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

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

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

Bit Error Rate Bound for the Z-Channel 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. Given two codewords 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 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’. Transition matrix: For each transition in the product-state diagram the branch is labeled as:

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

Results : 6-user OR-MAC

Large number of users Main results: For any number of users, we achieve the same sum-rate with similar performance. Tight BER analytical bound for Z-Channel provided. NnSRBER

Concatenation with Outer Block Code A concatenation of an NLTC with a high rate block code provides a very low BER, at low cost in terms of rate. Results: 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. This RS-code corrects up to 8 erred bits. Although we don’t have simulations for the 100-user case, it may be inferred that a similar BER would be achieved. Block-Code EncoderNL-TC Encoder Z-Channel Block-Code DecoderNL-TC Decoder RateSum-ratepBER

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

Parallel Concatenated NL-TCs 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. Maximum-likelihood decoding is assumed. However, this analysis doesn’t directly apply to our codes: 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 6 users Parallel concatenation of 8-state, duo-binary NLTCs. Sum-rate = 0.6 Block-length = iterations in message-passing algorithm

General Model for Optical MAC User 1User 2User 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 The can be chosen any way, depending on the actual model to be used. Examples: Coherent interference: constant threshold

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

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

Progress since last meeting New FPGA demo for 6-user optical multiple access. Design of NL-TC for optical MAC with coherent interference, for large number of users. BER bounding technique for BAC. (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 Presented in IEEE ISIT 2006 by Miguel Griot. 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. 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 rd Design Automation Conference, July 24-28, San Francisco. Winner of the 2006 DAC/ISSCC Student Design Contest 1 st Prize award, on the Operational System Design category. Presented by Herwin Chan. Journal Papers under preparation: Non-linear Trellis Codes for Interleaver-Division Multiple Access on optical channels. (IEEE Trans. Telecommunications) Includes material presented on ISIT 2006, and NL-TC codes for BAC. Non-linear Turbo Codes for Interleaver-Division Multiple Access on optical channels. Includes material to be presented on GlobeCom 2006, and PC-NLTC codes for BAC. (IEEE Trans. Telecommunications) Demonstration of Uncoordinated Multiple Access in Optical Communications. Includes material presented in DAC Conference 2006.

BER analytical bound

Results for 6-user MAC 6-user MAC 64-state, rate 1/30 NLTC (Sum-rate = 0.2) Coherent interference model (CI-MAC): Z-Channel: threshold

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

Model: Coherent interference 128-state NL-TC Sum-rate = 0.2 UserspαβBER Results for Optical MAC

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

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

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

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

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