Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
  • H04L1/0056—Systems characterized by the type of code used
  • H04L1/0064—Concatenated codes
  • H04L1/0066—Parallel concatenated codes
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
  • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
  • H03M13/2957—Turbo codes and decoding
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
  • H03M13/63—Joint error correction and other techniques
  • H03M13/635—Error control coding in combination with rate matching
  • H03M13/6362—Error control coding in combination with rate matching by puncturing
  • H03M13/6368—Error control coding in combination with rate matching by puncturing using rate compatible puncturing or complementary puncturing
  • H03M13/6381—Rate compatible punctured turbo [RCPT] codes
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
  • H04L1/0041—Arrangements at the transmitter end
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
  • H04L1/0056—Systems characterized by the type of code used
  • H04L1/0067—Rate matching
  • H04L1/0068—Rate matching by puncturing
  • H04L1/0069—Puncturing patterns
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
  • H03M13/35—Unequal or adaptive error protection, e.g. by providing a different level of protection according to significance of source information or by adapting the coding according to the change of transmission channel characteristics
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
  • H03M13/63—Joint error correction and other techniques
  • H03M13/6306—Error control coding in combination with Automatic Repeat reQuest [ARQ] and diversity transmission, e.g. coding schemes for the multiple transmission of the same information or the transmission of incremental redundancy
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/12—Arrangements for detecting or preventing errors in the information received by using return channel
  • H04L1/16—Arrangements for detecting or preventing errors in the information received by using return channel in which the return channel carries supervisory signals, e.g. repetition request signals
  • H04L1/18—Automatic repetition systems, e.g. Van Duuren systems
  • H04L1/1812—Hybrid protocols; Hybrid automatic repeat request [HARQ]
  • H04L1/1819—Hybrid protocols; Hybrid automatic repeat request [HARQ] with retransmission of additional or different redundancy

Definitions

• the present invention relates to error correction in data communications, and more particularly, to forward error correction (FEC) . Even more particularly, the present invention relates to the selection and use of optimal Turbo Codes in high performance data communication systems, such as emerging third generation terrestrial cellular mobile radio and satellite telephone systems, for which flexibility in supporting a wide range of system requirements with respect to transmission data rates, channel coding rates, quality of service measures (e.g., latency, bit-error rate, frame error rate), and implementation complexity is highly desirable.
• FEC forward error correction
• FEC Forward error correction
• RF propagation channel which induces signal waveform and spectrum distortions, including signal attenuation (freespace propagation loss) and multi-path mduced fading.
• These impairments drive the design of the radio transmission and receiver equipment, the design ob]ect ⁇ ve which is to select modulation formats, error control schemes, demodulation and decoding techniques and hardware components that together provide an efficient balance between system performance and implementation complexity.
• Differences in propagation channel characteristics, such as between terrestrial and satellite communication channels naturally result in significantly different system designs.
• existing communication system continue to evolve in order to satisfy increased system requirements for new higher rate or higher fidelity communication services .
• Analog Mobile Phone System is an exemplary first generation system
• the U.S. IS-136 and European GSM time-division multiple-access (TDMA) standards and the U.S. IS-95 code-division multiple-access (CDMA) standard are second generation systems
• the wideband CDMA standards currently under development e.g., CDMA 2000 in the U.S. and UTRA in Europe
• CDMA 2000 in the U.S. and UTRA in Europe are third generation systems.
• Desirable features include the ability to perform rate adaptation and to satisfy a multiplicity of quality-of-service (QOS) requirements.
• QOS quality-of-service
• FEC forward error correction
• Turbo Codes are a relatively new class of block codes that have been demonstrated to yield bit error rate (BER) performance close to theoretical limits on important classes of idealized channels by means of an iterative soft-decision decoding method.
• BER bit error rate
• a Turbo encoder consists of a parallel concatenation of typically two systematic, recursive convolutional codes ("constituent codes”) separated by an mterleaver that randomizes the order of presentation of information bits to a second constituent encoder with respect to a first constituent encoder.
• the performance of a Turbo Code depends on the choice of constituent codes, mterleaver, information block size (which generally increases with higher data rates), and number of decoder iterations. For a particular Turbo Code, which the constituent codes are fixed, one can ideally adjust the block size and number of decoder iterations to tradeoff performance, latency and implementation complexity requirements. As the block size changes, however, a new mterleaver matched to that block size is required.
• forward link channels can be designed to be orthogonal, using, for example, alsh- Hadamand spreading sequences. This is generally not possible, however, for reverse link channels (from user terminal to base station) , which therefore operate asynchronously usmg spreading sequences that are only quasi-orthogonal.
• the reverse links in a synchronous CDMA network typically experience more interference and therefore may require stronger FEC (via lower rate codes) than the forward link channels do.
• the forward and reverse link channels are more similar m terms of interference leveis, so it is possible to use a common FEC scheme (or at least more similar FEC schemes) on the two links.
• the present invention advantageously addresses the above and other needs by providing methods for designing and using universally optimized Turbo Codes and rate-compatible punctur gs to support incremental redundancy schemes sucn as automatic repeat request (ARQ) .
• the invention can be characterized, m one embodiment as a method of processing data, in data services, with a set of rate-compatible Turbo Codes optimized at high code rates and derived from a universal constituent code, the Turbo Codes having compatible puncturing patterns.
• the method comprises: encoding a signal at a first and second encoder using a best rate 1/2 constituent code universal with higher and lower code rates, the first encoder and the second encoder each producing a respective plurality of parity bits for a data bit; puncturing the respective plurality of parity bits at each encoder with a higher rate best puncturing pattern; and puncturing the respective plurality of parity bits at each encoder with a lower rate best puncturing pattern.
• a method of processing data m data services uses a set of rate-compatible Turbo Codes derived from an optimal universal rate 1/3 constituent co ⁇ e, the Turbo Codes having similar constituent codes and compatible puncturing patterns, and comprises: encoding a signal with a best rate 1/3 constituent code at a first and a second encoder, each encoder producing a respective plurality of parity bits for each data bit; puncturing the plurality of parity bits with the a higher rate best puncturing pattern; and puncturing the plurality of parity bits with a lower rate best puncturing pattern.
• a method of rate-compatible Turbo encoding uses a set of rate-compatible Turbo Codes, the set optimized for code rate 1/4, comprising Turbo Codes with differing code rates and rate-compatible puncturing patterns.
• the method comprises: encoding a signal at a first and second encoder using a best rate 1/4 constituent code universal with higher and lower code rates, the first encoder and the second encoder each producing a respective plurality of parity bits for a data bit; puncturing the respective plurality of parity bits at each encoder with a higher rate best puncturing pattern; and puncturing the respective plurality of parity bits at each encoder with a lower rate best puncturing pattern.
• an encoding system uses a set of rate-compatible Turbo Codes derived from a best universal rate 1/2 constituent code, the set having compatible puncturing patterns, and comprises: a first and second encoder, each encoder comprising: a plurality of shift registers; a plurality of adders each adder coupled to a selected portion of the adders m a configuration corresponding to the best universal rate 1/2 constituent code; and a puncturer configured with the first and second encoder to puncture a plurality of data outputs from each of the first and second encoder, the puncturing determined by a desired Turbo Code rate in accordance with the set of the compatible puncturing patterns .
• an encoding system uses a set of rate-compatible Turbo Codes derived from an optimal universal rate 1/3 constituent code, the rate compatible Turbo Codes having similar constituent codes and compatible puncturing patterns, and comprises: a first and second encoder, each encoder comprising: a plurality of shift registers; a plurality of adders, each of the adders coupled to a selected portion of the adders in a configuration corresponding to the rate 1/3 constituent code of; and a puncturer configured with the first and second encoder such to puncture a plurality of data outputs from the first and second encoder, the puncturing determined by a desired Turbo Code rate in accordance with the set of the compatible puncturing patterns.
• Yet another variation of the system uses a set of rate- compatible Turbo Codes comprising Turbo Codes having a universal constituent code and rate-compatible puncturing patterns for different code rates, and comprises: a plurality of shift registers; a plurality of adders each adder coupled to a selected portion of the plurality of adders in a configuration corresponding to the universal constituent code; and a puncturer configured with the first and second encoder for puncturing a plurality of data outputs from the first and second encoder, the puncturing determined by a desired Turbo Code rate in accordance with the set of compatible puncturing patterns .
• a set of rate- compatible Turbo Codes comprising Turbo Codes having a universal constituent code and rate-compatible puncturing patterns for different code rates, and comprises: a plurality of shift registers; a plurality of adders each adder coupled to a selected portion of the plurality of adders in a configuration corresponding to the universal constituent code; and a puncturer configured with the first and second encoder for puncturing a plurality of data outputs from the first
• FIG. 1 is a diagram of a code-division multiple-access (CDMA) digital cellular mobile radio system hardware;
• CDMA code-division multiple-access
• FIG. 2 is a diagram of a CDMA digital cellular mobile radio system hardware which can implement an embodiment of the present invention
• FIG. 3 is a functional block diagram of a Turbo Code encoder modified for use with the present invention.
• Figure 4 is a functional block diagram of a generic turbo decoder
• Figures 5, 6, 7, 8 illustrate the Bit Error Rate (BER) performance against signal to noise ratio (SNR) for Turbo Code rates 1/2 and rate 1/3 at Interleaver sizes 1000, 512 and 1024 bits when the Turbo Codes use a candidate constituent code represented by d(D) and n(D);
• BER Bit Error Rate
• SNR signal to noise ratio
• Figure 9 illustrates the puncturing schemes studied for optimizing the rate 1/4 Turbo Codes
• Figures 10, 11, 12 illustrate the BER/FER performance of Constituent Codes #1-3 at a frame size of 512 bits
• Figure 13 illustrates the BER/FER performance of Constituent Code #1, wherein Constituent Code #1 is at a frame size of 1024 bits, and with consistent results found at sizes 2048 and 3072 bits, respectively;
• Figure 14 illustrates the BER/FER performance of selected rate 1/4 Turbo Codes at frame size 512, with consistent results found at sizes 1024, 2048 and 3072 bits, respectively;
• Figure 15 is a comparison of preferred Turbo Code B against other puncturing schemes at frame size 512 bits;
• Figure 16 is a lay-out of candidate puncturing patterns for Turbo Codes of rate 1/3 and 1/2 when the constituent codes have rate 1/3;
• Figure 17 illustrates a comparison of rate 1/3 puncturing schemes at frame size 512 bits
• Figure 18 illustrates rate 1/2 puncturing schemes at frame size 512 bits, with consistent results found at 1024, 2048 and 3072 bits, respectively;
• Figure 19 illustrates a block diagram of a preferred universal constituent encoder for Turbo Codes optimized at code rate 1/2 and rate 1/3 of varying Interleaver depths;
• Figure 20 is a functional block diagram for rate 1/4 Turbo Codes optimized at code rate 1/2 and rate 1/3, including interleaving and puncturing, (rate 1/3, and rate 1/2 use analogous processing) ;
• Figure 21 illustrates puncturing patterns for rate 3/8 Turbo Codes
• Figure 22 illustrates rate 3/8 Turbo Codes optimized at co ⁇ e rate 1/2 and rate 1/3 at frame size 512 bits, wherein results are consistent at 1024, 2048 and 3072 bits, respectively;
• Figure 23 illustrates puncturing patterns for rate 4/9 Turbo Codes
• Figure 24 illustrates rate 4/9 Turbo Codes optimized code rate 1/2 and rate 1/3 using frame size 512 bits
• Figure 25 is a functional block diagram of a preferred constituent encoder for a Turbo Codes optimized at code rate 1/4;
• F gure 26 illustrates a functional block diagram of a rate 1/4 Turbo Codes optimized at rate 1/4, including interleaving and puncturing, (rate 1/3 and rate 1/2 use analogous processing) ;
• Figure 27 illustrates puncturing patterns for rate 2/9 Turbo Codes
• Figure 28 illustrates rate 2/9 Turbo Codes optimized at code rate 1/4 using frame size 512 bits
• Figure 29 illustrates initial puncturing patterns for rate 3/8 Turbo Codes
• Figure 30 illustrates rate 3/8 Turbo Codes optimized at code rate 1/4 using frame size 512 bits
• Figure 31 is a functional block diagram of a preferred universal constituent encoder for rate 1/2 and rate 1/3 Turbo Codes of varying Interleaver depths.
• Figure 32 illustrates a performance comparison of rate 1/4 FER-optimized Turbo Codes with convolutional codes, at frame size 512 bits, wherein results are consistent at 1024, 2048 and 3072 bits.
• Appendix A is a compilation of figures collectively referred to herein as Analogous' figures, curves or simulations or the equivalent.
• Turbo Codes are particularly well-suited to data applications because of their excellent error correction capabilities at low signal-to-no se (SNR) ratios and their flexibility in trading off bit error rate (BER) and frame error rate (FER) performance for processing delay.
• SNR signal-to-no se
• BER bit error rate
• FER frame error rate
• the universal Turbo Codes specified herein are also applicable to data services in other cellular mobile radio systems (e.g., the European Time-Division Multiple Access (TDMA) standard used in GSM) as well as other systems, such as satellite or other wireless communications systems.
• TDMA European Time-Division Multiple Access
• GSM Global System for Mobile communications
• Several specific Turbo Codes are therefor identified that provide different optimizations regarding these requirements. Others would also be possible.
• FIG. 1 an exemplary conventional digital cellular mobile radio system using Direct Sequence Code Division Multiple Access (CDMA) Mobile-station-to-base- station (or reverse) link is shown using a convolutional encoder and a Viterbi decoder.
• CDMA Direct Sequence Code Division Multiple Access
• This basic coding and interleaving can be applied, equally well, to other multiple access systems such as the Time Division Multiple Access (TDMA) used in a well-known GSM standard.
• TDMA Time Division Multiple Access
• Figure 1 also represents a base-station-to-mobile-station (or forward) .link in a cellular mobile radio system.
• the system comprises a segmentation processor 104 where user information bits from a data terminal equipment (not shown) are assembled into fixed length frames of N bits per frame 106 which are input to a convolutional encoder 108, (of rate r) .
• Convolutional encoder 108 is coupled to a synchronization and framing processor 104 which produces N/r code symbols 110 at an input of a Channel Interleaver 112 coupled to the convolutional encoder 108.
• the channel interleaver 112 performs pseudo-random shuffling of code symbols 110 and outputs the code symbols 110 to a Spread Spectrum modulator 114 coupled to the channel interleaver 112.
• the Spread Spectrum modulator 114 uses a user specific Transmit PN-code generated by a PN converter 116 coupled to the Spread Spectrum modulator 114 to produce a spread spectrum signal carried on a RF carrier to a mobile RF transmitter 118.
• Mobile RF transmitter 118 is also coupled to the Spread Spectrum modulator 114, where a high power amplifier (not shown) coupled to a transmit antenna 120 radiates a signal to a base station.
• a high power amplifier (not shown) coupled to a transmit antenna 120 radiates a signal to a base station.
• the techniques of spread spectrum modulation and RF transmission are well known art to one familiar with spread spectrum communication systems.
• the demodulated symbols are de-interleaved by a Channel De- Interleaver 130 and input to a ⁇ Viterbi decoder 132.
• the decoded information bits are reconstructed into receive data blocks 136 and forwarded to the data terminal equipment at the receive end of the system.
• FIG. 2 a hardware system for a digital cellular mobile radio system is shown which implements an embodiment of the present invention.
• a reverse link is illustrated although the same block diagram represents a forward link.
• CDMA Code Division Multiple Access
• TDMA Time Division Multiple Access
• Transmit data blocks 202 from data terminal equipment is segmented and framed at a Segmentation Processor 204 into fixed frame length and applied to a Turbo Code encoder 208.
• An output from the encoder 208 is fed to a Channel Interleaver 212 to pseudo-randomize the code symbols.
• the Channel Interleaver 212 provides output to a Spread Spectrum Modulator 214 which uses a user specific PN-code from a PN Generator 216 to create a spread spectrum signal, carried on a RF carrier to a mobile RF transmitter 218.
• the channel interleaver 212 is distinguished from a Turbo Code interleaver (not shown) which is a component of the encoder 208.
• the mobile RF Transmitter 218, coupled to a Transmit Antenna 220, uses a high power amplifier (not shown) at the Transmit Antenna 220 to radiate the signal to the base station.
• a signal from the mobile station received at a base receive antenna 222 is amplified a base RF receiver 224 and demodulated m a spread Spectrum demodulator 228, which uses the same PN-code as used by the mobile RF transmitter 218, to de-spread the signal.
• the demodulated symbols are de- mterleaved by the Channel DE-Interleaver 230, and input to the Turbo Code decoder 232.
• Decoded information bits from Turbo Code decoder 232 are reconstructed at a Reconstruction Processor 234 into receive data blocks 236 and forwarded to the data terminal equipment at the receive end.
• the basic structure of a Turbo Code is characterized by the parallel concatenation of two simpler constituent codes at encoder #1 306 and encoder #2 308.
• Both constituent encoders i.e., encoder #1 306 and encoder #2 308 process the same information bit stream 302, but the encoder #2 308 processes information bits 302 in a different order than the order in which encoder #1 306 processes the information bits 302, since the Interleaver 304 reorders the information bits in a pseudo-random manner before they reach encoder #2 308 (the constituent encoder 308) .
• This arrangement reduces the likelihood that a sequence of information bits 302 causing encoder #1 306 to produce a low- Hamming weight output 310 would also cause encoder #2 308 to do the same with its output 314, which makes possible the excellent performance of Turbo Codes.
• Both encoders 306, 308 produce, in addition to the information bits 302 (also referred to as systematic bits 302), parity bits 310, 314 which are punctured by puncturer 312 to achieve a desired overall Turbo Code rate. It is also possible to puncture systematic bits.
• the constituent codes of a Turbo Code are usually systematic, recursive convolutional codes.
• the simplest and most widely known recursive convolutional codes have rate 1/2 and transfer function:
• n(D) and d(D) are binary polynomials specifying the feed forward and feedback connections of the encoder, respectively .
• the rate of a Turbo Code is changed by changing the selection of output bits 310, 314 for puncturing or transmitting. In all the cases herein, a "1" indicates transmitting; a "0" indicates puncturing.
• G(D) [1, n_(D)/d(D), n 2 (D)/d(D)]. ⁇ sing two such constituent codes provides any Turbo Code rate between 1/5 and 1 through puncturing, or deleting.
• Each of the constituent codes are decoded separately using likelihood estimates of the other constituent decoder 406 or 416 as A priori' information.
• the constituent decoder 406, 416 must be of a soft-mput/soft-output type, such as the Maximum A Posteriori (MAP) algorithm, the sub-optimal Soft- Output Viterbi Algorithm (SOVA) , or variations. After both constituent decoders have processed the data, the process can be repeated.
• MAP Maximum A Posteriori
• SOVA sub-optimal Soft- Output Viterbi Algorithm
• turbo decoders 406, 416 are usually limited to a fixed number of iterations consistent with the implementation complexity and performance objectives of the system.
• Figure 4 is a general block diagram of a turbo decoder.
• Soft information regarding the information bits 404, parity bits for the first encoder 402, and parity bits of the secon ⁇ encoder 402' are received from the demodulator.
• a first decoder 406 uses received information bits 404 and received parity bits 402 to produce a soft decision 408 on information bits.
• the soft decision 408 is interleaved by an interleaver 412, the output of which s soft decision 414.
• Soft decision 414 is fed to a second decoder 416 as a priori information.
• the second decoder 416 accepts the soft decision 414 described above and produces an improved soft decision 420 on information bits which are then interleaved by an mterleaver 422 and fed to the first decoder 406 as a priori information. The whole process is repeated as many times as desired. Final output 420 is obtained by making hard decisions or the soft decisions out of the first or second decoder.
• a single mother Turbo Code and various puncturing patterns are sought to derive uniformly good codes for various code rates and information block sizes.
• a methodology for determining universal constituent codes is developed by first limiting the initial pool of possible universal constituent codes in accordance with trade-off studies between performance and implementation complexity.
• performance studies using different state codes have shown that eight-state constituent codes provide a good performance trade-off.
• Universal constituent codes are first optimized according to the primary code rate of the targeted application. For example, in the case of CDMA data communications, separate optimizations can be done for the forward and reverse links since the reverse links usually requires lower code rates for higher coding gain.
• G(D) [1, n(D)/d(D)], where d(D) is a primitive polynomial and n(D) starts with 1 and ends with D ;
• Table 1 lists the determined denominator polynomials d(D) and numerator polynomials n(D) in octal notation. There are twelve constituent code candidates considered for initial screening purposes . Table 1. Candidate 8-State Constituent Encoders of Rate 1/2
• Each of the twelve (12) polynomials is expressed in octal form in Table 1, and has a corresponding binary and polynomial notation.
• the binary equivalent, for example of octal 13, is binary 1011.
• Binary 1011 corresponds to a polynomial
• the candidate Turbo Codes are simulated with an interleaver size of 1000 bits and three decoder iterations.
• the preliminary screening which results are shown in Figure 5 and Figure 6, evaluates the Bit Error Rate (BER) versus Ebi/No performance of all candidate Turbo Codes of rate 1/2 and rate 1/3 as it is described above. Measurement of Ebi/No is equivalent to a relative SNR.
• Table 2 shows the approximate SNR loss for simulated data due to using a non-optimized code at rates 1/2 and 1/3 and Interleaver depths of 512, 1024, 2048, and 3072 bits .
• pairs denoted as 31-33 and 31-27 are also shown in sample Figures 7 and 8 using four (4) decoder iterations for each sixteen-state code in order to provide similar complexity comparison with the eight-state codes using eight (8) decoder iterations.
• Eight-state codes with eight iterations out perform sixteen state codes with four iterations significantly.
• This constituent code is thus selected as the basis for Turbo Code designs where higher code rates such as 1/2 and 1/3 are dominant .
• rate 1/3 constituent codes are determined. Similar to the rate 1/2 constituent codes, rate 1/3 constituent code candidates are identified in Table 3 below for building near optimal Turbo Code rates of 1/4 and 1/5. For this case, the constituent code candidates for a Turbo Code must have three (3) polynomials instead of two (2).
• the puncturing patterns of Figure 9, namely 910, 920, 930 and 940 are selected based upon the previously mentioned design principles, to meet stipulated code rates.
• each of the three (3) code triads of Table 3 is combined with the four (4) puncturing patterns 910, 920, 930 and 940, of Figure 9 to produce twelve (12) possible Turbo Codes to be evaluated with simulated data shown in Figure 10 through 12 for a fixed Interleaver depth of 512, for example.
• Turbo Code B Constituent Code No. 2 with puncturing Pattern No. 1
• Turbo Code C Constituent Code No. 3 with puncturing Pattern No. 1.
• One of the Turbo Codes of Codes A through C is next selected for further evaluation using simulated data at various additional Interleaver frame sizes to verify that the puncturing patterns are also good at other Interleaver depths.
• Figure 14 shows the BER/FER performance of simulated data using the three rate 1/4 Turbo Code Candidates A through C at an Interleaver depth of 512 bits. Consistent results are also achieved at Interleaver sizes 1024, 2048 and 3072 bits.
• a rate 1/4 Turbo Code candidate is selected from Candidate Turbo Codes A through C which provides the best overall performance at all Interleaver depths, m the simulation resulting m Figure 14 and analogous figures, such as those depicted in Appendix A.
• rate 1/4 Turbo Code optimization based on BER performance gives a different result than optimization based on FER performance.
• Turbo Code B has the best overall FER performance and Turbo Code C the best overall BER performance, for the simulated data.
• Figure 15 shows the performance of Turbo Code B as compared to other puncturing schemes .
• FER optimized Turbo Code B is selected as the basis for the design since FER performance is usually the more important criteria for data services.
• Turbo Code A can be punctured to give the same universal Turbo Code identified previously as optimal for rate 1/3 (by puncturing all parity bits from the n 2 (D) polynomial) .
• Turbo Code A is the preferred choice for the forward lm ⁇ rate 1/4 codes in order to have a single universal mother code to implement all of the different code rates.
• rate 1/3 and rate 1/2 channel coding may be required for some of the highest rate data channels.
• a universal Turbo Code for rate 1/4, rate 1/3 and rate 1/2 can be designed, wherein the underlying constituent code is the same and only the puncturing pattern used is different. The method for generating the higher rate Turbo Codes from the rate 1/3 constituent code follows.
• Figure 16 shows seven (7) basic puncturing patterns that can be used to produce a rate 1/3 Turbo Code and four (4) basic puncturing patterns to produce a rate 1/2 Turbo Code.
• the seven (7) rate 1/3 patterns, 1602 through 1614 in block diagram 1600 show the consecutive information puncturing oit patterns, 1620, 1626, and the four (4) corresponding row parity bit puncturing patterns 1622, 1624, 1628, and 1630, for the two (2) encoder puncturing block patterns 1616 and 1618.
• the pattern "1111" shown in row 1620 always transmits all the information bits from encoder 1.
• the pattern "0000" of row 1626 always punctures the information b ts that enter by encoder No. 2. This is because it is not necessary to transmit the information bit twice.
• Patterns 2 and 5 are selected based upon curves 1710 and 1720, as having the best and next best overall relative FER, respectively.
• Pattern 2 is then selected as the best performer over the various Interleaver depths from further simulations analogous to that of Figure 17 at additional Interleaver sizes for 1024, 2048 and 3072 bits.
• Rate 1/2 Codes can also be optimized at lower rate codes fcr similar compatibility as described above.
• Figure 18 compares the BER and FER simulated performance of all the rate 1/2 Turbo Codes at an Interleaver depth of 512 bits.
• Figure 18 is generated using Constituent Code No. 2 and the four (4) puncturing patterns shown in Figure 16 for a rate 1/2 Turbo Code. Patterns 1 and 4 are determined to be the best based upon simulated curves 1810 and 1820 for FER performance.
• Patterns 1 and 4 are interleaver depths of 1024, 2048 and 3072 bits. Based upon the resulting performance/curves Pattern 1 is judged to be the best pattern for FER performance.
• Figure 19 shows a block diagram for the constituent encoder optimized m accordance with the previously described method for Turbo Code rates 1/2 and 1/3.
• Figure 20 shows the block diagram for the corresponding Turbo Code punctured to rate 1/4.
• Information bit stream X(t) 1902 is received at a switch 1922, and is processed in accordance with several modular adders 1904, 1908, 1920, 1910, 1914, 1918, 1919, and several shift registers 1906, 1912 and 1916 which are hard-wired to represent two (2) numerator polynomials and one denominator polynomial .
• a first numerator polynomial over a denominator polynomial, represented by "1101" is hardwired to return output Y 0 (t) by combining: X(t) 1992 with a result of modulator adder 1920 to create a first bit (t); the modular sum (second bit) of shift register 1906 and W(t) from the modular adder 1908; another zero bit (third bit) indicated by the lack of connection to the register 1912; and the modular sum (fourth bit) of another register 1916 and a result of modular adder 1908 from modular adder 1998.
• a second numerator polynomial over a denominator polynomial, represented by "1111”, is hardwired to return output Y ⁇ (t) by combining: X(t) 1902 with a result of adder 1920 to create a first bit W(t); adding contents of a further register 1906 to W(t) with the contents of the modular adder 1910 (second bit) ; adding contents of the register 1912 a result of adder 1710 with the modular adder 1914 (third bit) ; and adding contents of the other register 1916 to a result of adder 1914 with modular adder 1919 (fourth bit) .
• Output Y 0 (t) represents the output from numerator Polynomial No. 1 and the denominator polynomial.
• Output Y ⁇ (t) represents numerator Polynomial No. 2 and denominator polynomial.
• the optimal puncturing matrices shows a "1" for transmitted bits and a "0" for punctured bits.
• Exemplary Figure 20 shows encoder 2000 with incoming bit X(t) and Interleaver 2002 passing interleaved bits X (t) to encoder 2006 to produce output bit X (t) and parity bits Y D (t) , and Yi (t) . None of the interleaved bits x (t) are processed in the rate 1/4 encoder 2004, only in the second rate 1/4 encoder 2006.
• Block 2010 shows the puncturing pattern matrices. More complicated puncturing patterns can be used to achieve other possible coding rates. For example, it is possible to select optimal puncturing patterns to achieve rate 3/8 and 4/9 for Turbo Codes optimized at rates 1/2 and 1/3; ana to achieve rates 2/9 and 3/8 for Turbo Codes optimized at rate 1/4 using the preferred Turbo Codes identified in the invention.
• FIG. 10 Similar to Figure 9 the block diagram for an optimal Turbo Code rate 3/8 uses the rate 1/3 mother constituent code of Figure 20.
• the encoder for the constituent code of Figure 20 is shown in Figure 19.
• the puncturing pattern of the rate 3/8 Turbo Codes shown Figure 21 punctures 1 out of every 6 bits associated with the first numerator polynomial from both encoders to generate a rate 3/8 Turbo Code.
• the second pattern is a extension of the first pattern allowing both constituent encoders to have the same rate, namely 6/11.
• the extension pattern duplicates the same pattern (matrix) for another three (3) bits but moves the location of one transmission bit from one encoder to another, essentially flipping a "1" in one encoder while flipping a "0" in another encoder at the analogous locations .
• Figure 22 shows the performance of these patterns at an Interleaver depth of 512 bits. Based on these and analogous curves at 1024, 2048 and 3072 Interleaver depths, Pattern 2 is chosen to implement the rate 3/8 Turbo Codes.
• Figure 23 shows the puncturing patterns selected for rate 4/9 Turbo Codes used with the mother of codes of Figure 20.
• the second pattern is an extension of tne first, which allows both constituent encodes to have the same rate, namely 8/13. — ⁇ y—
• Figure 24 snows the corresponding performance curves.
• Pattern 2 is chosen to implement the rate 4/9 Turbo Codes.
• the preferred puncturing patterns for various code rates are :
• This universal Turbo Code design supports a minimum code rate equal to 1/3 (instead of 1/5) .
• the corresponding preferred set of puncturing patterns are:
• Rate 1/2 alternately puncturing parity bits nl from both encoders; 3. Rate 3/8 - puncturing one out of every 6 parity bits ni from both encoders; and
• Figure 26 is an encoder block diagram for the preferred rate 1/4 Turbo Code.
• the second parity bits are alternately punctured by the two constituent encoders.
• the preferred puncturing patterns described in earlier section can then be applied to produce rate 1/3 and rate 1/2 Turbo Codes.
• Figure 27 shows the puncturing patterns for a 2/9 reverse link code.
• Three (3) different patterns are compared by performance curves in Figure 28 and analogous curves, such as those set forth, for example, in Appendix A, showing performance at various frame Interleaver sizes. From a Pattern 2 FER curve 2810 and analogous curves, Pattern No. 2 is chosen as the optimal FER pattern for rate 2/9.
• Figure 29 illustrates six (6) initial screening puncturing patterns for optimizing a rate 3/8 reverse link codes.
• the performance of these patterns is simulated at a fixed Interleaver length of 512 bits . Based on the simulation, Pattern 5 and Pattern 6, are chosen as the optimal puncturing patterns for further review.
• Two more extension Patterns 7 and 8 of the above Patterns 5 and 6 duplicate the same patterns for another three information bits, but move the location of one of the transmission bits in the parity sequence from one encoder pattern to another.
• the extension allows both constituent encoders to have the same rate, namely 6/11 at each encoder.
• Figure 30 shows exemplary performance curves of the above four (4) candidate puncturing Patterns 5, 6, 7 and 8 for rate 3/8 Turbo Codes. Based on these results, a Pattern 8 FER curve 3010 and analogous curves such as those shown, for example, in Appendix A, demonstrate that Pattern 8 is the optimal puncturing pattern for rate 3/8 Turbo Codes.
• ni represents output bits associated with a first numerator polynomial
• n 2 represents output bits associated with a second numerator polynomial
• Rate 3/8 - puncture parity bits ni and one out of every six parity bits n 2 are equivalent.
• the set of preferred universal Turbo Codes described heretofore in this invention provide a suite of flexible high performance channel codes that are well suited for sophisticated data communication systems requiring a variety of low speed and high speed data services .
• This suite of preferred universal Turbo Codes allows the crafting of different Turbo encoding schemes to meet the specific requirements of particular data communication systems.
• either of the following two FEC schemes is well-suited and recommended for a synchronous CDMA data communications network (such as the third generation CDMA 2000 system currently under development) :
• either of the following FEC schemes is well-suited and recommended for an asynchronous CDMA data communications network (such as the third generation UTRA system currently in development in Europe and Asia) : 1) The preferred universal Turbo Code optimized at code rates 1/2 and 1/3, described above, along with a subset of associated puncturing patterns, on both the forward and reverse links;
• the universal Turbo Codes identified for high-speed data services are especially suitable for third generation CDMA cellular mobile radio systems but could be easily applied to other systems as well.
• FOCTC Frame Oriented Convolutional Turbo Coding
• the exemplary preferred puncturing patterns described herein can be refined or modified m various ways by those skilled m the art. For example, a cyclic shift of a preferred puncturing pattern offers substantially equivalent performance as the preferred puncturing pattern described herein. Furthermore, specific data communication systems may require different and additional puncturing patterns to support rate matching. These puncturing patterns may be designed accordance with the teachings of the present invention.
• one embodiment includes a set of rate- compatible Turbo Codes at various code rates of 1/5, 1/4, 1/3 and 1/2 and also at various Interleaver depths from 512 to 3072 bits.
• Another preferred embodiment provides multiple sets of Turbo Codes optimized under different conditions allowing a system designer to trade off degree of universality (and thus, complexity) with performance and vice a versa.
• the selection of sets of rate-compatible Turbo Codes is based upon the universal constituent encoder described herein below.
• the universal constituent encoder of the present invention provides optimal or nearly optimal performance over a large range of code rates and Interleaver depths. Different optimization criteria such as reverse link or forward link dominance and degree of universality, result m different sets of rate-compatible Turbo Codes.
• the sets of rate-compatible codes are especially well suited for use in hybrid ARQ schemes applied m satellite broadcast and telephony.
• Several preferred embodiments comprise different sets of rate-compatible codes based upon different universal constituent codes and different rate puncturing patterns optimized according to different design criteria.
• the first two (2) sets are optimized for high-rate Turbo Codes, wherein higher-rates dominate.
• the second two (2) sets are optimized for lower-rate codes, where lower-rates dominate.
• the sets are referred to herein as Sets A-D.
• the first preferred set is derived from a best universal constituent code of rate 1/2.
• the second set is derived from another best constituent code of rate 1/3 which is also compatible with the universal constituent code of rate 1/2.
• the first set, "Set A” has two generator polynomials while the second set, “Set B” has three generator polynomials of which two are in common with “Set A”.
• “Set B” is optimally compatible with "Set A”, reducing the amount of design changes for encoding and decoding.
• the thir ⁇ polynomial is necessary for the additional encoder parity bits of a rate 1/3 or lower Turbo Code.
• the second set, "Set B” includes “Set A” and also extends the ramily of Turbo Codes to rate 1/5 and higher.
• a third and fourth preferred set of rate- compatible Turbo Codes are optimized for lower-rates, in particular for rate 1/4.
• "Set C” and “Set D”, respectively, also use three generator polynomials which are the same as those in “Set B”, but a different order.
• Rate-Compatible Set Derived from Universal Constituent Codes of Rate 1/2 Set A (Rates 1/3, 1/2)
• Rate-compatible Set A comprises generator polynomials corresponding to octal pairs 13-15, wherein a denominator polynomial is 1+D +D (octal 13) and a numerator polynomial is 1+D+D (octal 15) .
• the puncturing patterns are designed such that all bits transmitted by a rate of 1/2 code (or higher rate) of the set are also transmitted by a rate 1/3 code, or lower rate code of the set.
• Exemplary preferred patterns as demonstrated by simulations and design principles are:
• Figure 31 shows a block diagram for the Set A constituent encoder.
• modular adders 3104, 3108 (connected to shift register 3106) , and 3116 (connected to shift register 3114) comprise the encoding apparatus for a numerator polynomial representing octal 15 or binary 1101.
• Modular adders 3104, 3108, 3112 and 3116 add the contents of shift registers 3106, 3110 and 3114 and X(t) in an analogous fashion as Figure 19.
• the Turbo Codes of Set A compare favorably in performance to the best known 256-state convolutional codes, when simulated for the critical performance parameters.
• Rate-Compatible Set Derived from Universal Constituent Code of Rate 1/3 Set B (Rates 1/2, 1/3, 1/4, 1/5)
• a second best individual rate 1/2 constituent code is chosen from Table 2.
• this method results in two (2) octal pairs with an overlap. Both octal pairs, octal 13-15 and octal 13-17 provide uniformly excellent performance.
• Combining the two (2) pairs together provides three (3) generator polynomials, comprising the triad octal 13-15/17.
• the denominator polynomial is 1+D+D 3 (octal 13); the first numerator polynomial is 1+D " +D J (octal 15); and the second numerator polynomial is 1+D+D +D (octal 17).
• the preferred design for Set B comprises these generator polynomials above for all Interleaver depths and for Turbo Code rates 1/2, 1/3, 1/4 and 1/5.
• the puncturing patterns are designed such that all bits transmitted at any higher rate Turbo Code of Set B are also transmitted at any lower code rate of Set B.
• Exemplary preferred patterns as demonstrated by simulations and design principles, are:
• Rate 1/2 always puncture the second numerator parity bits, n 2 and alternately puncture the first numerator parity bits, ni .
• Turbo Code Set B is the preferred design choice when strict rate- compatibility is required in all code rates.
• the optimal Turbo Codes for rates 1/4 and 1/5 are selected based upon the candidate constituent codes listed in Table 3 which are selected based upon the results of Table 2 as previously described above.
• Constituent Code No. 1 of Table 3, or octal 13-15/17 is the basis for code Set A.
• each three (3) mother Turbo Code triad of Table 3 is considered with each of four (4) different puncturing patterns to obtain a newly optimized 1/4 Turbo Code.
• Turbo Codes A, B, and C are found optimal from respective performance curves 1010, 1110 and 1210 of Figures 10, 11 and 12 respectively.
• Figure 14 shows a sample corresponding performance of the triads matched with the selected puncturing patterns at 512 bits. From Figure 14 and analogous results for other Interleaver sizes, the best overall BER performance at all simulated Interleaver depths are used as a final design criterion to determine the optimal candidate.
• Rate-Compatible Set Derived from Rate 1/4 Turbo Code Set C (Rates 1/5, 1/4, 1/3)
• Turbo Code Set C implements Code No. 3 and Pattern No. 1 (Turbo Code C) from Figure 9 in accordance with performance curve 1310 of Figure 14 and analogous curves for other Interleaver sizes.
• Turbo Code Set C comprises a generator polynomial from Table 3 including denominator polynomial 1+D+D +D , first
• Rate-Compatible Set Derived from Rate 1/4 Turbo Code Set D (Rates 1/5, 1/4)
• Turbo Code Set D comprises a single constituent code for all Interleaver depths and Turbo Code rates 1/4 and 1/5.
• Turbo Code Set D implements Code No. 1 with Pattern No. 2 (Turbo Code A) from Figure No. 9 in accordance with performance curve 1420 of Figure 14 and analogous curves at other Interleaver sizes.
• the set comprises generator polynomials including a denominator polynomial d, 1+D+D , a first numerator polynomial, n x , 1+D +D " and second numerator polynomial, n 2 , 1+D+D +D .
• More complicated puncturing patterns may be used in convolutional coding to achieve any code rate greater than or equal to that of the base Turbo Code in each rate-compatible Set.
• rates higher than 1/2 or intermediate rates such as 5/12 can be achieved.
• puncturing patterns this can often be done in a rate- compatible manner without sacrificing error correction performance .
• An exemplary application of the rate-compatible turbo codes described herein is for rate matching in which the code rate is selected to match the payload of an available physical channel.
• the data services use the same basic channel encoding but may not use the same physical channel, especially if the quality of service specifications are different for the different data services.
• this is accomodated by selecting different puncturing patterns to produce the code rate compatible with the physical channel. If the puncturing patterns are rate-compatible, the selection of code rate does not have to be completed by single decision unit at a single point in time. Instead, the decision can be distributed in time as well as across decisioning units.
• the turbo encoder first produces the coded output sequence corresponding to the lowest code rate to be supported by the system.
• all the possible parity bits might be output initially.
• an initial puncturing might be performed, by one puncturing unit in response to say quality-of-service (QoS) considerations for the given data service.
• the data service may permit a range of quality-of-service in which, for example, the highest quality within that range does not require the lowest possible code rate available in the system but some intermediate code rate, and the lowest quality within that range can allow an even higher code rate.
• the first puncturing unit removes coded bits in accordance with the puncturing pattern corresponding to the lowest rate in order to provide the highest quality within the data service's QoS range.
• the non- punctured coded bits are output to the rest of the system for further processing.
• a decision might be made to adjust the code rate higher for that message based on dynamic traffic management considerations .
• a physical channel with smaller payload might be substituted, on a temporary as-needed basis, for the physical channel nominally associated with that data service in order to accomodate messages from a higher priority data service.
• the higher code rate is achieved by performing a second puncturing in accordance with the puncturing pattern associated with the new code rate. Since the puncturing patterns are rate-compatible, it is not necessary to regenerate coded bits deleted by the first puncturing unit; the second puncturing unit simply deletes those bits specified by the higher rate puncturing pattern that have not already been deleted by the first puncturing unit.
• a second exemplary application of the rate-compatible turbo codes described herein is for incremental redundancy schemes such as error control based on ARQ protocols.
• the turbo encoder first produces coded output corresponding to the highest code rate available in the system.
• the receiver may or may not be able to successfully decode the message. If the message is not successfully decoded, the receiver typically sends a negative acknowledgement (NAK) back to the transmitter to request further transmissions to aide the decoding of that packet.
• NAK negative acknowledgement
• the extra encoded bits produced by one of the lower-rate compatible encodings for that packet can be sent to augment the information available to the decoder at the receiver.
• the decoder uses that new information along with the original information received for that packet to perform the decoding.
• the effect is as if the packet had been originally encoded with the lower rate code. This process can be repeated until the packet is successfully decoded. By only sending the excess coded bits each retransmission, the traffic loading required for re-transmission is significantly lowered.
• the criterion for designing a good convolutional code is different from the conventional approach of maximizing minimum Hamming distance, when the convolutional code is used as a constituent code in turbo codes.
• the systematic, recursive convolutional code should be designed [1] so as to maximize the minimum parity weight corresponding to information sequences of weight two that cause the trellis diverge from the zero state and later remerge to it.
• THIS DOCUMENT CONTAINS PROPRIETARY INFORMATION ANO EXCEPT WITH WRITTEN PERMISSION OF HUGHES AIRCRAFT COMPANY, SUCH INFORMATION SHALL NOT BE PUBUSHED, OR DISCLOSED TO OTHERS. OR USED FOR ANY PURPOSE AND THE DOCUMENT SHALL NOT BE DUPLICATED IN WHOLE OR IN PART.
• THIS DOCUMENT CONTAINS PROPRIETARY INFORMATION ANO EXCEPT WITH WRTTTEN PERMISSION OF HUGHES AIRCRAFT COMPANY, SUCH INFORMATION SHALL NOT BE PUBUSHEO. OR DISCLOSED TO OTHERS. OR USED FOR ANY PURPOSE AND THE DOCUMENT SHALL NOT BE DUPLICATED IN WHOLE OR IN PART.
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• Appendix Fig. A-6 Selected rate 1/2 turbo codes on AWGN channel, 512 bit frame size
• Appendix Fig. A-7 Selected rate 1 2 turbo codes on AWGN channel, 1024 bit frame size
• THIS DOCUMENT CONTAINS PROPRIETARY INFORMATION ANO EXCEPT WITH WRITTEN PERMISSION OF HUGHES AIRCRAFT COMPANY. SUCH INFORMATION SHALL NOT BE PUBUSHED. OR DISCLOSED TO OTHERS. OR USED FOR ANY PURPOSE ANO THE DOCUMENT SHALL NOT BE DUPUCATED IN WHOLE OR IN PART.
• Appendix Fig. A-9 Selected rate 1 2 turbo codes on AWGN channel, 3072 bit frame size
• Appendix Fig. A- 10 Selected rate 1/3 turbo codes on AWGN channel, 512 bit frame size
• Appendix Fig. A-12 Selected rate 1 3 turbo codes on AWGN channel, 2048 bit frame size
• Appendix Fig. A-13 Selected rate 1/3 turbo codes on AWGN channel, 3072 bit frame size
• THIS DOCUMENT CONTAINS PROPRIETARY INFORMATION ANO EXCEPT WITH WRITTEN PERMISSION OF HUGHES AIRCRAFT COMPANY. SUCH INFORMATION SHA ⁇ NOT BE PUBUSHED. OR DISCLOSED TO OTHERS. OR USED FOR ANY PURPOSE AND THE DOCUMENT SHAU NOT BE DUPUCATEO IN WHOLE OR IN PART. THIS LEGEND SHAU BE APPLIED TO AU DOCUMENTS CONTAINING THIS INFORMATION.
• THIS DOCCMENT CONTAINS PROPRIETARY INFORMATION ANO EXCEPT WITH WR ⁇ TEN PERMISSION OF HUGHES AIRCRAFT COMPANY. SUCH INFORMATION SHAU NOT-BE PUBUSHED, OR DISCLOSED TO OTHERS. OR USED FOR ANY PURPOSE ANO THE DOCUMENT SHAU NOT BE DUPUCATEO IN WHOLE OR IN PART.
• THIS LEGEND SHALL BE APPLIED TO AU OOCUMCNTS CONTAINING THIS INFORMATION.
• THISOOCUMENT CONTAINS PROPRIETARY INFORMATION AND EXCEPT WITH WR ⁇ TEN PERMISSION OF HUGHES AIRCRAFT COMPANY. SUCH INFORMATION SHAU. NOT BE PUBUSHED. OR OISCLOSED TO OTHERS, OR USED FOR ANY PURPOSE AND THE DOCUMENT SHAU NOT BE DUPUCATEO IN WHOLE OR IN PART.
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