Uniquely Decodable Ternary Codes for Synchronous CDMA Systems

Abstract

In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multipleaccess (CDMA) systems. The proposed code set achieves larger number of users K < K t max than any other known state-of-the-art ternary codes that offer low-complexity decoders in the noisy transmission. Moreover, we propose a simple decoder that uses only a few comparisons and can allow the user to uniquely recover the information bits. Compared to maximum likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has much lower computational complexity. We also derived the computational complexity of the proposed recursive decoder analytically. Simulation results show that the performance of the proposed decoder is almost as good as the ML decoder. * where γ(n) function is the number of ones in the binary expansion of all positive integers less than n.

Low-Complexity Decoder for Overloaded Uniquely Decodable Synchronous CDMA

“…By definition the UD codes are those in which the data of different users can be unambiguously decoded in a noiseless channel using linear recursive decoders [31]. Low-complexity linear decoders were introduced for these UD code sets using either binary {0, 1}, or antipodal {±1}, or alternatively ternary {0, ±1} chips in [27]- [30], [32]- [35]. On the other hand, Lu et al [36] proposed M -ary code sets for the multiple-access adder channel.…”

“…Similarly, in [30] the authors propose overloaded code sets over the ternary alphabet that has a twin tree structured cross-correlation hierarchy that can be decoded with a simple multi-stage detector. Yet another construction of ternary codes that increases the number of columns, K , of UD codes for a such length compared to those proposed in [29] and [30] with a low-complexity polynomial time decoder is proposed in [32]. The primary reason for such low-complexity decoders is that the code sets are constructed with a certain criteria, which entails lowering the maximum number of users K < K max , as shown in Table 3.…”

Uniquely Decodable Multi-Amplitude Sequence for Grant-Free Multiple-Access Adder Channels

“…The well-known pseudo random sequences are composed of binary bits {0, 1}, e.g., m-sequence, golden sequences [14], Reed-Muller codes [15], Walsh sequences, and etc. With the development of spreading sequences, many papers discuss uniquelydecodable (UD) ternary code sets {−1, 0, +1} for the overloaded synchronous code division multiple-access (CDMA) systems [16]- [21], which can support lager number of users than the classical orthogonal spreading codes. To design lowcomplexity detectors is one of the important topics of the overloaded synchronous CDMA systems.…”

Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA

“…To address these challenges, numerous non-UD [2]- [14], and UD [15]- [36] construction based code sets have been proposed. Examples of such non-UD code sets are pseudonoise spreading (PN) [2], [3], OCDMA/OCDMA (O/O), [4]- [5], PN/OCDMA (PN/O) [6], multiple-OCDMA (MO) [7], improved O/O CDMA [8].…”

“…Similarly, in [35] the authors propose overloaded code sets over the ternary alphabet that has twin tree structured cross-correlation hierarchy with a simple multi-stage detection. Yet another construction of ternary codes that has K greater than those proposed in [34] and [35] with a very fast decoder is proposed in [36]. The primary reason for such low complexity decoders is that the code sets are constructed with a certain criteria, which entails lowering the maximum number of vectors K < K max , as shown in Table III.…”