In some embodiments, a bandwidth constrained equalized transport (BCET) communication system comprises a transmitter that transmits a signal, a communication channel that transports the signal, and a receiver that receives the signal. The transmitter can comprise a pulse-shaping filter that intentionally introduces memory into the signal, and an error control code encoder that is a low-density parity-check (LDPC) error control code encoder. The error control encoder comprises code that is optimized based on the intentionally introduced memory into the signal, a code rate, a signal-to-noise ratio, and an equalizer structure in the receiver. In some embodiments, the communication system is bandwidth constrained, and the transmitted signal comprises an information rate that is higher than for an equivalent system without intentional introduction of the memory at the transmitter.

According to an embodiment, a memory system includes: a test pattern decoding unit that detects an intermediate decoding word from a plurality of test patterns; a Euclid distance calculating unit that calculates a Euclid distance between the intermediate decoding word and a received word; and a maximum likelihood decoding word selecting unit that maintains a maximum likelihood decoding word candidate. In a case where a Euclid distance of the intermediate decoding word is shorter than a Euclid distance of the maximum likelihood decoding word candidate, the maximum likelihood decoding word selecting unit updates the maximum likelihood decoding word candidate by using the intermediate decoding word and the test pattern decoding unit does not execute decoding of a test pattern having no possibility that the Euclid distance of the intermediate decoding word becomes shorter than the Euclid distance of the maximum likelihood decoding word candidate.

A method, system, and non-transitory computer-readable recording medium of decoding a signal are provided. The method includes receiving signal to be decoded, where signal includes at least one symbol; decoding signal in stages, where each at least one symbol of signal is decoded into at least one bit per stage, wherein Log-Likelihood Ratio (LLR) and a path metric are determined for each possible path for each at least one bit at each stage; determining magnitudes of the LLRs; identifying K bits of the signal with smallest corresponding LLR magnitudes; identifying, for each of the K bits, L possible paths with largest path metrics at each decoder stage for a user-definable number of decoder stages; performing forward and backward traces, for each of the L possible paths, to determine candidate codewords; performing a Cyclic Redundancy Check (CRC) on the candidate codewords; and stopping after a first candidate codeword passes the CRC.

Method for decoding signal includes receiving signal, where signal includes at least one symbol; decoding signal in stages, where each at least one symbol of signal is decoded into at least one bit per stage, wherein Log-Likelihood Ratio (LLR) for each at least one bit at each stage is determined, and identified in vector L.sub.APP; performing Cyclic Redundancy Check (CRC) on L.sub.APP, and stopping if L.sub.APP passes CRC; otherwise, determining magnitudes of LLRs in L.sub.APP; identifying K LLRs in L.sub.APP with smallest magnitudes and indexing K LLRs as r={r(1), r(2), . . . , r(K)}; setting L.sub.max to maximum magnitude of LLRs in L.sub.APP or maximum possible LLR quantization value; setting v=1; generating {tilde over (L)}.sub.A(r(k))=L.sub.A(r(k))L.sub.maxv.sub.ksign[L.sub.APP(r(k))], for k=1, 2, . . . , K; decoding with {tilde over (L)}.sub.A to identify {tilde over (L)}.sub.APP, wherein {tilde over (L)}.sub.APP is LLR vector; and performing CRC on {tilde over (L)}.sub.APP, and stopping if {tilde over (L)}.sub.APP passes CRC or v=2.sup.K-1; otherwise, incrementing v and returning to generating {tilde over (L)}.sub.A(r(k)).

A LDPC encoding method is provided, which is highly scalable and may support a variety of code cases and allow a high processing speed. The LDPC encoding includes: receiving an information sequence to be encoded; segmenting the information sequence into blocks of a predetermined length; deriving parity bits for each of the segmented blocks by using a predetermined parity check matrix; and generating a codeword by combining the parity bits into a corresponding segmented block. The operation of deriving parity bits for each of the segmented blocks includes: performing multiplications with at least one element of the parity check matrix by circularly shifting the segmented block a number of times corresponding to the at least one element of the parity check matrix; and performing XOR operations on a plurality of bits of a circularly-shifted segmented block in parallel.

A method is performed by an information decoder. The method comprises obtaining (S102) an encoded sequence having been encoded using a polar code. The method comprises successively decoding (S104) the encoded sequence into the successive bits of the decoded sequence. Successively decoding the encoded sequence comprises performing a threshold check (S106) for evaluating a bit uncertainty criterion. Successively decoding the encoded sequence comprises branching (S108) the decoded sequence into two candidate decoded sequences whenever the threshold check fails.

Disclosed is a method for decoding an optical data signal. Said optical data signal is phase and amplitude modulated according to a constellation diagram with at least eight constellation points representing non-binary symbols. Said decoding method comprises the following steps: carrying out a carrier phase recovery of a received signal ignoring the possible occurrence of phase slips, decoding said signal after phase recovery, wherein in said decoding, possible cycle slips occurring during phase recovery are modelled as virtual input to an equivalent encoder assumed by the decoding scheme. Further disclosed are a related encoding method as well as a receiver and a transmitter.

According to an embodiment, a memory system includes: a test pattern decoding unit that detects an intermediate decoding word from a plurality of test patterns; a Euclid distance calculating unit that calculates a Euclid distance between the intermediate decoding word and a received word; and a maximum likelihood decoding word selecting unit that maintains a maximum likelihood decoding word candidate. In a case where a Euclid distance of the intermediate decoding word is shorter than a Euclid distance of the maximum likelihood decoding word candidate, the maximum likelihood decoding word selecting unit updates the maximum likelihood decoding word candidate by using the intermediate decoding word and the test pattern decoding unit does not execute decoding of a test pattern having no possibility that the Euclid distance of the intermediate decoding word becomes shorter than the Euclid distance of the maximum likelihood decoding word candidate.

A method and system for decoding a signal are provided. The method includes receiving a signal, where the signal includes at least one symbol; decoding the signal in stages, where each at least one symbol is decoded into at least one bit per stage, wherein a Log-Likelihood Ratio (LLR) and a path metric are determined for each possible path for each at least one bit at each stage; determining the magnitudes of the LLRs; identifying K bits of the signal with the smallest corresponding LLR magnitudes; identifying, for each of the K bits, L possible paths with the largest path metrics at each decoder stage for a user-definable number of decoder stages; performing forward and backward traces, for each of the L possible paths, to determine candidate codewords; performing a Cyclic Redundancy Check (CRC) on the candidate codewords, and stopping after a first candidate codeword passes the CRC.

A method and system for demodulating high-order Quadrature Amplitude Modulation (QAM) signals is disclosed. In one embodiment, the system includes a cyclic prefix (CP) removal unit for removing a CP from a received signal to provide a first intermediate signal, wherein the first intermediate signal comprises a plurality of bits; a fast Fourier transform (FFT) unit configured to convert the first intermediate signal into a frequency domain; a soft de-mapper configured to derive a plurality of soft bits based on log-likelihood estimates of the plurality of bits, wherein the soft de-mapper derives each soft bit by using a single linear function to approximate each soft bit; and a decoder configured to decode a signal derived from the soft de-mapper into information.