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In this paper, we present an all-analog implementation of the rate-l/3, block length 40, universal mobile telecommunications system (UMTS) turbo decoder. The prototype was designed and fabricated in 0.35 [micro]m complementary metal-oxide-semiconductor technology and operates at 3.3 V. We also introduce a discrete-time first-order model for analog decoders which allows fast bit-error rate simulations, while taking into account circuit transient behavior and component mismatch. The model is applied to the rate-l/3 analog turbo decoder for UMTS defined in the Third Generation Partnership Project standard, and the discrete-time model predictions are compared with the decoder experimental performance and the transistor-level simulations. These results demonstrated that this model can be successfully used as a tool to both predict analog decoder performance and give design guidelines for complex decoders, for which circuit-level simulations are impractical. Index Terms--Analog decoding, device mismatch, discrete-time model, iterative decoding, turbo codes.

We deal with the design of interleavers in a coded code-division multiple-access (CDMA) scenario, where at the receiver an iterative turbo-like structure to perform multiuser detection is employed. The choice of the interleavers affects both the maximum-likelihood (ML) performance and the impact of the suboptimality of the iterative receiver. First, heuristic criteria of goodness for a set of interleavers, each assigned to a given active user, are introduced and motivated. One of these criteria is based on the intersection between the equivalent codes seen after the interleavers for each user pair. The design rules are valid for any kind of channel code. In particular, when the channel code used by every user is a terminated convolutional code, a very simple design rule, in the subset of congruential interleavers, is specified. The suitability of an interleaver set to iterative decoding is also treated. The analysis leads to a design rule which is shown to have great importance on the performance of a turbo-like receiver. Numerical results assess the validity of the derived design rules by showing that, for iterative multiuser receivers and reasonable block lengths, the suitability to iterative decoding is more important than the performance optimization. Index Terms--Coded code-division multiple access (CDMA), interleaver design, iterative multiuser receivers, permutations.

For high-data-rate applications, the implementation of iterative turbo-like decoders requires the use of parallel architectures posing some collision-free constraints to the reading/writing process from/into the memory. This consideration applies to the two main classes of turbo-like codes, i.e., turbo codes and low-density parity-check (LDPC) codes. Contrary to the literature belief, we prove in this paper that there is no need for an ad hoc code design to meet the parallelism requirement, because, for any code and any choice of the scheduling of the reading/writing operations, there is a suitable mapping of the variables in the memory that grants a collision-free access. The proof is constructive, i.e., it gives an algorithm that obtains the desired collision-free mapping. The algorithm is applied to two simple examples, one for turbo codes and one for LDPC codes, to illustrate how the algorithm works. Index Terms--Low-density parity-check (LDPC) codes, memory mapping, parallel implementation, turbo codes.

In this letter, we propose and compare some design criteria for the search of good rate-compatible systematic turbo codes (RCPTC) families. The considerations presented by Benedetto et al. to find "best" component encoders for turbo-code construction are extended to find good rate-compatible puncturing patterns leading to codes with promising performances. Index Terms--Iterative decoding, rate-compatible punctured codes (RCPCs), turbo codes.

This correspondence deals with the design and decoding of high-rate convolutional codes. After proving that every (n, n - 1) convolutional code can be reduced to a structure that concatenates a block encoder associated to the parallel edges with a convolutional encoder defining the trellis section, the results of an exhaustive search for the optimal (n, n - 1) convolutional codes is presented through various tables of best high-rate codes. The search is also extended to find the "best" recursive systematic convolutional encoders to be used as component encoders of parallel concatenated "turbo" codes. A decoding algorithm working on the dual code is introduced (in both multiplicative and additive form), by showing that changing in a proper way the representation of the soft information passed between constituent decoders in the iterative decoding process, the soft-inpu soft-output (SISO) modules of the decoder based on the dual code become equal to those used for the original code. A new technique to terminate the code trellis that significantly reduces the rate loss induced by the addition of terminating bits is described. Finally, an inverse puncturing technique applied to the highest rate "mother" code to yield a sequence of almost optimal codes with decreasing rates is proposed. Simulation results applied to the case of parallel concatenated codes show the significant advantages of the newly found codes in terms of performance and decoding complexity. Index Terms--Block codes, convolutional codes, dual codes, high-rate codes, inverse puncturing, iterative decoding, puncturing, trellis termination, turbo-like codes.

In this letter, the performance of turbo codes is evaluated through analysis and simulation over the Rice multiplicative fading channel. The analysis is conducted extending the results presented by Viterbi and Viterbi (1998) to the Rice multiplicative fading channel case. Simulation results are obtained using an extended version of the improved Jakes' channel simulator, first presented by Pop and Beaulieu (2001). Index Terms--Concatenated coding, fading channels, multipath channels, simulation, turbo codes.

The well-known uniform error property for signal constellations and codes is extended to encompass information bits. We introduce a class of binary labelings for signal constellations, called bit geometrically uniform (BGU) labelings, for which the uniform bit error property holds, i.e., the bit error probability does not depend on the transmitted signal. Strong connections between the symmetries of constellations and binary Hamming spaces are involved. For block-coded modulation (BCM) and trellis-coded modulation (TCM) Euclidean-space codes, BGU encoders are introduced and studied. The properties of BGU encoders prove quite useful for the analysis and design of codes aimed at minimizing the bit, rather than symbol, error probability. Applications to the analysis and the design of serially concatenated trellis codes are presented, together with a case study which realizes a spectral efficiency of 2 b/s/Hz. Index Terms--Coding, concatenated codes, constellations, encoding, labeling, trellis codes, uniform error property.

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the "best" recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error probability performances of some turbo codes using them. Index Terms - Concatenated coding, convolutional codes, encoders, 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. The construction can be generalized to h cascaded encoders separated by h - 1 interleavers. We obtain upper bounds to the average maximum-likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding algorithm. Throughout the paper, extensive comparisons with parallel concatenated convolutional codes known as "turbo codes" are performed, showing that the new scheme can offer superior performance. Index Terms - Concatenated codes, iterative decoding, serial concatenation, turbo codes.

Summary: In this paper, we propose a simple method for generating short‐length rate‐compatible codes that are robust to noncoherent detection forM‐PSK constellations. For any given constellation set, first we use a greedy algorithm to construct a family of rotationally invariant codes. Then, by properly modifying such codes, we obtain a new family of codes that are robust to noncoherent detection. We briefly discuss the optimality of the constructed codes for special cases of BPSK and QPSK constellations. Our method provides an upper bound for the length of optimal codes with a given desired noncoherent distance. We also derive a simple asymptotic upper bound on the frame error rate (FER) of such codes and provide some simulations. Finally, the problem of designing binary codes that are robust to noncoherent detection for QPSK constellation is briefly discussed. [ABSTRACT FROM AUTHOR]

The theory of geometrically uniform signal sets and codes over groups is applied to the case of LxMPSK constellations. Conditions for rotational invariance of group codes are discussed. The tables of geometrically uniform partitions recently found in (1) are used to construct good geometrically uniform trellis codes over nonbinary Abelian groups. We consider Lx4PSK and Lx8PSK constellations used to transmit information rates of 1 and 2 bit/two dimensions, respectively, and present tables of good codes over generating groups (Z4)(super L) and (Z8)(super L), for L ranging from 1 to 4. In most cases, they improve the tables of codes known so far. Moreover, the geometrical uniformity of codes allows a very easy performance evaluation, so that we also present a complete set of curves of error event probability for the obtained codes.

The recently developed theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK constellations. The symmetry group of an L X MPSK constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L X MPSK (M = 4, 8, 16 and L = 1, 2, 3, 4) constellations are found, which present good characteristics in terms of the set of distances at a given partition level, the maximum obtainable rotational invariance, and the isomorphism of the quotient group associated with the partition. These partitions are used as starting points in a search for good geometrically uniform trellis codes based on binary convolutional codes.