Announcement:

1) Flooding and Layered Scheduling Iterative Message-Passing (Belief Propagation) Decoding Bit Error Rate (BER) results for Protograph-Based Low-Density Parity-Check (LDPC) Coded Signaling over a Coherent Memoryless Channel with AWGN has now been published on this website.. The T1 Professional (T1 V2) system tool now supports Permutation and Quasi-Cyclic Protograph-Based LDPC Code construction. Also, the T1 Professional (T1 V2) system tool supports Layered (in addition to Flooding Scheduling) Sum-Product Algorithm (SPA) Decoding of Permutation and Quasi-Cyclic Protograph-Based LDPC Coded Signaling over Additive White Gaussian Noise (AWGN) Memoryless Channels, Memory Channels and Parallel MultiChannels. Along with the enhanced SPA LDPC Channel Decoder feature of Scheduling, Offset Min-Sum (OMS) Check Message Passing and Message Quantization (Finite Precision) has now been added to T1 V2.

FIGURE 1. Bit Error Probability for Flooding and Layered Sum-Product Algorithm 
(Offset Min Sum [OMS, {Offset equal to 1]} Check Message Implementation) Decoding of 
(N = 504) Protograph-Based Coded (Permutation II & Quasi-Cyclic II) BPSK Signaling 
over a Coherent Memoryless Channel with Additive White Gaussian Noise (AWGN).

VIEW these Flooding & Layered SPA Decoding of Protograph-Based LDPC Coded Signaling over a Coherent Memoryless Channel with AWGN BER results and its analysis and LEARN more about this feature.

2) Iterative Message-Passing (Belief Propagation) Decoding Bit Error Rate (BER) results for Low-Density Parity-Check (LDPC) Coded Signaling over a Parallel MultiChannel with Fading and AWGN has now been published on this website. The T1 Professional (T1 V2) system tool now supports LDPC Coded Signaling and Sum-Product Algorithm (SPA) Decoding for Additive White Gaussian Noise (AWGN) Parallel MultiChannels with Fading (Rayleigh or Rician) and AWGN; and Discrete MultiTone (DMT) Modulation MultiCarrier/MultiChannel [Orthogonal frequency-division Multiplexing (OFDM) FFT-Based] with Fading (Rayleigh or Rician) and AWGN models.

Note: T1 Professional supports Orthogonal Binary PSK (PI/2 BPSK) and Square 256-QAM for Low-Density Parity-Check Coded Signaling over a Parallel MultiChannel. These schemes are in addition to the other T1 supported Modulation Schemes (PSK: M = 2, 4, 8, 16, 32, 64; PAM: M = 2, 4, 8, 16, 32, 64; QAM; M = 4, 16, 64; FSK: M = 2, 4, 8, 16, 32, 64).

Figure 2. Bit Error Probability for (N = 504, j = 3, k = 4) Gallager Coded 
          Signaling over a Discrete-Time Waveform (DTW) AWGN Parallel MultiChannel 
          (PMC) without or with Rayleigh Fading & with AWGN.

VIEW these SPA Decoding of LDPC Coded Signaling over a Parallel MultiChannel with Fading BER results and its analysis and LEARN more about this feature.

3) Iterative Message-Passing (Belief Propagation) Decoding Bit Error Rate (BER) results for Low-Density Parity-Check (LDPC) Coded Signaling over a Discrete MultiTone (DMT) Modulation MultiCarrier/MultiChannel [Orthogonal frequency-division Multiplexing (OFDM) FFT-Based] with AWGN are published on this website. The T1 Professional (T1 V2) system tool now supports LDPC Coded Signaling and Sum-Product Algorithm (SPA) Decoding for Additive White Gaussian Noise (AWGN) and Crosstalk (Xtalk) Parallel MultiChannels with AWGN; and Discrete MultiTone (DMT) Modulation MultiCarrier/MultiChannel [Orthogonal frequency-division Multiplexing (OFDM) FFT-Based] with AWGN models.

Figure 3. Bit Error Probability for UnCoded and (N = 504, j = 3, k = 4) Gallager 
          Coded Signaling over a Discrete-Time Discrete MultiTone (DMT) Modulation 
          Parallel MultiCarrier/MultiChannel (PMC) with Additive White Gaussian 
          Noise (AWGN).

VIEW these SPA Decoding of LDPC Coded Signaling over a DMT MultiCarrier/MultiChannel [Orthogonal frequency-division Multiplexing (OFDM) FFT-Based] BER results and its analysis and LEARN more about this feature.

4) Iterative Message-Passing (Belief Propagation) Decoding Bit Error Rate (BER) results for Low-Density Parity-Check (LDPC) Coded Signaling over a Rayleigh Fading Channel (Memory Channel) are published on this website. The T1 Professional (T1 V2) system tool now supports LDPC Coded Signaling and Sum-Product Algorithm (SPA) Decoding for the Burst Channel (Classic Bursty with Background Noise & Gilbert-Elliot Burst); Fading Channel (Rayleigh, Rician, & Frequency-Selective); and InterSymbol Interference (ISI) Channel (with Linear Equalizer) Memory Channel models.

Figure 4. Bit Error Probability for UnCoded, Convolutional, and (N = 1008, j = 3, 
          k = 4) Gallager Coded BFSK Signaling over a Rayleigh Fading Memory 
          Channel with Additive White Gaussian Noise (AWGN).

VIEW these SPA Decoding of LDPC Coded Signaling over a Rayleigh Fading Channel (Memory Channel) BER results and its analysis and LEARN more about this feature.

5) Iterative Message-Passing (Belief Propagation) Decoding Bit Error Rate (BER) results & their important impact on the use of Low-Density Parity-Check (LDPC) Codes for Reliable Digital Communications are published on this website. These results pertain to the T1 Professional (T1 V2) use of the Sum-Product Algorithm (SPA) in decoding Gallager, Array, and Repeat-Accumulate Coded Signaling over an Additive White Gaussian Noise Memoryless Channel.

VIEW these Low-Density Parity-Check (LDPC) Code Sum-Product Algorithm (SPA) Decoding BER results and its analysis and LEARN more about this feature.

6) Turbo Decoding Bit Error Rate (BER) results for Turbo Coded Signaling over a Rayleigh Fading Channel (Memory Channel) are published on this website. The T1 Professional (T1 V2) system tool now supports Turbo Coded Signaling and Turbo Decoding for the Burst Channel (Classic Bursty with Background Noise & Gilbert-Elliot Burst); Fading Channel (Rayleigh, Rician, & Frequency-Selective); and InterSymbol Interference (ISI) Channel (with Linear Equalizer) Memory Channel models.

Figure 5. Bit Error Probability for UnCoded, Convolutional, and Turbo Coded BFSK 
          Signaling over a Rayleigh Fading Memory Channel with Additive 
          White Gaussian Noise (AWGN).

VIEW these Turbo Decoding of Turbo Coded Signaling over a Rayleigh Fading Channel (Memory Channel) BER results and its analysis and LEARN more about this feature.

7) Turbo Decoding Bit Error Rate (BER) results for Rate Matching Punctured Turbo Coded Signaling over a Rayleigh Fading Channel (Memory Channel) are published on this website. The T1 Professional (T1 V2) system tool now supports Rate Matching Punctured Turbo Coded Signaling and Turbo Decoding for the Burst Channel (Classic Bursty with Background Noise & Gilbert-Elliot Burst); Fading Channel (Rayleigh, Rician, & Frequency-Selective); and InterSymbol Interference (ISI) Channel (with Linear Equalizer) Memory Channel models.

Figure 6. Bit Error Probability for UnCoded, Convolutional, and Rate Matching 
          Punctured Turbo Coded (RM PTC) 16-FSK Signaling over a Rayleigh Fading 
          Memory Channel with Additive White Gaussian Noise (AWGN).

VIEW these Turbo Decoding of Rate Matching Punctured Turbo Coded Signaling over a Rayleigh Fading Channel (Memory Channel) BER results and its analysis and LEARN more about this feature.

8) Turbo Decoding Bit Error Rate (BER) results & their important impact on the use of Turbo Codes for Reliable Digital Communications are published on this website. These results pertain to the use of the Cross-Entropy (CE) Iterative Stopping Rule (SR) in a Turbo Decoder. The T1 Professional (T1 V2) system tool now contains a CE SR feature in the Turbo Decoder model along with the Fixed Number SR.

VIEW these Turbo Decoding & Cross-Entropy Stopping Rule BER results and its analysis and LEARN more about this feature.

Today, many possible powerful and complex Digital Communication (Information-theoretic) systems could be designed and built in an attempt to satisfy a set of System Requirements for a Target (field) design. The physical study, analysis, design, and/or evaluation of such a Real World system with all of its possible channel impairments (corruption) in the laboratory or field is nearly impossible using the scientific approach.

Consider the following points:

1) this prototyping hardware effort (building & testing a laboratory mock-up) would be a very expensive and time consuming endeavor because of the total number of possible system models (apparatus) that might need to be considered;

2) the creation/duplication of possible physical channel impairments such as AWGN (Additive White Gaussian Noise), Fading, ISI (InterSymbol Interference), etc. that would occur in the field operation of a particular system model is an extremely difficult task; and

3) the knowledge and technical skills required to actually build such a hardware prototype in a laboratory is only found in a few universities, corporations or institutions in the world.

These are some of the reasons why engineers, scientists, and mathematicians build computer models (software-based) of these systems and simulate (computer-based) their performance of these systems to study, analyze, design, and/or evaluate Coding methods to reduce the Error Rate of Information transfer of these systems.

Buy and Use the novel PC Computer-Based Advanced Digital Communication System Modeler (AdvDCSM) software system tool product: AdvDCSM DCSS (Digital Communication System Simulator) T1.

And Use T1's easy-to-use Bit Error Rate (BER)/Bit Error Probability (P_b) Plot Generation Feature to produce BER Plots of your P_b performance simulation results.

VIEW a BER Plot Generation Example and LEARN more about this feature.

REVIEW BER/P_b PLOT GENERATION GUIDE and LEARN more about this feature.

T1 is available Worldwide via software DOWNLOADS (Electronic Distribution) to Customers in USA, CANADA, and OTHER SELECTED COUNTRIES.

LEARN additional REASONS to BUY & USE AdvDCSM DCSS (T1).