A Soft-Input Soft-Output APP Module for Iterative Decoding of Concatenated Codes
Concatenated coding schemes consist of the combination of two or more simple constituent encoders and interleavers.
turbo code↗
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High rate concatenated coding systems using multidimensional bandwidth-efficient trellis inner codes
A concatenated coding system using two-dimensional trellis-coded MPSK inner codes and Reed-Solomon outer codes for application in high-speed satellite communication systems was proposed previously by the authors (1989). The authors extend their results to systems using symbol-oriented, multidimensional, trellis-coded MPSK inner codes. The concatenated coding systems are divided into two classes according to their achievable effective information rates. The first class uses multidimensional trellis-coded 8-PSK inner codes and achieves effective information rates around 1 b/dimension (spectral efficiency 2 b/s/Hz). The second class employs multidimensional trellis-coded 16-PSK inner codes and provides effective information rates around 1.5 b/dimension (spectral efficiency 3 b/s/Hz). Both classes provide significant coding gains over an uncoded reference system with the same effective information rate as the coded system. The results show that the symbol-oriented nature of multidimensional inner codes can provide an improvement of up to 1 dB in the overall performance of a concatenated coding system when these codes replace bit-oriented two-dimensional codes.
Deng, Robert H.↗
Continuous MAP Algorithms and Their Applications to Decode Parallel and Serial Code Concatenations
Concatenated coding schemes with interleavers consist of the combination of two simple constituent encoders and an interleaver. The parallel concatenation known as.
algorithms decoding parallel code concatenations s↗
A note on the performance of concatenated codes
Inner code concatenation with outer code to yield error probability uniform bound with exponential decrease
Savage, J. E.↗
High rate concatenated coding systems using bandwidth efficient trellis inner codes
High-rate concatenated coding systems with bandwidth-efficient trellis inner codes and Reed-Solomon (RS) outer codes are investigated for application in high-speed satellite communication systems. Two concatenated coding schemes are proposed. In one the inner code is decoded with soft-decision Viterbi decoding, and the outer RS code performs error-correction-only decoding (decoding without side information). In the other, the inner code is decoded with a modified Viterbi algorithm, which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, whereas branch metrics are used to provide reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. The two schemes have been proposed for high-speed data communication on NASA satellite channels. The rates considered are at least double those used in current NASA systems, and the results indicate that high system reliability can still be achieved.
Deng, Robert H.↗
Probability of undetected error after decoding for a concatenated coding scheme
A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.
Costello, D. J., Jr.↗
Herative Decoding of Serially Concatenated Codes with Interleavers and Comparison with Turbo Codes
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.
low-complexity iterative decoding simulation compa↗
Reliability and throughput analysis of a concatenated coding scheme
The performance of a concatenated coding scheme for error control in ARQ systems is analyzed for both random-noise and burst-noise channels. In particular, the probability of undetected error and the system throughput are calculated. In this scheme, the inner code is used for both error correction and error detection, and the outer code is used for error detection only. Interleaving/deinterleaving is assumed within the outer code. A retransmission is requested if either the inner code or the outer code detects the presence of errors. Various coding examples are considered. The results show that concatenated coding can provide extremely high system reliability (i.e., low probability of undetected error) and high system throughput.
Deng, Robert H.↗
Serial and Hybrid Concatenated Codes with Applications
Analytical bounds on the performance of concatenated codes on a tree structure are obtained. Analytical results are applied to examples of parallel concatenation of two codes (turbo codes), serial concatenation of two codes, hybrid concatenation of three codes, and self concatenated codes, over AWGN and fading channels.
AWGN MPSK modulations Rayleigh fading channels↗
Capacity and cutoff rate calculations for a concatenated coding system
A model is developed for a concatenated coding system, and from it the overall channel cutoff rate and capacity is found using random coding arguments. The effects of interleaving between the inner and outer codes and of the availability of side information to the outer decoder are considered. The performance of several specific concatenated coding systems is calculated and used for comparison with the random coding results. From the analysis, a number of general conclusions regarding the design of concatenated coding systems are presented. All the results are derived assuming a block inner code.
Herro, Mark A.↗
Performance of Galileo's concatenated codes with nonideal interleaving
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.
Cheung, K.-M.↗
Concatenated coding for space communications
Concatenated coding technique for PCM deep space communications
Miller, W.↗
Frame error rate of the NASA concatenated coding system
For a concatenated coding system, the effect of interleaving depth on interleaved frame-error rate is compiled by simulation. Comparisons are made for three different inner convolutional codes; all three systems have a (255,223) 8-bit Reed-Solomon code as an outer code. For all the inner convolutional codes tested, an interleaving depth smaller that 4 causes substantial loss.
Swanson, L.↗
Concatenated coding systems employing a unit-memory convolutional code and a byte-oriented decoding algorithm
Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively small coding complexity, it is proposed to concatenate a byte oriented unit memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real time minimal byte error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.
Lee, L. N.↗
Concatenated coding systems employing a unit-memory convolutional code and a byte-oriented decoding algorithm
Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively modest coding complexity, it is proposed to concatenate a byte-oriented unit-memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real-time minimal-byte-error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.
Lee, L.-N.↗
A low-complexity and high performance concatenated coding scheme for high-speed satellite communications
This report presents a low-complexity and high performance concatenated coding scheme for high-speed satellite communications. In this proposed scheme, the NASA Standard Reed-Solomon (RS) code over GF(2(exp 8) is used as the outer code and the second-order Reed-Muller (RM) code of Hamming distance 8 is used as the inner code. The RM inner code has a very simple trellis structure and is decoded with the soft-decision Viterbi decoding algorithm. It is shown that the proposed concatenated coding scheme achieves an error performance which is comparable to that of the NASA TDRS concatenated coding scheme in which the NASA Standard rate-1/2 convolutional code of constraint length 7 and d sub free = 10 is used as the inner code. However, the proposed RM inner code has much smaller decoding complexity, less decoding delay, and much higher decoding speed. Consequently, the proposed concatenated coding scheme is suitable for reliable high-speed satellite communications, and it may be considered as an alternate coding scheme for the NASA TDRS system.
Lin, Shu↗
Concatenated coding for low date rate space communications.
In deep space communications with distant planets, the data rate as well as the operating SNR may be very low. To maintain the error rate also at a very low level, it is necessary to use a sophisticated coding system (longer code) without excessive decoding complexity. The concatenated coding has been shown to meet such requirements in that the error rate decreases exponentially with the overall length of the code while the decoder complexity increases only algebraically. Three methods of concatenating an inner code with an outer code are considered. Performance comparison of the three concatenated codes is made.
Chen, C. H.↗
Analysis, Design and Iterative Decoding of Double Serially Concatenated Codes with Interleavers
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.
encoder interleaver permuting algorithm concatenat↗