UCLA Graduate School of Engineering Electrical Engineering Program

UCLA Graduate School of Engineering - Electrical Engineering Program Communication Systems Laboratory Progress report Miguel Griot Andres I. Vila Casado Wen-Yen Weng Richard Wesel

Results up to last meeting n Non-linear trellis codes for OR-MAC (Completed) n Design criteria. n BER analytical bounding technique. n Results for any number of users. n Parallel concatenated NLTC for OR-MAC n Design criteria. n BER analytical bounding technique. n Results for 6 and 24 users. n Theoretically achievable Sum-rates for more general channels, in particular coherent interference model. n Preliminary results for 6 -user optical MAC with coherent interference, using NLTC.

Non-linear trellis codes for OR-MAC n Design Criteria: n Extension to Ungerboeck’s rules. n We maximize the minimum free distance of the code, using the proper directional distance definition for the Z-Channel. n BER bounding technique for Z-Channel n Transfer function bound technique.

Bit Error Rate Bound for the Z-Channel n We use the transfer function bound technique on [Viterbi ‘ 71] for linear codes, and extended by [Biglieri ‘ 90] for non-linear codes, modifying the pairwise error probability measure. n Given two codewords n Replace and the transfer function bound technique can be readily applied to the NLTC to yield an upper bound to its BER over the Z-Channel.

Bit Error Rate Bound for the Z-Channel n Product states: where and denote the state at the encoder and receiver respectively. G denotes a ‘good product-state’ and B denotes a ‘bad product-state’. n Transition matrix: n For each transition in the product-state diagram the branch is labeled as: n

Bit Error Bound for the Z-Channel n Transfer function: where: n Then:

Results : 6 -user OR-MAC

Large number of users n Main results: n For any number of users, we achieve the same sum -rate with similar performance. N n SR 6 20 0. 3 0. 439 100 344 0. 291 0. 4777 300 1000 0. 3 0. 4901 900 3000 0. 3 0. 4906 1500 5000 0. 3 0. 4907 n BER Tight BER analytical bound for Z-Channel provided.

Concatenation with Outer Block Code n A concatenation of an NLTC with a high rate block code provides a very low BER, at low cost in terms of rate. Block-Code Encoder NL-TC Encoder Z-Channel Block-Code Decoder n n NL-TC Decoder Results: n A concatenation of the rate-1/20 NL-TCM code with (255 bytes, 247 bytes) Reed-Solomon code has been tested for the 6 -user OR-MAC scenario. n This RS-code corrects up to 8 erred bits. Rate Sum-rate p 0. 0484 0. 29 0. 125 BER 0. 4652 Although we don’t have simulations for the 100 -user case, it may be inferred that a similar BER would be achieved.

Parallel Concatenated NL-TCs n Capacity achieving. NL-TC Interleaver NL-TC n Design criteria: n An extension of Benedetto’s uniform interleaver analysis for parallel concatenated non-linear codes has been derived. n This analysis provides a good tool to design the constituent trellis codes.

Parallel Concatenated NL-TCs n The uniform interleaver analysis proposed by Benedetto, evaluates the bit error probability of a parallel concatenated scheme averaged over all (equally likely) interleavers of a certain length. n Maximum-likelihood decoding is assumed. n However, this analysis doesn’t directly apply to our codes: n n n It is applied to linear codes, the all-zero codeword is assumed to be transmitted. The constituent NL-TCM codes are non-linear, hence all the possible codewords need to be considered. In order to have a better control of the ones density, non-systematic trellis codes are used in our design. Benedetto’s analysis assumes systematic constituent codes. An extension of the uniform interleaver analysis for non -linear constituent codes has been derived.

Results • Parallel concatenation of 8 -state, duo-binary NLTCs. • Sum-rate = 0. 6 • Block-length = 8192 • 12 iterations in message-passing algorithm 6 users

General Model for Optical MAC User 1 User 2 User N Receiver if all users transmit a 0 if one and only one user transmits a 1 if m users transmit a 1 and the rest a 0

Model n The can be chosen any way, depending on the actual model to be used. n Examples: n Coherent interference: threshold n n constant

Achievable sum-rates n n users with equal ones density p. n Joint Decoding n Treating other users as noise – Binary Asymmetric Channel: 1 1 0 0

Sum-rate for coherent interence We provide an analytical lower bound to the achievable sum-rate for ANY number of users, for both joint decoding and treating other users as noise.

Lower bound for different n This figure shows the lower bounds and the actual sum-rates for 200 users for the worst case ( Coherent interference JD : Joint Decoding OUN: Other Users Noise constant).

Progress since last meeting n New FPGA demo for 6 -user optical multiple access. n Design of NL-TC for optical MAC with coherent interference, for large number of users. n BER bounding technique for BAC. n (Ongoing work) Design of parallel concatenated NLTC for optical MAC with coherent interference.

Progress: publications & presentations Trellis Codes with Low Ones Density for the OR Multiple Access Channel, M. Griot, A. Vila Casado, W-Y Weng, H. Chan, J. Basak, E. Yablanovitch, I. Verbauwhede, B. Jalali, R. Wesel. IEEE ISIT, Seattle, 9 -14 July 2006. n Presented in IEEE ISIT 2006 by Miguel Griot. n Non-linear Turbo Codes for Interleaver-Division Multiple Access on the OR Channel, M. Griot, A. Vila Casado, R. Wesel. To be presented at IEEE GLOBECOM Technical Conference 2006, Nov. 27 – Dec. 1, San Francisco. n Presentation: Demonstration of Uncoordinated Multiple Access in Optical Communications, H. Chan, A. Vila Casado, J. Basak, M. Griot, W-Y Weng, E. Yablanovitch, I. Verbauwhede, R. Wesel. 2006 43 rd Design Automation Conference, July 24 -28, San Francisco. n Winner of the 2006 DAC/ISSCC Student Design Contest 1 st Prize award, on the Operational System Design category. n Presented by Herwin Chan. n Journal Papers under preparation: n Non-linear Trellis Codes for Interleaver-Division Multiple Access on optical channels. (IEEE Trans. Telecommunications) n Includes material presented on ISIT 2006, and NL-TC codes for BAC. n Non-linear Turbo Codes for Interleaver-Division Multiple Access on optical channels. n Includes material to be presented on Globe. Com 2006, and PC-NLTC codes for BAC. (IEEE Trans. Telecommunications) n Demonstration of Uncoordinated Multiple Access in Optical Communications. n Includes material presented in DAC Conference 2006. n

BER analytical bound

Results for 6 -user MAC n 64 -state, rate 1/30 NLTC (Sum-rate = 0. 2) n Coherent interference model (CI-MAC): threshold n Z-Channel:

BER bound for 6 -user CI-MAC • 64 -state NL-TC

Results for Optical MAC n Model: Coherent interference n 128 -state NL-TC n Sum-rate = 0. 2 Users 6 32 104 p α 0. 2832 0. 3107 0. 3147 β 0. 0622 0. 0664 0. 0677 BER

Simulator Features n Random data is generated and encoded n The signal passes through a parameterizable channel model n Probes are placed at different point of the receiver to see how the codes react to changes in the channel

Channel Model n a and b simulate the degradation of the transmitted signal due to interference from other transmitters n a – non-coherent combination Probability that a 0 bit turns into 1 n b – coherent combination Probability that a 1 bit turns into 0

FPGA Channel Simulator FPGA transmitter Channel Model a Trellis Decoder Rate: 1/20 BER < 10 -5 Reed Solomon Decoder (255, 237) b n Hardware transmitter, receiver and channel model simulated on a single FPGA n Effects of changing channel parameters can be evaluated in real time n New Channel codes can be easily tested BER < 10 -9

Measurement Points FPGA transmitter Channel Model a • Ones density • Channel Errors • One to zero transitions Trellis Decoder Rate: 1/20 BER < 10 -5 Reed Solomon Decoder (255, 237) b Non-linear trellis code bit error rate Total bit error rate BER < 10 -9

Simulation Interface Real time channel conditions Bit error rate measurement at receiver Channel parameter selection n Real-time Matlab graphical user interface n Real-time control of channel parameters a and b