Systems and methods are disclosed for detecting sequences of symbols in a received signal in the presence of inter-symbol interference. Maximum Likelihood Sequence Detection (MLSD) is a known method for optimum detection of such sequences. To reduce the complexity of the MLSD, a Reduced-State Sequence Detection (RSSD) technique has been considered based on partitioning the states of the MLSD. In this approach, a simplified sequence detector is placed within a global decision feedback loop. The disclosed architecture shortens the feedback loop by moving the sequence detector outside the loop and converting the interaction between the two to a feed-forward manner. This is achieved through slicing the signal and closing a nested loop around the sliced bins. A further variant simplifies the detector even more by reducing the number of bins.

Methods and devices are disclosed for receiving and decoding sparsely encoded data sequences using a message passing algorithm (MPA) or maximum likelihood sequence estimation (MLSE). Such data sequences may be used in wireless communications systems supporting multiple access, such as sparse code multiple access (SCMA) systems. The Methods and devices reduce the number of states in a search space for each received signal and associated function node based on a search threshold based on a characteristic related to the received signal and/or to a quality of a resource element over which the received signal is transmitted.

The present disclosure includes an ML (Maximum Likelihood) detector. An embodiment of the ML detector comprises a search value selecting circuit and an ML detecting circuit. The search value selecting circuit is configured to select a search value according to a communication index and a modulation type or determine the search value according to a predetermined value, in which the communication index is related to a reception signal or a derivative thereof, the search value is associated with a search range, and a number of candidate signal value(s) in the search range is not greater than a number of all candidate signal values of the modulation type. The ML detecting circuit is configured to execute an ML calculation according to the search value and one of the reception signal and the derivative thereof, so as to calculate a log likelihood ratio of every candidate signal value in the search range.

An apparatus and method for optimizing the performance of satellite communication system receivers by using the Soft-Input Soft-Output (SISO) BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm to detect a transmitted information sequence is disclosed. A Sliding Window technique is used with a plurality of reduced state sequence estimation (RSSE) equalizers to execute the BCJR algorithm in parallel. A serial data stream is converted into a plurality of data blocks using a serial-to-parallel converter. After processing in parallel by the equalizers, the output blocks are converted back to a serial data stream by a parallel-to-serial converter. A path history is determined using maximum likelihood (ML) path history calculation.

A method may include: initializing four states of a trellis, the four states corresponding to the four possible symbol levels in PAM4, where a respective initial state starts with an initial score and an empty survivor path; for respective possible transitions between the four initial states and four possible current states of the trellis, determining expected PAM4 symbols; determining error associated with respective transitions based on differences between a received PAM4 symbol and the expected PAM4 symbols; discarding transitions where the error indicates a difference greater than a single signal level, and keep the other transitions; and for respective current state groups of a two state trellis, determining one of the incoming transitions that was not discarded having the highest likelihood of being associated with a transmitted symbol.

Methods and devices are disclosed for receiving and decoding sparsely encoded data sequences using a message passing algorithm (MPA) or maximum likelihood sequence estimation (MLSE). Such data sequences may be used in wireless communications systems supporting multiple access, such as sparse code multiple access (SCMA) systems. The Methods and devices reduce the number of states in a search space for each received signal and associated function node based on a search threshold based on a characteristic related to the received signal and/or to a quality of a resource element over which the received signal is transmitted.