CN1166900A

CN1166900A - Method and apparatus for providing and receiving symbols

Info

Publication number: CN1166900A
Application number: CN96191306.1A
Authority: CN
Inventors: 格里高利·C·怀特; 斯特芬·P·埃莫特; 约翰·G·龙克; 帕切克·J·多兰
Original assignee: Motorola Inc
Current assignee: Motorola Solutions Inc
Priority date: 1995-10-31
Filing date: 1996-10-18
Publication date: 1997-12-03
Also published as: BR9607557A; FR2740634A1; MX9704951A; WO1997016910A1; IL119467A0; GB9713516D0; AR004249A1; GB2312814A

Abstract

A symbol constellation is logically divided into a plurality of multi-symbol subsets (201-204). Additionally, a series of primary bits and a series of secondary bits are provided. At least a first selected primary bit is error control encoded (303) to provide an M bit pre-symbol (603) that uniquely corresponds to a multi-symbol subset (602). The M bit pre-symbol is modulated (304) by at least a first selected secondary bit to provide an N bit symbol (605) that uniquely corresponds to a symbol included in the multi-symbol subset. Recovered primary bits are determined by comparing a received symbol (609) with only one symbol in each of the multi-symbol subsets. Additionally, recovered secondary bits are determined by comparing the received symbol with predetermined decision boundaries (622). In this manner, varying degrees of error protection are provided allowing for a wider variety of coding rates.

Description

Method and apparatus with receiving symbol is provided

A kind of method and apparatus that provides with receiving symbol especially is provided relate generally to radio digital communication equipment of the present invention.

In the radio digital communication apparatus field, the use of error correction is in order to resist the Channel Transmission mistake, particularly trellis coded modulation (TCM) is a kind of method of known error correction, and it handles the symbol that generation will be transmitted to digital signal data (as binary bits) with the error correcting technique of knowing.

But also knownly provide variable level of error correction on the same group speech coding parameters not, particularly high to error sensitivity parameter is (if incorrect as receiving, the voice quality generation extremely passive effect of its meeting to recovering) want given stronger mistake proofing rank, yet for the parameter low to error sensitivity (as, if receive incorrect, it is very little or harmless to the influence of voice quality) if having a bit, just give the prevention of its lower mistake.

Although TCM occupies superiority in the system of the variable mistake proofing ability of needs, but under given modulation type, spendable code check is quantitatively restricted sometimes for TCM, and it is the ratio of K/n that the typical case of error correction code rate describes, here k is the bit number that is encoded, and n is a bit number of forming final symbol.For example, the sign indicating number of code check 1/2 is that 1 bit of every input is produced a symbol by two coded-bits definition, and the sign indicating number of code check 2/3 is that the dibit to every input produces one by symbol of three coded-bits definition or the like.Generally speaking, along with code check reduces/increases, the error correcting capability of sign indicating number also increases/reduces, and table 1 has shown the TCM sign indicating number code check to the different quadrature amplitude modulation (QAM) and phase shift keying (PSK) the modulation scheme limit.

Modulation	Code check
Modulation	Code check	8PSK	2/3, (1/3, Fei Angebaike (non-Ungerboeck)
16QAM	3/4, (2/4,1/4 Fei Angebaike)	8PSK	2/3, (1/3, Fei Angebaike (non-Ungerboeck)
16QAM	3/4, (2/4,1/4 Fei Angebaike)	64QAM	5/6, (4/6,3/6,2/6,1/6 Fei Angebaike)

Table 1

As shown in table 1, only there is a kind of An Gebaike (Ungerboeck) code check (being the ratio of N/N+1) available to every kind of modulation type.Although can obtain non--Ungerboeck code check, but they are difficult to be designed to correct mistake proofing performance, generally need not in the reality, given available restricted code check uses TCM down, the designer often is faced with selection, make seldom bit have the mistake proofing of height, perhaps make most of bit have mistake proofing than low degree.But so alternately can not provide suitable error-correcting performance to needs fail-safe system in various degree, as voice system.

Therefore, in other system of the variable mistake proofing level of needs, allowing more, the method for the interior TCM of selection of wide region code check will be of great use.

Fig. 1 is the scheme diagram that prior art derives symbol.

Fig. 2 is the scheme diagram according to the derivation symbol of first kind of embodiment of the present invention.

Fig. 3 is according to the flow chart based on symbol that a plurality of bit sequence produces of the present invention.

Fig. 4 is the block diagram according to radio digital communication equipment of the present invention.

Fig. 5 recovers the flow chart of the method for main and less important bit according to the present invention is based on the symbol that receives.

Fig. 6 is the block diagram that has shown symbol sign indicating number example according to the present invention.

The present invention proposes a kind of method and apparatus that symbol is provided on the TCM basis, allow a plurality of bit sequences that in various degree mistake proofing is arranged, and this method and apparatus can be used in the radio digital communication equipment.

The symbol conformation can be divided into character subset more than a group in logic; and provide the main bit sequence that needs first order protection; protect less important bit sequence with the needs second level; its degree of protection is lower than the first order; at least one main bit of at first selecting is done error control coding; its produces M bit symbol (pre-symbol) that prelists generally speaking, and the M bit prelists symbol uniquely corresponding to character subset more than in many character subsets group.The M bit prelists symbol by at least one less important symbol-modulated of at first selecting, and (N＞M), this N bit symbol is unique corresponding to a symbol that is included in many character subsets here to produce the N bit symbol.In the environment of the present invention, modulation is meant in the zone of the symbol definition that prelists selects a special symbol.

At receiving terminal, the N bit symbol by only with each many character subset in a symbol relatively decode, produce the main bit that recovers.In addition, the N bit symbol produces the less important bit that recovers by comparing with predefined decision boundaries.In this way, a plurality of bit sequences can have error confinement in various degree.The more code check of wide range variable can be provided in addition.

With reference to figure 1～6, the present invention can be illustrated in more detail.Fig. 1 is the scheme diagram that prior art derives symbol, makes in this way, and each bit has only approximate same prevention degree to channel error in a certain bit sequence.Example shows that at first input bit is transformed into the symbol of being made up of 42 original bits through convolution coding, the Euclidean distance of original symbol quite little (I-Q plane, the left side).Other two of selecteed symbol 101 responses not coded-bit are shifted successively, produce 1 of 44 possible bit symbols 102～105.Make that the Euclidean distance between such 4 possibility symbols is bigger than the Euclidean distance of original symbol.

Euclidean distance between the method symbolization that Fig. 1 shows provides mistake proofing to two coded-bits and adopt convolution code that mistake proofing is provided to input bit at first not.This just has the net effect that input bit at first and two input bits of not encoding is provided other protection of similar level.By this way the symbol that receives of Chan Shenging in decoder by relatively deciding the transmission sequence of input bit with all possible candidate symbol.

Fig. 2 is the scheme diagram of the derivation symbol of first embodiment according to the invention.In the example of Fig. 2, main bit uses convolution code or lattice type (trellis) encoder to be encoded, and produces the 2 bits symbol that prelists, and its same regional 201～204 (or many character subset) is corresponding uniquely.This processing procedure below will more be described in detail.(the present invention expects that a symbol conformation can be divided into character subset more than two at least, for example, 16QAM symbol conformation can be divided into character subset more than 2, each subclass comprises 8 symbols, or being divided into character subset more than 4, each subclass comprises 4 symbols, or is divided into character subset more than 8, each subclass comprises 2 symbols, perhaps there is no need each symbol in the conformation as the member of many character subsets.For example, 8 symbols in the 16QAM symbol conformation can be divided into character subset more than 4, and each subclass comprises 2 symbols.Other 8 symbols can.Which many character subset which symbol is included in is the thing of design alternative.

In fact, the present invention is meant and decides the encoder state transitions to many character subsets, rather than all single symbols of the prior art.In the embodiment that recommends, it is for each many character subset that the selection of many character subsets requires, the Euclidean distance maximum between the nearest symbol of any symbol in many character subsets in other all many character subsets.In this manner, coded-bit is not only benefited from coding, and benefits from Euclidean distance greatly.

In case and the symbol that prelists of many character subsets correspondence is selected, two not coded-bit be used for selecting 4 specific bits (being N=M+2) symbol 205～208 from many character subsets of choosing.Balance between Fig. 1 and Fig. 2 is that uncoded bit can not benefit from bigger Euclidean distance.And decode procedure is also not too complicated, as described below.

Fig. 3 is the flow chart that produces the method for symbol among the present invention based on a plurality of bit sequences.Main bit sequence and less important bit sequence are provided in step 301.Another kind method is to produce a plurality of main bit sequences and/or less important bit sequence.Although these bit sequences can comprise the information of any kind usually, in the embodiment that recommends, they have comprised the speech coding parameters that different error sensitivities are arranged.Among the another kind of embodiment, bit sequence includes the picture coding parameter of different error sensitivities.In environment of the present invention, suppose to have one or more main bit sequences to have higher error sensitivity, therefore need be subjected to stronger protection; There is one or several less important bit sequence to have lower error sensitivity, therefore only need be subjected to weak protection.

In step 302, main bit and a less important bit of from main bit sequence and less important bit sequence, at least respectively selecting a bit to produce to choose at least at first.This selection course is selected next available bit from each bit sequence, or does not select those predetermined bits from each bit sequence in order.In addition, if a more than main and/or less important bit sequence is arranged, so, the main bit of choosing at least at first and less important bit of at first choosing can be respectively chosen from separately a plurality of main bit sequence and less important bit sequence.

In step 303, at least at first the main bit of choosing is encoded, produce and character subset is corresponding uniquely more than one the M bit symbol that prelists, in a preferred embodiment, the coding of the main bit of choosing at least at first adopts known lattice type sign indicating number to produce the M bit symbol that prelists, in another embodiment, adopt known convolution code to produce the M bit, they are transformed into the M bit symbol that prelists.According to prior art, lattice type sign indicating number and convolution code transition state are transferred to candidate symbol.In this manner, the state transitions that is produced by the input bit sequence produces the symbol sebolic addressing that allows.In contrast, the present invention transforms to many character subsets (or zone) to the state transitions that input bit produces, and these subclass are by the M bit Symbol recognition that prelists.If many character subsets have the Euclidean distance maximum to select according to making between each many character subset, be used to produce the prelist input bit of symbol of M bit so and not only benefit from the redundancy that coding brings, and benefit from the Euclidean distance of many character subsets.

In step 304, the M bit symbol that prelists produces the N bit symbol by the less important bit modulation of choosing at least at first, here N＞M and k=N-M.In the reality, each N bit symbol is expressed as a N bit symbol index." modulation " step is equivalent to prelisting with the M bit and selects a special symbol in the corresponding uniquely many character subsets of symbol.As mentioned above, each many character subset is by having 2 in logic ^KThe diversity of individual symbol is formed.Symbol can from 0 to 2 ^K-1 is indexed.(" zone " is often referred to the generation of many character subsets because be included in symbol in each many character subset be in typical case select approximating).Selection (or modulation) process can be by directly finishing at the appropriate N bit symbol index that interior K less important bit transforms in the many character subsets of appointment comprising the less important bit of choosing at least at first.Among another embodiment, selection can adopt second encoder (lattice type or convolution) to finish.

In step 305, the N bit symbol can send alternatively by suitable communication sources such as radio-frequency carrier.How do not consider step 305, in step 306, judge, all be encoded if be included in main and inferior all bits in bit sequence, modulation, emission, then process finishes.If have remaining bits need be encoded, modulate, launch alternatively, then repeat in 302 processes.In preferred embodiment, selection main and less important bit should make the bit of every sequence use up simultaneously.For example, all bits are formed a vocoder frames.

Fig. 4 is the block diagram according to radio digital communication equipment 400 of the present invention.Radio digital communication equipment 400 comprises 402, one of 401, one encoders of a speech coder, 403, one transmitting sets 404 of Symbol modulator that prelist.Although do not show, in preferred embodiment, one or more processing apparatus (as microprocessor and/or digital signal processor) and memory device (as random access memory and/or read-only memory) are also contained in the radio digital communication equipment 400 in order to realize the method as the present invention's description of software algorithm.

Algorithm press to be compiled in voice encryption device 401 combine digital speeches, exports the digital voice coding parameter that two-way at least represents to import speech waveform feature (not have demonstration).Give an example, voice encryption device can be carried out and be known as VSELP (VSELP) or be called improved Multi-Band Excitation (IMBE).First channel 406 comprises a sequence speech coding parameter, these parameters have high error sensitivity (being called main bit sequence in the above), and second channel comprises the speech coding parameter (being called less important bit sequence in the above) that a sequence has low error sensitivity.

First channel 406 is sent to encoder 402.The cataloged procedure that 303 steps were described above encoder 402 was carried out.Produce the M bit symbol 408 that prelists.In addition, second channel 407 is sent to the Symbol modulator 403 that prelists, less important bit modulation M bit in these modulator 403 usefulness second channels symbol 408 that prelists, as described above, in step 304, produce N bit symbol 409 (encoder 402 and the Symbol modulator 403 that prelists are formed a symbol encoder altogether, can realize the task of tabling look-up), N bit symbol 409 can contain PSK or qam symbol in a preferential embodiment.Final N bit symbol 409 is sent to transmitting set 404, radio frequency sending set for example, and this transmitter is by wireless communication resources 410 radio-frequency carriers emission symbol 409.

Fig. 5 is the flow chart that recovers the method for main and less important bit based on the symbol that receives according to of the present invention.The method that Fig. 5 describes for example can be introduced in the Wireless Telecom Equipment.In step 501, can receiving symbol by any suitable transmission medium such as RF Carrier.The symbol that receives is owing to be subjected to the symbol that the influence of transmitted noise and interference can be different from emission.As mentioned above, suppose that the symbol that receives is to use at least one main bit and at least one less important bit to produce.

In step 502, as mentioned above, the symbol conformation is divided into many character subsets.Although among the preferential embodiment, the operation to each receiving symbol shown in Figure 5 is as an independent step, determine that the step of many character subsets is to finish at system design stage.

In step 503, determine receiving symbol each symbol in each many character subset, and the distance between symbol only.This is determined to be selected at as described below with reference to Figure 6 usually nearest in each a many character subset symbol.Method of the prior art adopts all candidates' symbol, and the method has here reduced complexity than prior art.

In step 504, the distance of Que Dinging is used at least one main bit is produced all main bit decoding of recovery above.In the embodiment that recommends,

step

503 and 504 adopts Viterbi (viterbl) decoders to operate, in this decoder branch metric corresponding to receiving symbol to Euclidean distance between many character subsets rather than the Euclidean distance between receiving symbol and candidate symbol.In fact,

step

503 and 504 adopts and determines that maximal phase recovers at least one main bit like many character subsets.

In step 505, receiving symbol is determined with respect to the position of at least one predetermined Decision boundaries.In this case, at least one less important bit can be determined and produce the less important bit of recovery, and Fig. 6 has shown an example.In one embodiment of the invention, the part that step 505 can be used as viterbi algorithm is performed, so utilized the advantage of the ability that the trellis code error correction is arranged.

Be understood that the present invention by an example.Fig. 6 has shown according to the present invention the coding and the decoded instance block diagram of symbol.Especially, Fig. 6 with graphical display the out of phase of above-mentioned symbol sign indicating number.

Encoder 601 carries out lattice type (or convolution) coding to one or two main bit in this example, produces M bit symbol 603, and bit symbol 603 is corresponding with certain many character subset 602.The symbol 603 that prelists is transferred to the Symbol modulator 604 that prelists, and in this example, this modulator 604 uses a less important bit to select a symbol 605 from many character subsets 602.Symbol 605 is launched by wireless communication resources 607 then.

A received symbol 609 because the influence of transmitted noise and/or interference very likely is changed, is sent to soft decision decoder 610, for example, and Viterbi (Viterbi) decoder.The symbol 609 that receives is made comparisons with the only candidate symbol 612～619 in each many character subset.As mentioned above, candidate symbol 612～619 is selected as and the symbol 609 that receives has these symbols of each subclass of minimum Euclidean distance.As mentioned above, the branch metric of soft decision decoder 610 uses is corresponding to the Euclidean distance of many character subsets group.Decoder soft-decision 610 adopts maximal phase to determine many character subsets 611 like decision rule, and like this, one or two main bit (corresponding to one or two main bit of encoding in the past) just has been determined.

In case determine, maximal phase is sent to Hard decision decoding device 621 like many character subsets 611.The symbol 609 that Hard decision decoding device 621 relatively receives and decide a symbol 623 in many character subsets that most probable is launched corresponding to the decision boundaries 622 of many character subsets 611.Do like this, the less important bit of recovery (corresponding to the less important bit that is used to modulate precoded symbol 603) is just decided.

Shown the 16QAM conformation although be appreciated that Fig. 6, the present invention does not limit the conformation of this type or size.For example adopt device of the present invention can implement 64QAM or 8PSK conformation.

Utilize a kind of method and apparatus provided by the invention can make many bit sequences have in various degree mistake proofing ability.A tangible benefit of the present invention is owing to having used many character subsets to reduce the complexity of decoder.In addition, owing to use a plurality of bit sequences, each needs different code checks (or mistake proofing in various degree), and the present invention has greater flexibility aspect code rate selection.For example, the sign indicating number of 16QAM 1/3 code check can show as with 2/4 code check encoder to be realized, 1/3 code check coding is provided and uses a less important bit of not encoding just can increase effective code check to 2/4 but be actually main input bit.

Claims

1. A method comprising the following steps:

- generate a primary bit sequence for error prevention requiring first level protection;

- generate a secondary bit sequence for error prevention requiring a second level of protection, which is secondary to the first;

- error control encoding of at least the first selected primary bits of the primary bit sequence to generate an M-bit precoded symbol corresponding to at least the first selected primary bits, wherein the symbol constellation is divided into a set of multi-symbol subsets , the M-bit precoded symbols uniquely correspond to a certain multi-symbol subset in the multi-symbol subset group; and,

- modulating the M-bit precoded symbol with at least the first selected secondary bit in the secondary bit sequence to generate an N-bit symbol uniquely corresponding to a symbol contained in the multi-symbol subset, wherein M in the N-bit symbol bits correspond to at least the first selected major bits, and the N-M bits in the N-bit symbol correspond to at least the first selected minor bits.

2. The method of claim 1, the step of providing the primary bit sequence further comprising the step of providing digital speech coding parameters having a higher level of error sensitivity requiring a first level of error prevention.

3. The method of claim 1, the step of generating the secondary bit sequence further comprising providing digital speech with a lower level of error sensitivity and error prevention using one-to-one bit-to-symbol-bit transformation without eventual redundancy protection Steps to encode parameters.

4. The method of claim 1 , wherein the step of performing error control encoding on at least the first selected primary bits to generate the M-bit precoded symbols further comprises trellis coding the at least first selected primary bits to generate the M bit precoded symbols The steps of , wherein the lattice state transition has a one-to-one correspondence with the multi-symbol subset group.

5. The method of claim 1 , wherein the step of performing error control coding on at least the first selected primary bits to generate M-bit precoded symbols further comprises convolutionally encoding at least the first selected primary bits to generate M bits of precoded symbols. The steps of the symbols, where the convolutional state transitions have a one-to-one correspondence with groups of multi-symbol subsets.

6. The method of claim 1 , wherein the step of error control encoding at least the first selected major bits to generate the M-bit precoded symbols further comprises error control encoding the at least first selected major bits to generate the 3 bit precoded symbols. Symbol steps.

7. The method of claim 1, wherein the step of modulating the M-bit precoded symbols with at least the first selected secondary bits to generate N-bit symbols further comprises modulating the M-bit precoded symbols with at least the first selected secondary bits to generate 2 ^N quadrature amplitude modulation symbols.

8. The method of claim 1, further comprising the step of transmitting the N-bit symbols via wireless communication resources.

9. A method comprising the following steps:

- generate an error prevention secondary bit sequence requiring a second level of protection, which is secondary to the first level;

- Performing error control coding on at least the first selected primary bit sequence to generate M-bit precoded symbols corresponding to the first selected primary bit, wherein the symbol constellation is divided into a set of multi-symbol subsets, and the M-bit precoded symbols are unique corresponds to a certain multi-symbol subset in the multi-symbol subset group; and,

- modulate the M-bit precoded symbol with the first selected secondary bits of at least the first secondary bit sequence to generate an N-bit symbol uniquely corresponding to a symbol in the multi-symbol subset, where M is not less than 2 and N is greater than M, where M bits in the N-bit symbol correspond to at least the first selected major bits, and N-M bits in the N-bit symbol correspond to the first selected minor bits.

10. The method of claim 9, further comprising the steps of:

- generating at least a second secondary bit sequence requiring error prevention of the second level of protection,

- error control encoding of at least the first selected bits in the secondary bit sequence group to generate an N-2-bit precoded symbol corresponding to the first selected primary bit, wherein the N-2-bit precoded symbol uniquely corresponds to in a subset of multi-symbols; and

- modulate the N-2 bit precoded symbol with the first selected secondary bit and the second selected secondary bit of at least a second sequence of secondary bits to generate N uniquely corresponding to a symbol in the multi-symbol subset bit symbols where N is greater than 3, where at least two bits in the N-bit symbol correspond to at least the first selected major bit, 1 bit in the N-bit symbol corresponds to the first selected minor bit, and 1 bit in the N-bit symbol Corresponds to the second selected minor bit.

11. The method in claim 9, wherein the step of carrying out error control coding on the first selected main bits to generate N-1 bit precoded symbols further comprises trellis coding on the first selected main bits to generate N-1 The step of bit precoding symbols, wherein the lattice state transition and the multi-symbol subset group have a one-to-one correspondence.

12. The method of claim 9, wherein the step of performing error control coding on the first selected main bits to generate N-1 bit precoded symbols further comprises convolutionally encoding the first selected main bits to generate N-1 bits The step of precoding symbols, wherein there is a one-to-one correspondence between convolutional state transitions and multi-symbol subset groups.

13. Means of symbol encoder comprising:

- an encoder receiving a primary bit sequence requiring error prevention of the first level of protection and generating at least one M-bit precoded symbol corresponding to at least one primary bit in the primary bit sequence, wherein the symbol constellations are grouped a multi-symbol subset, at least M-bit precoded symbols uniquely corresponding to a multi-symbol subset in the multi-symbol subset group; and

- a pre-coded symbol modulator connected to an encoder which receives at least one M-bit coded symbol and a secondary bit sequence for error prevention requiring a second level of protection, which is secondary to the first level, with secondary At least one secondary bit in the desired bit sequence modulates the M-bit precoded symbol to produce one at least one N-bit symbol uniquely corresponding to a symbol in the multi-symbol subset, wherein M bits of the N-bit symbol correspond to at least one primary bits, N-M bits in an N-bit symbol correspond to at least one minor bit.

14. The symbol encoder of claim 13, further comprising a trellis encoder, wherein the state transitions of the trellis encoder have a one-to-one correspondence with the multi-symbol subset groups.

15. The symbol encoder of claim 13, the encoder further comprising a convolutional encoder, wherein state transitions of the convolutional encoder have a one-to-one correspondence with sets of multi-symbol subsets.

16. Apparatus for wireless digital communication equipment comprising:

- an encoder, receiving the primary bit sequence requiring error prevention of the first level of protection, generating at least one M-bit precoded symbol corresponding to at least one primary bit in the primary bit sequence, wherein the symbol constellation is divided into a set of multiple In the symbol subset, at least one M-bit precoded symbol corresponds to a multi-symbol subset in the multi-symbol subset group.

- a precoded symbol modulator connected to an encoder receiving at least one M-bit precoded symbol and a secondary bit sequence requiring error prevention for a second level of protection, which is inferior to the first level , modulate M-bit precoded symbols with at least one secondary bit in the secondary bit sequence to generate at least one N-bit symbol uniquely corresponding to one symbol in the multi-symbol subset, wherein M in the at least one N-bit symbol bits correspond to at least one major bit, and N-M bits in an N-bit symbol correspond to at least one minor bit.

- A wireless transmitter, coupled to the precoded symbol modulator, receives at least one N-bit symbol and transmits the N-bit symbol over the wireless communication resource.

17. The wireless digital communication device of claim 16, the encoder further comprising a trellis encoder, wherein there is a one-to-one correspondence between the trellis state transitions of the trellis encoder and the multi-symbol subset groups.

18. The wireless digital communication device of claim 16, the encoder further comprising a convolutional encoder, the state transitions of the convolutional encoder having a one-to-one correspondence with the multi-symbol subset groups.

19. The wireless digital communication device of claim 16, the wireless transmitter further comprising a wireless radio frequency transmitter.

20. The wireless digital communication device of claim 16, further comprising:

A speech coder, coupled to the coder and the precoded symbol modulator, generates speech coding parameters with a high level of error sensitivity as a primary bit sequence and speech coding parameters with a low level of error sensitivity as a secondary bit sequence.

21. A method comprising the steps of:

- receiving an N-bit symbol, wherein M bits of the N-bit symbol correspond to at least one major bit and N-M bits of the N-bit symbol correspond to at least one minor bit.

- Split symbol conformations into a set of multi-symbol subsets.

- Decoding the N-bit symbols with determining the distance between the N-bit symbols and only one symbol of each multi-symbol subset.

22. The method of claim 21, the step of decoding the N-bit symbols further comprising Viterbi encoding the N-bit symbols to produce at least one recovered primary bit.

23. The method of claim 22, the step of decoding the N-bit symbols further comprising:

- determine the position of the N-bit symbol relative to at least one predetermined decision boundary; and

- determining at least one recovered minor bit as a function of the position of the N-bit symbol for at least one predetermined decision boundary.