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It is shown how turbo codes and decoders can be used to improve the coding gain for deep-space communications, while decreasing the decoding complexity with respect to the large constraint length convolutional codes currently in use. Similar code constructions were used to build multiple-encoder turbo codes. This generalizes the turbo decoding concept to a truly distributed decoding system.
A description is given of multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders.
In this article, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially different from the decoder for two-code-based encoders. We analyze the effect of interleaver choice on the weight distribution of the code, and we describe simulation results on the improved performance of these new codes.
Bootstrap Hybrid Decoding (BHD) (Jelinek and Cocke, 1971) is a coding/decoding scheme that adds extra redundancy to a set of convolutionally encoded codewords and uses this redundancy to provide reliability information to a sequential decoder. Theoretical results indicate that bit error probability performance (BER) of BHD is close to that of Turbo-codes, without some of their drawbacks. In this report we study the use of the Multiple Stack Algorithm (MSA) (Chevillat and Costello, Jr., 1977) as the underlying sequential decoding algorithm in BHD, which makes possible an iterative version of BHD.
In this article, we design new turbo codes that can achieve near-Shannon-limit performance. The design criterion for random interleavers is based on maximizing the effective free distance of the turbo code, i.e., the minimum output weight of codewords due to weight-2 input sequences. An upper bound on the effective free distance of a turbo code is derived. This upper bound can be achieved if the feedback connection of convolutional codes uses primitive polynomials. We review multiple turbo codes (parallel concatenation of q convolutional codes), which increase the so-called 'interleaving gain' as q and the interleaver size increase, and a suitable decoder structure derived from an approximation to the maximum a posteriori probability decision rule. We develop new rate 1/3, 2/3, 3/4, and 4/5 constituent codes to be used in the turbo encoder structure. These codes, for from 2 to 32 states, are designed by using primitive polynomials. The resulting turbo codes have rates b/n (b = 1, 2, 3, 4 and n = 2, 3, 4, 5, 6), and include random interleavers for better asymptotic performance. These codes are suitable for deep-space communications with low throughput and for near-Earth communications where high throughput is desirable. The performance of these codes is within 1 dB of the Shannon limit at a bit-error rate of 10(exp -6) for throughputs from 1/15 up to 4 bits/s/Hz.
The purpose of this paper is to describe some key technical ideas behind our vision of a future satcom based digital communication network for avionics applications The key features of our design are as follows: (a) Packetized transmission to permit efficient use of system resources for multimedia traffic; (b) A time division multiplexed (TDM) satellite downlink whose physical layer is designed to operate the satellite link at maximum power efficiency. We show how powerful turbo codes (invented originally for linear modulation) can be used with nonlinear constant envelope modulation, thus permitting the satellite amplifier to operate in a power efficient nonlinear regime; (c) A code division multiple access (CDMA) satellite uplink, which permits efficient access to the satellite from multiple asynchronous users. Closed loop power control is difficult for bursty packetized traffic, especially given the large round trip delay to the satellite. We show how adaptive interference suppression techniques can be used to deal with the ensuing near-far problem; (d) Joint source-channel coding techniques are required both at the physical and the data transport layer to optimize the end-to-end performance. We describe a novel approach to multiple description image encoding at the data transport layer in this paper.
A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.