the two encoders. The parity bits generated by each RSC encoder are punctured 1750, 1760 with a puncturing rate of 5/6, tlhat is, 5 of 6 parity bits are punctured. For every three information bits (v2 , v3, v4), one parity bit vl is generated.
(vl, v2,..., v2m) are mapped 1790 into one QAM symbol using set-partition mapping and Gray mapping. It is preferrable that this mapping be operated in one dimension, that is, two halves of (vl, v2,..., v2m) are mapped into two 2m -ASK signals. This system may be used for at least the following: coding rate 3/4 16QAM; coding rate 5/6 64QAM;
coding rate 7/8 256QAM; coding rate 9/10 1024QAM; coding rate 11/12 4096QAM; and, coding rate 13/14 16384QAM.
Referring to FIG. 18, there is shown a block diagram of a universal turbo TCM
encoder system 1800 for MQAM in accordance with another embodiment of the invention.
Here, the data paths of embodiments 1600 and 1700 are combined via the interleaver which interleaves the bits at even numbered positions to even numbered positions and the bits at odd numbered positions to odd numbered positions. The puncture rate 1840 for each RSC encoder 1820, 1830 is either 1/2 or 5/6 which ins selected based on the even or odd status of the number of information bits. The information bits are passed into the RSC encoders 1820, 1830 and their parity bits are grouped 1850 into 4-bit by 4-bit for MQAM (M>4) or they are grouped 1850 into 2-bit by 2-bit for 4QAM. In general, this embodiment of the invention includes the following: a pair of recursive systematic convolutional (RSC) encoders 1820, 1830 for generating parity bits from input bits; an interleaver 1810 for interleaving input bits to the encodlers; a puncture unit 1840 for determining a puncture rate for the parity bits in response to the even or odd status of the number of information bits; and, a bit grouping module 1850 for receiving the punctured bits and the input bits and grouping the bits for mapping into a symbol. The interleaver 1810 may include a pair of interleavers. This pair of interl~eavers may be implemented by an interlearver with even and odd patterns. The mapping; 1860 may comprise mapping one two-dimensional QAM into two one-dimensional ASK. The mapping 1860 may include a mixed Gray mapping and set partition mapping; And, the mapping 1860 may include concatenated Gray mapping.
For embodiments of the invention including 1600, 1700, and 1800, and with reference to the discussion of concatenated Gray mapping and FIG. 2 above, note that two unique mapping schemes may be employed to achieve better error performance. The first mapping scheme may be a mixed Gray mapping with set partition mapping. With this mapping scheme, the mapping of (vl, v2, ... v2m) into 2~2m QAM is operated by mapping each half of (vl, v2, ... v2m) into one 2m -ASK signal. For example, (vl, v3, ...

v2m-1) may be mapped into one 2m -ASK signal and (v:Z, v4, ... v2m) may be mapped into another 2m -ASK signal. Again, FIG. 2 illustrates this unique mapping (i.e. set partition plus Gray mapping) for 4-ASK 210 and 8-ASIA 220. For 4-ASK 210, Gray mapping is employed. For 8-ASK 220, the first most significant bit employs set partition mapping and the two least significant bits employ Gray mapping. For general 2m -ASK, the first (m-2) most significant bits employ set partition mapping and the two least significant bits employ Gray mapping. For example, suppose that Bl, B2, ..., B2m are a mapping for 2m -ASK (m>1), where Bk (1<k<_2m) is an m-bit string, then the mapping for 2m+1 -ASK may be generated as 1B1, 1B2, ..., lB2m, OBl, OB2, ..., OB2m, that is, a 1 bit is appended to all Bl, B2, ..., B2m to obtain the first half and a 0 bit is appended to all B1, B2, ..., B2m to obtain the second half. The second unique mapping scheme may be concatenated Gray mapping. With this second schemE;, both the coded bits, such as (vl, v3) or (v2, v4), and the uncoded bits, such as (v5, v7, ".., v2m-1) or (v6, v8, ..., v2m), both employ Gray mapping and these mappings are conca~.tenated. For example, for m =
4, both (vl, v3) and (v5, v7) are Gray mappings. The concatenated Gray code is illustrated in line diagram 230 of FIG. 2. The two leas significant bits are the Gray mapping of coded bits (vl, v3), which will repeat every four mappings. The two most significant bits are the Gray mapping of the uncoded bits (v5, v7), which are the same for each group of 4 mappings.
Function Block fog Small Constellation Sizes Referrin~; to FIG. 19, there is shown a block diagram of a turbo TCM system 1900 in accordance with the prior art (refer to D.V. Bruyssel, "G.gen: Performance Simulation Res~!lts on Turbo Coding", ITU
Telecommunication Standardization Sector NT-112, Nashville, Tennesse, Nov. 1-5, 1999). In this scheme, parallel bit streams pass through two parallel convolutional encoders 1910, 1920. The scheme includes an interlea~~er 1930 located between the encoders. Two sets of coded bits are mapped 1940, 1950 into a constellation point independently. These points are then alternately 1960 pas;>ed to the channel, that is, one constellation point is punctured out for a given DMT symbol. One drawback with this scheme is that it can only support a minimum constellation of size of eight, that is, it a cannot map to bins or subchannels with smaller constellation sizes of, say, two or four.
This may become problematic as loop reach increases and SNR are lowered.
Referring to FIG. 20, there is shown a block diagram oiF a turbo TCM encoder system 2000 in accordance with another embodiment of the invention. This system includes a mufti-dimensional constellation construction function block 2010 which enables smaller constellations to be grouped together to accommodate a minimum of 3 coded bits. The function block (i.e. tone ordering bin grouping) 2010 is introduced to order the tones based on constellation sizes and to group them accordingly to form mufti-dimensional constellations. The function block 2010 interfaces with the signal mappers 2020, 2030 to control bits-to-point mapping. The bin grouping may be flexible enough to handle different bin loading scenarios. Table 24 lists exemplary mufti-dimensional constellation construction scenarios for small constellations.
Case Grouping Scenario Constellation Dimension 1 Four b=1 bins 4 2 Two b=1 bins and One b=2 4 bin 3 Two b=2 bins 4 *b is the humbe~ of bits that a bin (i.e. subcizannel) caries.
Table 24: Bin Group Summary This embodiment of the invention may be used with many different mapping alternatives.
In general, for a given encoder, the mapping scheme should give roughly the same error protection for each constellation dimension. For example, consider Case 3 from Table 24 above. Here, one of three coded bits from the encoders, say the bottom one, may be used to select one of the two bins and the remaining two bits may be used to select points in each bin. The added function block 2010 allows. for the construction of multi-dimensional constellations with small constellation sizes of two and four.
This allows turbo codes to be applied in low SNR environments.

Y . ~ n Although the invention has been described with reference to certain specific embodiments, various modifications thereof will be app~~rent to those skilled in the art without departing from the spirit and scope of the invention as outlined in the claims appended hereto.

Claims (26)

1. A method of encoding a sequence of information bits in a communication system comprising the steps of:

a) dividing said information bits into encoding bits and parallel bits;

b) encoding said encoding bits to produce encoded bits;

c) mapping said encoded bits and said parallel bits into first and second PAM
signals; and, d) generating a QAM signal from said first and said second PAM signals.

2. The method of claim 1 and further comprising the step of transmitting said QAM
signal over a communication system associated with said coding system.

3. The method of claim 2 wherein said communication system is an ADSL
communication system.

4. The method of claim 1 and further comprising the step of identifying the odd or even status of the number of said information bits.

5. The method of claim 1 and further comprising the step of selecting a mode of operation based on said odd or even status of said number of said information bits.

6. The method of claim 4 wherein said mode of operation determines the number of said coding bits, the puncture pattern used in said encoding, the coding rate used in said encoding, and the number of said encoded bits and said parallel bits used in said mapping.

7. The method of claim 6 wherein there are two said modes of operation.

8. The method of claim 1 wherein, if said number of said information bits is even, the number of said coding bits is two.

9. The method of claim 1 wherein, if said number of said information bits is odd, the number of said coding bits is three.

10. The method of claim 1 wherein said coded bits consist of systematic bits and parity bits.

11. The method of claim 10 wherein, if said number of said information bits is even, the number of said systematic bits is two and the number of said parity bits is two.

12. The method of claim 10 wherein, if said number of sad information bits is odd, the number of said systematic bits is three and the number of said parity bits is one.

13. The method of claim 1, step (b), wherein said encoding is performed by a turbo encoder.

14. The method of claim 1, step (b), wherein said encoding is performed by multiple turbo encoders.

15. The method of claim 1, step (b), wherein said encoding is performed by a serial concatenated turbo encoder.

16. The method of claim 1, step (b), wherein said encoding is performed by a turbo product code encoder.

17. The method of claim 1, step (b), wherein said encoding is performed by an LDPC
encoder.

18. The method of claim 1, step (c), and further comprising the step of forming a first vector and a second vector from said coded bits and said parallel bits.

19. The method of claim 18 and further comprising the step of mapping said first vector to said first PAM signal and mapping said second vector to said second PAM
signal.

20. The method of claim 19 wherein each of said first and said second vectors is formed from alternate ones of said coded bits and said parallel bits.

21. The method of claim 20 wherein said alternate ones of said coded bits form the least significant bits and said alternate ones of said parallel bits form the most significant bits of each of said first and said second vectors.

22. The method of claim 1, step (c), wherein said mapping is a concatenated Gray mapping.

23. The method of claim 22 wherein said concatenated Gray mapping is a serial concatenation of an inner Gray mapping and an outer Gray mapping.

24. The method of claim 23 wherein said inner Gray mapping is applied to said coded bits and said outer Gray mapping is applied to said parallel bits.

25. The method of claim 8 wherein the number of said coding bits is greater than two.

26. The method of claim 9 wherein the number of said coding bits is greater than three.