Uncoordinated Optical Multiple Access using IDMA and Nonlinear TCM UCLA Electrical Engineering Department-Communication Systems Laboratory Uncoordinated Optical Multiple Access using IDMA and Nonlinear TCM PIs: Eli Yablanovitch, Rick Wesel, Ingrid Verbauwhede, Bahram Jalali, Ming Wu Students whose work is discussed here: Juthika Basak, Herwin Chan, Miguel Griot, Andres Vila Casado, Wen-Yen Weng

OCDMA Coding Architecture 1.2 Gbps 2 Gbps 60 Mbps Reed Solomon (255, 237) Trellis Code 1/20 int OR channel 93 Mbps 5 other tx Correct extra errors Separate different transmitters Asychronous Access code UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory The system Reed Solomon (255, 237) sync Trellis Code 1/20 int 5 other tx Initial synchroni-zation of tx-rx pair For uncoor-dinated access To distinguish between users OR channel To bring final BER to 1e-9 BER Tester Reed Solomon (255, 237) Trellis Code 1/20 int Bit align sync Large feedback loop for rx synchronization UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Experimental Setup FPGA XMIT 1 AMP AMP Optical MOD FPGA XMIT 2 AMP AMP Optical MOD FPGA XMIT 3 AMP AMP Optical MOD Optical to Electrical FPGA XMIT 4 AMP AMP Optical MOD D Flip-Flop AMP FPGA XMIT 5 AMP Optical MOD AMP AMP Optical MOD FPGA XMIT 6 FPGA RCV 1 UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Six Users UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory UCLA Electrical Engineering Communication Systems Laboratory

Probability of amplitudes for 6-users Height Probability 4.4880e-001 1 3.8468e-001 2 1.3739e-001 3 2.6169e-002 4 2.8038e-003 5 1.6022e-004 6 3.8147e-006 UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Asynchronous users UCLA Electrical Engineering Communication Systems Laboratory

Receiver Ones Densities for this code. Number of Users Receiver Ones Density 1 0.125 2 0.234 3 0.330 4 0.413 5 0.487 6 0.551 UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Performance results FPGA implementation: In order to prove that NL-TCM codes are feasible today for optical speeds, a hardware simulation engine was built on the Xilinx Virtex2-Pro 2V20 FPGA. Results for the rate-1/20 NL-TCM code are shown next. Transfer Bound: Wen-Yen Weng collaborated in this work, with the computation a Transfer Function Bound for NL-TCM codes. It proved to be a very accurate bound, thus providing a fast estimation of the performance of the NL-TCM codes designed in this work. UCLA Electrical Engineering Communication Systems Laboratory

C-Simulation Performance Results: 6-user OR-MAC 6-user BER 10-5 UCLA Electrical Engineering Communication Systems Laboratory

6-user OR-MAC: Simulation, Bound, FPGA (no optics) 6-user BER 10-5 UCLA Electrical Engineering Communication Systems Laboratory

Results: observations An error floor can observed for the FPGA rate-1/20 NL-TCM. This is mainly due to the fact that, while theoretically a 1-to-0 transition means an infinite distance, for implementation constraints those transitions are given a value of 20. Trace-back depth of 35. Additional coding required to lower BER to below 10-9. UCLA Electrical Engineering Communication Systems Laboratory

Dramatically lowering the BER : Concatenation with Outer Block Code Optical systems deliver a very low BER, in our work a is required. Using only a NL-TCM, the rate would have to be very low. A better solution is found using the fact that Viterbi decoding fails gradually, with relatively high probability only a small number of bits are in error. Thus, a high-rate block code that can correct a few errors can be attached as an outer code, dramatically lowering the BER. Block-Code Encoder NL-TCM Encoder Z-Channel Block-Code Decoder NL-TCM Decoder UCLA Electrical Engineering Communication Systems Laboratory

Reed-Solomon + NL-TCM : 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. The resulting rate for each user is (247/255).(1/20) The results were obtained using a C program to apply the RS-code to the FPGA NL-TCM output. Rate Sum-rate p BER 0.0484 0.29 0.125 0.4652 UCLA Electrical Engineering Communication Systems Laboratory

C-Simulation Performance Results: NL-TCM only, 100-user OR-MAC Rate Sum-rate p BER 1/360 0.2778 0.006944 0.49837 1/400 0.25 0.006875 0.49489 UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Current Status Decreased optical speed from 2 to 1.2 Gbps because FPGA can’t keep up at 2 Gbps. Single Amplifier Results: 2-Amplifier system in progress. We need more amplifiers for six users. Last night, worked for 4 users, but two users need more power. Users BER 1 < 10-9 2 3 10-8 4 5×10-6 UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Results Demonstrated scalability to 100 users in a C simulation. Working on our 6-user optical implementation. UCLA Electrical Engineering Communication Systems Laboratory

Outline of more detailed discussion Motivation : Optical Channel, Uncoordinated Multiple Access. Models and Capacity Calculation Basic Model: the OR Channel Treating other users as noise Capacity loss vs. complexity reduction. The Z channel The need for non-linear codes Optimal ones density Non-linear Trellis Coded Modulation (NL-TCM) Definition of distance in the Z-Channel Design Technique Conclusions Future Work UCLA Electrical Engineering Communication Systems Laboratory

Motivation: Optical Channels, Multiple Access provide very high data rates, up to tens to hundreds of gigabits per second. Typically deliver a very low Bit Error Rate Wavelength Division (WDMA) or Time Division (TDMA) are the most common forms of Multiple Access today. However, they require considerable coordination. Objective Uncoordinated access to the channel. Apply error correcting codes, in order to achieve the required BER. Maximizing the rate at feasible complexity for optical speeds. UCLA Electrical Engineering Communication Systems Laboratory

Basic Model: The OR Multiple Access Channel (OR-MAC) OR Channel model Basic model that can describe the multiple-user optical channel with non-coherent combining N users transmitting at the same time If all users transmit a 0, then a 0 is received If even one of them transmits a 1, a 1 is received 0+X=X, 1+X=1 User 1 User 2 Receiver User N UCLA Electrical Engineering Communication Systems Laboratory

OR Channel: Theoretical characteristics Achievable rate (Capacity): The theoretical limits for the MAC, were given by Liao and Ahslwede. In the case of the OR-MAC, the Theoretical Capacity is the triangle of all rate-pairs less than the maximum possible sum-rate, which is 1. This sum-rate can be theoretically achieved by: Joint Decoding. Sequential decoding (requires coordination). Time-Sharing or Wave-length sharing (requires coordination). UCLA Electrical Engineering Communication Systems Laboratory

Treating other users as noise: the Z-Channel Joint Decoding and Successive Decoding are fully efficient in that one useful bit of information is transmitted per time-wavelength slot. However, non of these are computationally feasible for optical speeds today. A practical alternative is to treat all but a desired user as noise. This alternative, while dramatically reducing the decoding complexity, looses up to 30% of full capacity, as we will see next. When treating other users as noise in an OR-MAC, each user “sees” what is called the Z-Channel. My research has been focused on the Z-Channel, resulting from the OR-MAC when treating other users as noise. UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory The Z-Channel N users, all transmitting with the same ones density p: P(X=1)=p, P(X=0)=1-p. Focus on a desired user If it transmits a 1, a 1 will be received. If it transmits a 0, a 0 will be received only if all other N-1 users transmit a 0 1 UCLA Electrical Engineering Communication Systems Laboratory

Maximum achievable sum-rate, when treating other users as noise. Information Theory tells us the optimal ones density to transmit for each user. When the number of users tends to infinity, the optimal ones density tends to , which is also the optimal density for joint decoding. In that case equal probabilities of 1 and 0 is perceived at the receiver. Note that for a large number of users, the optimal ones density becomes very small. Surprisingly, the maximum achievable sum-rate is always lower-bounded by ln(2)=0.6931 and tends to ln(2) when the number of users tends to infinity. UCLA Electrical Engineering Communication Systems Laboratory

Comparison of capacities Optimal ones densities: Users Joint Others noise 2 0.293 0.286 6 0.109 0.108 12 0.056 UCLA Electrical Engineering Communication Systems Laboratory

The need for non-linear codes Linear codes provide equal density of ones and zeros in their output (p=0.5). Most of the codes studied in the literature are linear codes. For linear codes, the achievable rate tends to zero as the number of users increase. As the number of users increase, the optimal ones density tends to zero. Non-linear codes with relatively low density of ones are required, to a achieve a good rate. Only recently, there has been work on LDPC codes with arbitrary density of ones. There is still no design technique described for these codes, and they can’t be decoded at optical speeds today. This work introduces a novel design technique for non-linear trellis codes with an arbitrary density of ones. UCLA Electrical Engineering Communication Systems Laboratory

Interleaver Division Multiple Access (IDMA) Every user has the same channel code, but each user’s code bits are interleaved by a randomly drawn interleaver, with very high probability of being unique. The receiver is assumed to know the interleaver of the desired user. With IDMA in the OR-MAC, a receiver should see the signal from a desired user, corrupted by a memoryless Z-Channel. Performance obtained for a 6-user OR-MAC using IDMA, and for the corresponding Z-Channel were the same in our C simulations. UCLA Electrical Engineering Communication Systems Laboratory

Non-linear Trellis Coded Modulation Desired density of ones p is given Rate of the form: 1/n (1 input bit, n output bits). states (represented by v bits) 2S branches Feed-forward encoder with 1 input: Design: Assign output values to the 2S branches of the trellis Objective: Maximize the minimum distance (“greedy definition”) Those outputs have to maintain the desired density of ones p. 1 State at time t: State at time (t+1): UCLA Electrical Engineering Communication Systems Laboratory

Assigning Hamming Weights First step: assign Hamming weights to the output of each branch. Using any of the definitions of distance given before, codewords with as equal Hamming weight between each other lead to better performance. In the case of codewords with different Hamming weights, the worst-case performance will be driven by those codewords with smaller Hamming weight. Criteria: assign as similar Hamming weights to the branches as possible, maintaining the density of ones as close to the desired density of ones as close to the desired p as possible. UCLA Electrical Engineering Communication Systems Laboratory

Assigning Hamming Weights Consider the following sub-graph: There are S/2 of these sub-graphs. Branches produced by an input bit equal to 0 for both states (or 1) go to the same state. Define In this subgroup of four branches, assign a Hamming weight of w+1 to i branches, and a Hamming weight of w to (4-i) branches. 1 UCLA Electrical Engineering Communication Systems Laboratory

Assigning Hamming Weights, Examples: 6-user OR-MAC, desired density of ones is . n=20 : w=2, i=2 2 branches with Hw=2, 2 with Hw=3 (p=1/8). n = 18 : w=2, i=1 3 branches with Hw=2, 1 with Hw=3 (p=1/8). n = 17 : w=2, i=round(0.5) 1 branch with Hw=3 and 3 with Hw=2 (p=0.132) all with Hw=2 (p=2/17=0.118). 100-user OR-MAC, n = 400 : w=2, i=3 (p = 0.006875) n = 360 : w=2, i=2 (p = 0.006944) UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Ungerboeck’s rule We can increase the minimum distance by applying Ungerboeck’s rule: maximize the distance between all splits and merges. Remember that all output values had at least a Hamming distance of w. For every two different codewords, their paths split and merge at least once, and there are at least v-1 branches between the split and the merge. Hence Ungerboeck’s rule delivers: split merge UCLA Electrical Engineering Communication Systems Laboratory

Extending Ungerboeck’s rule One can extend Ungerboeck’s rule into the trellis. 1 Maximize split UCLA Electrical Engineering Communication Systems Laboratory

Extending Ungerboeck’s rule One can extend Ungerboeck’s rule into the trellis. 1 1 1 Maximize UCLA Electrical Engineering Communication Systems Laboratory

Extending Ungerboeck’s rule One can extend Ungerboeck’s rule into the trellis. Note that by maximizing the distance between the 8 branches, coming from a split 2 trellis section before, we are maximizing all groups of 4 branches coming from a split in the previous trellis section, and all splits. 1 1 Maximize 1 UCLA Electrical Engineering Communication Systems Laboratory

Designing for a very low desired ones density For a low enough desired ones density, all the branches can be chosen to have maximum distance. The design becomes straight-forward. It is possible to choose all branches so that there is at most 1 branch that has a 1 in a given position. Straight-forward design: Assign Hamming weights to branches For each branch, add ones in positions that aren’t used in previous branches Example: 100-user OR-MAC, UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Performance Results For all implementations, states were used. 6-user OR-MAC n=20 : Sum-rate = 0.30 2 branches with Hw=2, 2 with Hw=3 (p=1/8). h=3, g=2 : n = 18 : Sum-rate = 1/3 3 branches with Hw=2, 1 with Hw=3 (p=1/8). h=2,g=2 : n = 17 : Sum-rate = 0.353 all with Hw=2 (p=2/17=0.118). 100-user OR-MAC, n = 400 : w=2, i=3 (p = 0.006875) n = 360 : w=2, i=2 (p = 0.006944) for both cases UCLA Electrical Engineering Communication Systems Laboratory

Communication Systems Laboratory Conclusions A novel design technique for non-linear trellis codes, that provide a wide range of ones density. These codes have been designed for the Z-Channel, that arises in the optical multiple access channel with IDMA. A relatively low ones density is essential for the OR-MAC channel, and asymmetric channels in general. An arbitrary number of users is supported, maintaining relatively the same efficiency (around 30%) Although these codes are not capacity achieving,a good part of the capacity is achieved, with a suitable BER fr optical needs, and a complexity feasible for optical speeds with today’s technology. An FPGA implementation has been built to prove this fact. UCLA Electrical Engineering Communication Systems Laboratory

Future work: Capacity achieving codes Although they may not be feasible for optical speeds, with today’s technology, Turbo codes and LDPC codes will be feasible in the near future Part of my immediate future’s work will be the design Turbo-Like codes, with an arbitrary ones density. Most common Turbo-like codes are Parallel concatenation of convolutional codes Serially concatenated convolutional codes. The convolutional codes will be replaced by properly designed NL-TCMs. UCLA Electrical Engineering Communication Systems Laboratory

Non-linear Turbo Like codes Serial concatenation CC + NL-TCM: Parallel concatenated NL-TCMs: CC Interleaver NL-TCM NL-TCM Interleaver NL-TCM UCLA Electrical Engineering Communication Systems Laboratory