Upper and Lower Bounds on Bit-Error Rate for Convolutional Codes

In this paper, we provide a new approach to the analytical estimation of the bit-error rate (BER) for convolutional codes for Viterbi decoding in the binary symmetric channel (BSC). The expressions we obtained for lower and upper BER bounds are based on the active distances of the code and their distance spectrum. The estimates are derived for convolutional codes with the rate $R=\frac{1}{2}$ but can be easily generalized for any convolutional code with rate $R=\frac 1n$ and systematic encoder. The suggested approach is not computationally expensive for any crossover probability of BSC channel and convolutional code memory, and it allows to obtain precise estimates of BER

On the Design of a Novel Joint Network-Channel Coding Scheme for the Multiple Access Relay Channel

This paper proposes a novel joint non-binary network-channel code for the Time-Division Decode-and-Forward Multiple Access Relay Channel (TD-DF-MARC), where the relay linearly combines -- over a non-binary finite field -- the coded sequences from the source nodes. A method based on an EXIT chart analysis is derived for selecting the best coefficients of the linear combination. Moreover, it is shown that for different setups of the system, different coefficients should be chosen in order to improve the performance. This conclusion contrasts with previous works where a random selection was considered. Monte Carlo simulations show that the proposed scheme outperforms, in terms of its gap to the outage probabilities, the previously published joint network-channel coding approaches. Besides, this gain is achieved by using very short-length codewords, which makes the scheme particularly attractive for low-latency applications.Comment: 28 pages, 9 figures; Submitted to IEEE Journal on Selected Areas in Communications - Special Issue on Theories and Methods for Advanced Wireless Relays, 201

Can Punctured Rate-1/2 Turbo Codes Achieve a Lower Error Floor than their Rate-1/3 Parent Codes?

In this paper we concentrate on rate-1/3 systematic parallel concatenated convolutional codes and their rate-1/2 punctured child codes. Assuming maximum-likelihood decoding over an additive white Gaussian channel, we demonstrate that a rate-1/2 non-systematic child code can exhibit a lower error floor than that of its rate-1/3 parent code, if a particular condition is met. However, assuming iterative decoding, convergence of the non-systematic code towards low bit-error rates is problematic. To alleviate this problem, we propose rate-1/2 partially-systematic codes that can still achieve a lower error floor than that of their rate-1/3 parent codes. Results obtained from extrinsic information transfer charts and simulations support our conclusion.Comment: 5 pages, 7 figures, Proceedings of the 2006 IEEE Information Theory Workshop, Chengdu, China, October 22-26, 200

Coding theorems for turbo code ensembles

This paper is devoted to a Shannon-theoretic study of turbo codes. We prove that ensembles of parallel and serial turbo codes are "good" in the following sense. For a turbo code ensemble defined by a fixed set of component codes (subject only to mild necessary restrictions), there exists a positive number γ0 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than γ0, the average maximum-likelihood (ML) decoder block error probability approaches zero, at least as fast as n -β, where β is the "interleaver gain" exponent defined by Benedetto et al. in 1996

Multilevel Coded Modulation for Unequal Error Protection and Multistage Decoding—Part I: Symmetric Constellations

In this paper, theoretical upper bounds and computer simulation results on the error performance of multilevel block coded modulations for unequal error protection (UEP) and multistage decoding are presented. It is shown that nonstandard signal set partitionings and multistage decoding provide excellent UEP capabilities beyond those achievable with conventional coded modulation. The coding scheme is designed in such a way that the most important information bits have a lower error rate than other information bits. The large effective error coefficients, normally associated with standard mapping by set partitioning, are reduced by considering nonstandard partitionings of the underlying signal set. The bits-to-signal mappings induced by these partitionings allow the use of soft-decision decoding of binary block codes. Moreover, parallel operation of some of the staged decoders is possible, to achieve high data rate transmission, so that there is no error propagation between these decoders. Hybrid partitionings are also considered that trade off increased intraset distances in the last partition levels with larger effective error coefficients in the middle partition levels. The error performance of specific examples of multilevel codes over 8-PSK and 64-QAM signal sets are simulated and compared with theoretical upper bounds on the error performance