Multi-non-binary turbo codes

Abstract

This paper presents a new family of turbo codes called multi-non-binary turbo codes (MNBTCs) that generalizes the concept of turbo codes to multi-non-binary (MNB) parallel concatenated convolutional codes (PCCC). An MNBTC incorporates, as component encoders, recursive and systematic multi-non-binary convolutional encoders. The more compact data structure for these encoders confers some advantages on MNBTCs over other types of turbo codes, such as better asymptotic behavior, better convergence, and reduced latency. This paper presents in detail the structure and operation of an MNBTC: MNB encoding, trellis termination, Max-Log-MAP decoding adapted to the MNB case. It also shows an example of MNBTC whose performance is compared with the state-of-the-art turbo code adopted in the DVB-RCS2 standard.

1/n Turbo codes from linear system point of view

“…In this context the image representation v(z) = G(z)u(z) is usually described through state-space equations like (2) where the input u(z) drives the output v(z). In contrast to this, system (1) is a state-space description where k components u(z) of the codeword v(z) drive the remaining n−k components y(z) of v(z).…”

“…Representation (2) has been considered the standard way in which convolutional codes were presented in terms of linear systems. However, many authors considered that linear system (1) is the better choice to study convolutional codes [29,31,34,38].…”

“…These new turbo code families aim to improve the performance, especially by lowering the error floor and reducing its latency (as the data block is more compact). See [2,6,20,28] for more details. In many realistic scenarios, codewords of a finite field of q elements, are converted to binary codewords in order to be transmitted in a binary channel (see for instance [17]).…”

Performance of duo‐binary turbo codes with optimized hierarchical modulation

“…For these reasons, DBTCs have recently been implemented in communication systems such as digital video broadcasting with return channel via satellite (DVB‐RCS) . Several researchers are also working on triple‐binary TCs . The prioritized quadrature amplitude mapping (QAM) constellation mapping scheme impacts the error performance of TCs positively, and several recent works have revealed the advantages that can be derived by incorporating it in the turbo coding system.…”