Transmission of Nonuniform Memoryless Sources via Nonsystematic Turbo Codes

Abstract

Abstract-We investigate the joint source-channel coding problem of transmitting nonuniform memoryless sources over binary phase-shift keying-modulated additive white Gaussian noise and Rayleigh fading channels via turbo codes. In contrast to previous work, recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources. We prove that under certain conditions, and when the length of the input source sequence tends to infinity, the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform, regardless of the degree of source nonuniformity. We also give a conjecture (which is empirically validated) on the condition for the higher order distribution of the encoder output to be asymptotically uniform, irrespective of the source distribution. Consequently, these conditions serve as design criteria for the choice of good encoder structures. As a result, the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input, since a uniformly distributed input maximizes the channel mutual information, and hence, achieves capacity. Simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes; furthermore, their performance is within 0.74-1.17 dB from the Shannon limit. Finally, we compare our joint source-channel coding system with two tandem schemes which employ a fourth-order Huffman code (performing near-optimal data compression) and a turbo code that either gives excellent waterfall bit-error rate (BER) performance or good error-floor performance. At the same overall transmission rate, our system offers robust and superior performance at low BERs ( 10 4 ), while its complexity is lower.Index Terms-Additive white Gaussian noise (AWGN) and Rayleigh fading channels, joint source-channel coding, nonsystematic turbo codes, nonuniform independent and identically distributed (i.i.d.) sources, Shannon limit.Paper approved by A. K. Khandani, the Editor for Coding and Information Theory of the IEEE Communications Society.

Density evolution-based analysis and design of LDPC codes with a priori information

“…In [15], the authors state that for separate channelswhich is the case of interest in this paper-the type of turbo-like code utilized for the encoding is not critical, and good results can be obtained provided that powerful codes are employed. In [16], recursive nonsystematic convolutional encoders are proposed as constituent encoders for heavily biased sources, obtaining a performance between 0.74 dB and 1.17 dB from the Shannon limit. In [17], we show how turbolike codes allow to achieve a performance better than "simple" (either regular or irregular) LDPC codes in scenarios with correlated sources.…”

Exploitation of 2D binary source correlation using turbo block codes with fine-tuning

“…It is worth being noticed here that there is no difference in terms of the calculation for the terms α t and β t as shown in (8) and (9), respectively, from the standard BCJR algorithm; the difference of the modified algorithm from the standard algorithm arises when calculating the branch metric γ t , where a new term a i ,i is added as shown in (11) in order to take into account the source correlation information. For block codes, the state and state transition probabilities associated with the trellis diagram are evaluated until t = N, which can be separated into two parts; the first part is the uncoded information data bit sequence and the second part is the parity bit sequence.…”

“…The JSCC techniques shown in [3][4][5][6] characterize the source by a Markov model and exploit the source statistic during decoding process at receiver. Source statistic is taken into account in encoder design in [7][8][9][10], and correspondingly decoding algorithm modification is also proposed. Recently, exploitation of the memory structure inherent within the source using serial concatenated convolutional codes has been proposed in [11], which demonstrates superiority in BER performance without requiring heavy decoding complexity.…”

LP Decoding for Joint Source-Channel Codes and for the Non-Ergodic Polya Channel

“…Roundinĝ x is a heuristic alternative to declaring decoding failure. Extended Polytope: The proposed technique works; however, it has been demonstrated (see [7], [8] and other works) that in scenarios with strong non-uniformity at the source, systematic codes perform worse than non-systematic codes.…”