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A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, and an inner encoder whose input words are the permuted outer codewords.
A method has been developed of computing bounds on the performance of a code comprised of two linear binary codes generated by two encoders serially concatenated through an interleaver. Originally intended for use in evaluating the performances of some codes proposed for deep-space communication links, the method can also be used in evaluating the performances of short-block-length codes in other applications. The method applies, more specifically, to a communication system in which following processes take place: At the transmitter, the original binary information that one seeks to transmit is first processed by an encoder into an outer code (Co) characterized by, among other things, a pair of numbers (n,k), where n (n > k)is the total number of code bits associated with k information bits and n k bits are used for correcting or at least detecting errors. Next, the outer code is processed through either a block or a convolutional interleaver. In the block interleaver, the words of the outer code are processed in blocks of I words. In the convolutional interleaver, the interleaving operation is performed bit-wise in N rows with delays that are multiples of B bits. The output of the interleaver is processed through a second encoder to obtain an inner code (Ci) characterized by (ni,ki). The output of the inner code is transmitted over an additive-white-Gaussian- noise channel characterized by a symbol signal-to-noise ratio (SNR) Es/No and a bit SNR Eb/No. At the receiver, an inner decoder generates estimates of bits. Depending on whether a block or a convolutional interleaver is used at the transmitter, the sequence of estimated bits is processed through a block or a convolutional de-interleaver, respectively, to obtain estimates of code words. Then the estimates of the code words are processed through an outer decoder, which generates estimates of the original information along with flags indicating which estimates are presumed to be correct and which are found to be erroneous. From the perspective of the present method, the topic of major interest is the performance of the communication system as quantified in the word-error rate and the undetected-error rate as functions of the SNRs and the total latency of the interleaver and inner code. The method is embodied in equations that describe bounds on these functions. Throughout the derivation of the equations that embody the method, it is assumed that the decoder for the outer code corrects any error pattern of t or fewer errors, detects any error pattern of s or fewer errors, may detect some error patterns of more than s errors, and does not correct any patterns of more than t errors. Because a mathematically complete description of the equations that embody the method and of the derivation of the equations would greatly exceed the space available for this article, it must suffice to summarize by reporting that the derivation includes consideration of several complex issues, including relationships between latency and memory requirements for block and convolutional codes, burst error statistics, enumeration of error-event intersections, and effects of different interleaving depths. In a demonstration, the method was used to calculate bounds on the performances of several communication systems, each based on serial concatenation of a (63,56) expurgated Hamming code with a convolutional inner code through a convolutional interleaver. The bounds calculated by use of the method were compared with results of numerical simulations of performances of the systems to show the regions where the bounds are tight (see figure).
The performance (bit-error rate vs. signal-to-noise ratio) of two different interleaving systems, block interleaving and the newer helical interleaving are compared. Both systems are studied with and without error forecasting. Without error forecasting, the two systems have identical performance. When error forecasting is used with shallow interleaving, helical interleaving gains, but less than 0.05 dB, over block interleaving. For higher interleaving depth, the systems have almost indistinguishable performance.
A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits and an inner encoder whose input words are the permuted middle codewords.
A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer code words bits, and an inner encoder whose input words are the permuted outer code words.
A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords.
In this paper, upper bounds to the average maximum-likelihood bit error probability of serially concatenated coding schemes are derived, design guidelines for the outer and inner codes that maximize the interleaver gain are presented, and finally, a highly-performing iterative decoding algorithm is proposed.
The Galileo spacecraft employs concatenated coding schemes with Reed-Solomon interleaving depth 2. The bit error rate (BER) performance of Galileo's concatenated codes, assuming different interleaving depths (including infinite interleaving depth) are compared. It is observed that Galileo's depth 2 interleaving, when used with the experimental (15, 1/4) code, requires about 0.4 to 0.5 dB additional signal-to-noise ratio to achieve the same BER performance as the concatenated code with ideal interleaving. When used with the standard (7, 1/2) code, depth 2 interleaving requires about 0.2 dB more signal-to-noise ratio than ideal interleaving.
Two interleaving schemes are presented for R-S Viterbi concatenated coding channels and several R-S code array synchronization configurations are investigated. A procedure for obtaining synchronization sequences for the R-S code array under specified conditions is developed and used to identify sequences with desirable properties. The two interleaving schemes are found to be comparable in terms of array synchronization.
Topics covered include: Software Tool Integrating Data Flow Diagrams and Petri Nets; Adaptive Nulling for Interferometric Detection of Planets; Reducing the Volume of NASA Earth-Science Data; Reception of Multiple Telemetry Signals via One Dish Antenna; Space-Qualified Traveling-Wave Tube; Smart Power Supply for Battery-Powered Systems; Parallel Processing of Broad-Band PPM Signals; Inexpensive Implementation of Many Strain Gauges; Constant-Differential-Pressure Two-Fluid Accumulator; Inflatable Tubular Structures Rigidized with Foams; Power Generator with Thermo-Differential Modules; Mechanical Extraction of Power From Ocean Currents and Tides; Nitrous Oxide/Paraffin Hybrid Rocket Engines; Optimized Li-Ion Electrolytes Containing Fluorinated Ester Co-Solvents; Probabilistic Multi-Factor Interaction Model for Complex Material Behavior; Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators; Compact Rare Earth Emitter Hollow Cathode; High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors; Rapid Active Sampling Package; Miniature Lightweight Ion Pump; Cryogenic Transport of High-Pressure-System Recharge Gas; Water-Vapor Raman Lidar System Reaches Higher Altitude; Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes; Wide-Field-of-View, High-Resolution, Stereoscopic Imager; Electrical Capacitance Volume Tomography with High-Contrast Dielectrics; Wavefront Control and Image Restoration with Less Computing; Polarization Imaging Apparatus; Stereoscopic Machine-Vision System Using Projected Circles; Metal Vapor Arcing Risk Assessment Tool; Performance Bounds on Two Concatenated, Interleaved Codes; Parameterizing Coefficients of a POD-Based Dynamical System; Confidence-Based Feature Acquisition; Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery; Universal Decoder for PPM of any Order; Algorithm for Stabilizing a POD-Based Dynamical System; Mission Reliability Estimation for Repairable Robot Teams; Processing AIRS Scientific Data Through Level 3; Web-Based Requesting and Scheduling Use of Facilities; AutoGen Version 5.0; Time-Tag Generation Script; PPM Receiver Implemented in Software; Tropospheric Emission Spectrometer Product File Readers; Reporting Differences Between Spacecraft Sequence Files; Coordinating "Execute" Data for ISS and Space Shuttle; Database for Safety-Oriented Tracking of Chemicals; Apparatus for Cold, Pressurized Biogeochemical Experiments; Growing B Lymphocytes in a Three-Dimensional Culture System; Tissue-like 3D Assemblies of Human Broncho-Epithelial Cells; Isolation of Resistance-Bearing Microorganisms; Oscillating Cell Culture Bioreactor; and Liquid Cooling/Warming Garment.
In this summary we present extremal average mutual information values carried by the extrinsic loglikelihood under the constraint of a given mean and variance while accounting for the consistency feature of loglikelihoods.
Self-concatenated trellis coded modulation with b(q-1) interleavers is a concatenated coded scheme based on only one rate bq/n convolutional code.
The Direct Broadcast Satellite-Radio (DBS-R) receiver is being developed for operation in a multipath Rayleigh channel. This receiver uses equalization and concatenated coding, in addition to open loop and closed loop architectures for carrier demodulation and symbol synchronization. Performance test results of this receiver are presented in both AWGN and multipath Rayleigh channels. Simulation results show that the performance of the receiver operating in a multipath Rayleigh channel is significantly improved by using equalization. These results show that fractional-symbol equalization offers a performance advantage over full symbol equalization. Also presented is the base-line performance of the DBS-R receiver using concatenated coding and interleaving.
Concatenated coding schemes with interleavers consist of the combination of two simple constituent encoders and an interleaver. The parallel concatenation known as.
In a proposed coding-and-modulation/demodulation-and-decoding scheme for a free-space optical communication system, an error-correcting code of the low-density parity-check (LDPC) type would be concatenated with a modulation code that consists of a mapping of bits to pulse-position-modulation (PPM) symbols. Hence, the scheme is denoted LDPC-PPM. This scheme could be considered a competitor of a related prior scheme in which an outer convolutional error-correcting code is concatenated with an interleaving operation, a bit-accumulation operation, and a PPM inner code. Both the prior and present schemes can be characterized as serially concatenated pulse-position modulation (SCPPM) coding schemes. Figure 1 represents a free-space optical communication system based on either the present LDPC-PPM scheme or the prior SCPPM scheme. At the transmitting terminal, the original data (u) are processed by an encoder into blocks of bits (a), and the encoded data are mapped to PPM of an optical signal (c). For the purpose of design and analysis, the optical channel in which the PPM signal propagates is modeled as a Poisson point process. At the receiving terminal, the arriving optical signal (y) is demodulated to obtain an estimate (a^) of the coded data, which is then processed by a decoder to obtain an estimate (u^) of the original data.
The capacity of an M-ary channel with N-ary coding is computed. It is found that the capacity of a very noisy channel is reduced by the factor (N-1)(log M)/(M-1)(log N). The results are applied to channels with noncoherent multifrequency shift keying and to concatenation of codes and interleaving.
The need for efficient space communication at very low bit error probabilities to the specification and implementation of a concatenated coding system using an interleaved Reed-Solomon code as the outer code and a Viterbi-decoded convolutional code as the inner code. Experimental results of this channel coding system are presented under an emulated S-band uplink and X-band downlink two-way space communication channel, where both uplink and downlink have strong carrier power. This work was performed under the NASA End-to-End Data Systems program at JPL. Test results verify that at a bit error probability of 10 to the -6 power or less, this concatenated coding system does provide a coding gain of 2.5 dB or more over the Viterbi-decoded convolutional-only coding system. These tests also show that a desirable interleaving depth for the Reed-Solomon outer code is 8 or more. The impact of this "virtually" error-free space communication link on the transmission of images is discussed and examples of simulation results are given.
Concatenated codes were long used as a practical means of achieving long block or constraint lengths for combating errors on very noisy channels. The inner and outer encoders are normally separated by an interleaver, so that decoded error bursts coming from the inner decoder are randomized before entering the outer decoder. The effectiveness of this interleaver is examined by calculating the cut-off rate of the outer channel seen by the outer decoder with and without interleaving. Interleaving never hurts the performance of a concatenated code, and when the inner code rate is near the cut-off rate of the inner channel, interleaving significantly improves code performance.